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stringlengths 7
6.48k
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stringlengths 8
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math_qa__TkSAK2l8Qzp5U0wR | Two trains of length 210 m and 120 m are 160 m apart. They start moving towards each other on parallel tracks, at speeds 74 kmph and 92 kmph. After how much time will the trains meet?
Choose the correct choice:
A) 35 / 10 B) 31 / 10 C) 31 / 10 D) 36 / 10 E) 37 / 10 | <gadget id="calculator">74 + 92</gadget>
<output>166</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">166 * (5/18)</gadget>
<output>415/9 = around 46.111111</output>
<gadget id="calculator">160 / (415/9)</gadget>
<output>288/83 = around 3.46988</output>
<result>A</result> | A | 3.5 | Two trains of length 210 m and 120 m are 160 m apart. They start moving towards each other on parallel tracks, at speeds 74 kmph and 92 kmph. After how much time will the trains meet? | {
"A": "35 / 10",
"B": "31 / 10",
"C": "31 / 10",
"D": "36 / 10",
"E": "37 / 10"
} | divide(160, multiply(add(74, 92), const_0_2778)) | add(n3,n4)|multiply(#0,const_0_2778)|divide(n2,#1) | they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 74 + 92 ) * 5 / 18 = 46.1 mps . the time required = d / s = 160 / 46.1 = 35 / 10 sec . answer : a | physics |
math_qa__oQIVgNIrUVQ9D76e | A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Pick: A) 5.98 B) 7.98 C) 7.96 D) 5.87 E) 5.82 | <gadget id="calculator">8 + 1.2</gadget>
<output>9.2</output>
<gadget id="calculator">8 - 1.2</gadget>
<output>6.8</output>
<gadget id="calculator">9.2 * 6.8</gadget>
<output>62.56</output>
<gadget id="calculator">9.2 + 6.8</gadget>
<output>16</output>
<gadget id="calculator">62.56 / 16</gadget>
<output>3.91</output>
<gadget id="calculator">3.91 * 2</gadget>
<output>7.82</output>
<result>C</result> | C | 7.96 | A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? | {
"A": "5.98",
"B": "7.98",
"C": "7.96",
"D": "5.87",
"E": "5.82"
} | multiply(divide(multiply(add(8, 1.2), subtract(8, 1.2)), add(add(8, 1.2), subtract(8, 1.2))), const_2) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|divide(#3,#2)|multiply(#4,const_2)| | "m = 8 s = 1.2 ds = 9.6 us = 6.8 x / 9.6 + x / 6.8 = 1 x = 3.98 d = 3.98 * 2 = 7.96 answer : c" | physics |
math_qa__K2wKVCApgrEZaH2n | After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount Choose the correct choice from the following answers:
A) 22 % B) 23 % C) 21 % D) 20 % E) 17 % | <gadget id="calculator">105 * 100</gadget>
<output>10_500</output>
<gadget id="calculator">100 - 12.55</gadget>
<output>87.45</output>
<gadget id="calculator">10_500 / 87.45</gadget>
<output>120.068611</output>
<gadget id="calculator">150 - 120.068611</gadget>
<output>29.931389</output>
<gadget id="calculator">29.931389 * 100</gadget>
<output>2_993.1389</output>
<gadget id="calculator">2_993.1389 / 150</gadget>
<output>19.954259</output>
<result>D</result> | D | 20 | After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount | {
"A": "22 %",
"B": "23 %",
"C": "21 %",
"D": "20 %",
"E": "17 %"
} | divide(multiply(subtract(150, divide(multiply(105, const_100), subtract(const_100, 12.55))), const_100), 150) | multiply(n2,const_100)|subtract(const_100,n3)|divide(#0,#1)|subtract(n1,#2)|multiply(#3,const_100)|divide(#4,n1) | let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % option d | gain |
math_qa__usjuGXnVBQOcl6Cu | From a pack of 52 cards, two cards are drawn together at random. What is the probability of one is a spade and one is a heart? Choose the correct choice from the following options
A) 102 / 102 B) 5 / 102 C) 1 / 102 D) 8 / 102 E) 13 / 102 | <gadget id="calculator">52 / 4</gadget>
<output>13</output>
<gadget id="calculator">13 * 13</gadget>
<output>169</output>
<gadget id="calculator">binomial(52, 2)</gadget>
<output>1_326</output>
<gadget id="calculator">169 / 1_326</gadget>
<output>13/102 = around 0.127451</output>
<result>E</result> | E | 0.127451 | From a pack of 52 cards, two cards are drawn together at random. What is the probability of one is a spade and one is a heart? | {
"A": "102 / 102",
"B": "5 / 102",
"C": "1 / 102",
"D": "8 / 102",
"E": "13 / 102"
} | divide(multiply(divide(52, const_4), divide(52, const_4)), choose(52, const_2)) | choose(n0,const_2)|divide(n0,const_4)|multiply(#1,#1)|divide(#2,#0) | solution let s be the sample space . then , n ( s ) = 52 c 2 = ( 52 × 51 ) / ( 2 × 1 ) = 1326 . let e = event of getting 1 spade and 1 heart . n ( e ) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 169 . p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 . answer e | probability |
math_qa__3eWURaDlYTaV68Jn | 10 is added to a certain number, the sum is multiplied by 2, the product is divided by 2 and 2 is subtracted from the quotient. The remainder left is half of 88. What is the number?
Choose the most appropriate option: A) 21 B) 20 C) 25 D) 36 E) 45 | <gadget id="calculator">88 / 2</gadget>
<output>44</output>
<gadget id="calculator">44 + 2</gadget>
<output>46</output>
<gadget id="calculator">46 * 2</gadget>
<output>92</output>
<gadget id="calculator">92 / 2</gadget>
<output>46</output>
<gadget id="calculator">46 - 10</gadget>
<output>36</output>
<result>D</result> | D | 36 | 10 is added to a certain number, the sum is multiplied by 2, the product is divided by 2 and 2 is subtracted from the quotient. The remainder left is half of 88. What is the number? | {
"A": "21",
"B": "20",
"C": "25",
"D": "36",
"E": "45"
} | subtract(divide(multiply(add(divide(88, const_2), 2), 2), 2), 10) | divide(n4,const_2)|add(n2,#0)|multiply(n2,#1)|divide(#2,n1)|subtract(#3,n0)| | "let number is x . when 10 added to it , = ( x + 10 ) 2 multiplied to sum , = 2 * ( x + 10 ) now , = [ { 2 * ( x + 10 ) } / 2 ] and , = [ { 2 * ( x + 10 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 10 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 20 ) / 2 ) = 44 + 2 x + 10 = 46 x + 10 = 46 x = 46 - 10 x = 36 so , required number is : 36 . answer : d" | general |
math_qa__ZsOqjcVRapdDNjMu | When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/2 of the remaining balance, what will be the final balance in her bank account? Choose the most appropriate option.
A) 300 B) 375 C) 450 D) 500 E) 575 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<gadget id="calculator">500 - 200</gadget>
<output>300</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">300 * (3/2)</gadget>
<output>450</output>
<result>C</result> | C | 450 | When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/2 of the remaining balance, what will be the final balance in her bank account? | {
"A": "300",
"B": "375",
"C": "450",
"D": "500",
"E": "575"
} | multiply(subtract(divide(200, subtract(1, divide(const_3, 5))), 200), add(1, divide(1, 2))) | divide(n3,n4)|divide(const_3,n2)|add(n3,#0)|subtract(n3,#1)|divide(n0,#3)|subtract(#4,n0)|multiply(#2,#5)| | "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 2 of 300 = 150 total amount in her account = 450 answer c" | general |
math_qa__KhuK0zE7vHdrEvtw | In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
Choose the correct answer.
A) 3.5 % B) 2.4 % C) 10.2 % D) 5 % E) 2.6 % | <gadget id="calculator">16 - 5</gadget>
<output>11</output>
<gadget id="calculator">16 * 5</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">11 - (4/5)</gadget>
<output>51/5 = around 10.2</output>
<result>C</result> | C | 10.2 | In measuring the sides of a rectangle, one side is taken 16% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. | {
"A": "3.5 %",
"B": "2.4 %",
"C": "10.2 %",
"D": "5 %",
"E": "2.6 %"
} | subtract(subtract(16, 5), divide(multiply(16, 5), const_100)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)| | "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 116 * 95 = 11,020 , which is 10.2 % greater than the actual area . answer : c ." | geometry |
math_qa__msaGVpZokW17NkCA | What is the least number should be added to 1100, so the sum of the number is completely divisible by 23? Options
A) 1 B) 2 C) 5 D) 4 E) 8 | <gadget id="calculator">1_100 / 23</gadget>
<output>1_100/23 = around 47.826087</output>
<gadget id="calculator">floor(1_100/23)</gadget>
<output>47</output>
<gadget id="calculator">47 + 1</gadget>
<output>48</output>
<gadget id="calculator">48 * 23</gadget>
<output>1_104</output>
<gadget id="calculator">1_104 - 1_100</gadget>
<output>4</output>
<result>D</result> | D | 4 | What is the least number should be added to 1100, so the sum of the number is completely divisible by 23? | {
"A": "1",
"B": "2",
"C": "5",
"D": "4",
"E": "8"
} | subtract(multiply(add(floor(divide(1100, 23)), const_1), 23), 1100) | divide(n0,n1)|floor(#0)|add(#1,const_1)|multiply(n1,#2)|subtract(#3,n0)| | "( 1100 / 23 ) gives remainder 19 19 + 4 = 23 , so we need to add 4 answer : d" | general |
math_qa__dferw7nOV2PKiEAT | If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.
Select: A) 8 / 25 B) 1 / 25 C) 2 / 25 D) 3 / 14 E) 25 / 8 | <gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(4/5) * (2/5)</gadget>
<output>8/25 = around 0.32</output>
<result>A</result> | A | 0.32 | If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events. | {
"A": "8 / 25",
"B": "1 / 25",
"C": "2 / 25",
"D": "3 / 14",
"E": "25 / 8"
} | multiply(divide(4, 5), divide(2, 5)) | divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)| | "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 5 . 2 / 5 p ( a n b ) = 8 / 25 . a" | general |
math_qa__9GNLVJQdyS3Hobq2 | a making a cube with dimension 5*5*5 using 1*1*1 cubes.what is the number of cubes needed to make hollow cube looking of the same shape.
Select: A) 98 B) 99 C) 100 D) 101 E) 102 | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">125 - 27</gadget>
<output>98</output>
<result>A</result> | A | 98 | a making a cube with dimension 5*5*5 using 1*1*1 cubes.what is the number of cubes needed to make hollow cube looking of the same shape. | {
"A": "98",
"B": "99",
"C": "100",
"D": "101",
"E": "102"
} | subtract(multiply(multiply(5, 5), 5), multiply(multiply(subtract(5, const_2), subtract(5, const_2)), const_3)) | multiply(n0,n0)|subtract(n0,const_2)|multiply(n0,#0)|multiply(#1,#1)|multiply(#3,const_3)|subtract(#2,#4) | 125 1 * 1 * 1 small cubes = 5 * 5 * 5 cubes because hallow in inner we do n ' t have 3 * 3 * 3 cubes so 125 - 27 = 98 cubes required answer : a | geometry |
math_qa__pQbxFGIQYVveBBwp | how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits f equal to 28 ?
Choose the correct option:
A) 14 B) 24 C) 28 D) 48 E) 96 | <gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">2 * 24</gadget>
<output>48</output>
<result>D</result> | D | 48 | how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits f equal to 28 ? | {
"A": "14",
"B": "24",
"C": "28",
"D": "48",
"E": "96"
} | multiply(const_2, factorial(4)) | factorial(n0)|multiply(#0,const_2) | first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so f = 24 + 24 = 48 . d | general |
math_qa__qA4DNHZpYUT9bZjp | Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many Q kilometers per hour did Tammy walk on the second day? Choose the correct choice from the following answers:
A) 3
B) 3.5
C) 4
D) 4.5
E) 6 | <gadget id="calculator">14 + 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">52 - 3</gadget>
<output>49</output>
<gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">49 / 14</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(7/2) + (1/2)</gadget>
<output>4</output>
<result>C</result> | C | 4 | Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many Q kilometers per hour did Tammy walk on the second day? | {
"A": "3",
"B": "3.5",
"C": "4",
"D": "4.5",
"E": "6"
} | add(divide(subtract(52, divide(subtract(divide(add(14, 2), 2), 2), 2)), add(subtract(divide(add(14, 2), 2), 2), divide(add(14, 2), 2))), divide(const_1, 2)) | add(n0,n1)|divide(const_1,n1)|divide(#0,n1)|subtract(#2,n1)|add(#2,#3)|divide(#3,n1)|subtract(n2,#5)|divide(#6,#4)|add(#7,#1)| | "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5" | physics |
math_qa__a1hZHR3zBvLHXvlh | Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.580? Choose the correct choice:
A) rs . 500 B) rs . 5100 C) rs . 530 D) rs . 540 E) none of these | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 5</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">(18/5) * 5</gadget>
<output>18</output>
<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">(9/50) + 1</gadget>
<output>59/50 = around 1.18</output>
<gadget id="calculator">580 / (59/50)</gadget>
<output>29_000/59 = around 491.525424</output>
<result>A</result> | A | 500 | Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.580? | {
"A": "rs . 500",
"B": "rs . 5100",
"C": "rs . 530",
"D": "rs . 540",
"E": "none of these"
} | divide(580, add(divide(multiply(divide(add(multiply(3, 5), 3), 5), 5), const_100), const_1)) | multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)| | "explanation : 580 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 500 answer : option a" | general |
math_qa__QWm19ZZeDepU7Nd2 | Of 300 surveyed students, 20% of those who read book A also read book B and 50% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B? Choose the correct choice from the following choices:
A) 120 B) 125 C) 130 D) 135 E) 150 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/2) / (1/5)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) + 1</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) - (1/2)</gadget>
<output>3</output>
<gadget id="calculator">300 / 3</gadget>
<output>100</output>
<gadget id="calculator">100 * (5/2)</gadget>
<output>250</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">250 * (4/5)</gadget>
<output>200</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">100 * (1/2)</gadget>
<output>50</output>
<gadget id="calculator">200 - 50</gadget>
<output>150</output>
<result>E</result> | E | 150 | Of 300 surveyed students, 20% of those who read book A also read book B and 50% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B? | {
"A": "120",
"B": "125",
"C": "130",
"D": "135",
"E": "150"
} | subtract(multiply(multiply(divide(300, subtract(add(divide(divide(50, const_100), divide(20, const_100)), const_1), divide(50, const_100))), divide(divide(50, const_100), divide(20, const_100))), subtract(const_1, divide(20, const_100))), multiply(divide(300, subtract(add(divide(divide(50, const_100), divide(20, const_100)), const_1), divide(50, const_100))), subtract(const_1, divide(50, const_100)))) | divide(n2,const_100)|divide(n1,const_100)|divide(#0,#1)|subtract(const_1,#1)|subtract(const_1,#0)|add(#2,const_1)|subtract(#5,#0)|divide(n0,#6)|multiply(#7,#2)|multiply(#7,#4)|multiply(#8,#3)|subtract(#10,#9)| | "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 50 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.5 b - - > a = 2.5 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 300 = 2.5 b + b - 0.5 b - - > b = 100 , a = 2.5 b = 250 and { both } = 0.5 b = 50 . the number of students who read only book a is { a } - { both } = 250 - 50 = 200 ; the number of students who read only book b is { b } - { both } = 100 - 50 = 50 ; the difference is 200 - 50 = 150 . answer : e ." | gain |
math_qa__DHEyQAmaPS7aIUKI | A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 3. What could be the ratio of Cats to dogs in the pet store? Options:
A) 12 : 15
B) 1 : 4
C) 1 : 5
D) 2 : 5
E) 1 : 3 | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">12 / 15</gadget>
<output>4/5 = around 0.8</output>
<result>A</result> | A | 0.8 | A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 3. What could be the ratio of Cats to dogs in the pet store? | {
"A": "12 : 15",
"B": "1 : 4",
"C": "1 : 5",
"D": "2 : 5",
"E": "1 : 3"
} | divide(multiply(3, const_4), add(multiply(3, const_4), 3)) | multiply(n0,const_4)|add(n0,#0)|divide(#0,#1)| | "say theratio of cats to dogs is a / b . then the numberof cats would be ax and the number of dogs bx , for some positive integer x . we are told that ax - bx = 3 - - > x ( a - b ) = 3 . since 3 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 13 . the above implies that either x = 1 and ( a - b ) = 3 or x = 3 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 3 * 4 = 12 and dogs = 3 * 5 = 15 . answer : a ." | other |
math_qa__tgep92tLgkVIpOmU | If the cost price is 80% of the selling price, then what is the profit percent? Choose the correct choice
A) 5 % B) 11 % C) 13 % D) 25 % E) 19 % | <gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">20 / 80</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>D</result> | D | 25 | If the cost price is 80% of the selling price, then what is the profit percent? | {
"A": "5 %",
"B": "11 %",
"C": "13 %",
"D": "25 %",
"E": "19 %"
} | multiply(divide(subtract(const_100, 80), 80), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | "let s . p . = $ 100 c . p . = $ 80 profit = $ 20 profit % = 20 / 80 * 100 = 25 / 6 = 25 % answer is d" | gain |
math_qa__u6dm9Gtil1XDZc4y | Dacid obtained 81, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Choose the correct choice from the following options:
A) 29 B) 38 C) 76 D) 37 E) 75 | <gadget id="calculator">81 + 65</gadget>
<output>146</output>
<gadget id="calculator">146 + 82</gadget>
<output>228</output>
<gadget id="calculator">228 + 67</gadget>
<output>295</output>
<gadget id="calculator">295 + 85</gadget>
<output>380</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">380 / 5</gadget>
<output>76</output>
<result>C</result> | C | 76 | Dacid obtained 81, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | {
"A": "29",
"B": "38",
"C": "76",
"D": "37",
"E": "75"
} | divide(add(add(add(add(81, 65), 82), 67), 85), divide(const_10, const_2)) | add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "average = ( 81 + 65 + 82 + 67 + 85 ) / 5 = 76 . answer : c" | general |
math_qa__dKdQNcwEsOsARPTV | he average of 30 numbers is zero. Of them, at the most, how many may be greater than zero? Select
A) 29
B) 1
C) 10
D) 30
E) 8 | <gadget id="calculator">30 - 1</gadget>
<output>29</output>
<result>A</result> | A | 29 | he average of 30 numbers is zero. Of them, at the most, how many may be greater than zero? | {
"A": "29",
"B": "1",
"C": "10",
"D": "30",
"E": "8"
} | subtract(30, const_1) | subtract(n0,const_1) | average of 30 numbers = 0 . sum of 30 numbers ( 0 x 30 ) = 0 . it is quite possible that 29 of these numbers may be positive and if their sum is a the 30 th number is ( - a ) . answer : option a | general |
math_qa__RoNLIVZ3rirD2PyH | A number when divided by 342 gives a remainder 47. When the same number if it divided by 19, what would be the remainder ? Choose one.
A) 1
B) 2
C) 5
D) 9
E) 11 | <gadget id="calculator">19 * 2</gadget>
<output>38</output>
<gadget id="calculator">47 - 38</gadget>
<output>9</output>
<result>D</result> | D | 9 | A number when divided by 342 gives a remainder 47. When the same number if it divided by 19, what would be the remainder ? | {
"A": "1",
"B": "2",
"C": "5",
"D": "9",
"E": "11"
} | subtract(47, multiply(19, const_2)) | multiply(n2,const_2)|subtract(n1,#0)| | "on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number – 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 . the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . answer d" | general |
math_qa__s2Jks9sarzejpHrT | √(36)^2
Answers:
A) 6 B) 14 C) 36 D) 21 E) none of these | <gadget id="calculator">36 ** 2</gadget>
<output>1_296</output>
<gadget id="calculator">1_296 ** (1/2)</gadget>
<output>36</output>
<result>C</result> | C | 36 | √(36)^2 | {
"A": "6",
"B": "14",
"C": "36",
"D": "21",
"E": "none of these"
} | sqrt(power(36, 2)) | power(n0,n1)|sqrt(#0) | explanation √ ( 36 ) ^ 2 = ? or , ? = 36 answer c | general |
math_qa__I1ZxCdGTsUFtnYPc | 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the most appropriate option.
A) 32 B) 87 C) 30 D) 99 E) 77 | <gadget id="calculator">21 * 8</gadget>
<output>168</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">168 * 45</gadget>
<output>7_560</output>
<gadget id="calculator">21 * 2</gadget>
<output>42</output>
<gadget id="calculator">42 * 6</gadget>
<output>252</output>
<gadget id="calculator">7_560 / 252</gadget>
<output>30</output>
<gadget id="calculator">floor(30)</gadget>
<output>30</output>
<gadget id="calculator">30 + 1</gadget>
<output>31</output>
<result>C</result> | C | 30 | 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? | {
"A": "32",
"B": "87",
"C": "30",
"D": "99",
"E": "77"
} | add(floor(divide(multiply(multiply(21, 8), multiply(15, 3)), multiply(multiply(21, 2), 6))), const_1) | multiply(n1,n2)|multiply(n0,n5)|multiply(n4,n6)|multiply(#0,#1)|multiply(n3,#2)|divide(#3,#4)|floor(#5)|add(#6,const_1)| | "3 w = 2 m 15 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 15 * 21 * 8 = 14 * x * 6 x = 30 answer : c" | physics |
math_qa__NVrr8DEFBllOg519 | he total marks obtained by a student in Physics, Chemistry and Mathematics is 140 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? Choose the most appropriate option:
A) 55 B) 70 C) 75 D) 85 E) 95 | <gadget id="calculator">140 / 2</gadget>
<output>70</output>
<result>B</result> | B | 70 | he total marks obtained by a student in Physics, Chemistry and Mathematics is 140 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? | {
"A": "55",
"B": "70",
"C": "75",
"D": "85",
"E": "95"
} | divide(140, const_2) | divide(n0,const_2)| | "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 140 + p c + m = 140 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 140 / 2 = 70 . answer : b" | general |
math_qa__elluAUBzvJ9Uhp1Y | 4 men can check exam papers in 8 days working 5 hours regularly. What is the total hours when 2 men will check the double of the papers in 20 days? Choices
A) 8 B) 9 C) 6 D) 1 E) 5 | <gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">32 * 5</gadget>
<output>160</output>
<gadget id="calculator">2 * 160</gadget>
<output>320</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">320 / 40</gadget>
<output>8</output>
<result>A</result> | A | 8 | 4 men can check exam papers in 8 days working 5 hours regularly. What is the total hours when 2 men will check the double of the papers in 20 days? | {
"A": "8",
"B": "9",
"C": "6",
"D": "1",
"E": "5"
} | divide(multiply(2, multiply(multiply(4, 8), 5)), multiply(2, 20)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|multiply(n3,#2)|divide(#3,#1) | let a man can do 1 unit of work in 1 hour . total units of work = 4 x 8 x 5 = 160 units . now work = 2 x 160 = 320 units . now 2 men work for 20 days . let in x hours they have to work per day . now total work = 2 × x × 20 = 40 x 40 x = 320 so x = 320 / 40 = 8 hours . answer : a | physics |
math_qa__Gib7vkR8StZ8M10d | Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +1? Choose the most appropriate option.
A) 7
B) 8
C) 9
D) 10
E) 11 | <gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<result>A</result> | A | 7 | Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +1? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | add(add(3, 3), 1) | add(n0,n0)|add(n3,#0)| | "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > only in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . i . e 0 , 1,5 or 6 intersection of values is 6 , thus the units digit of p + 1 is 6 + 1 = 9 . answer : a ." | general |
math_qa__n4OhdRMAz662J96R | Find the area of a parallelogram with base 18 cm and height 16 cm? Choose the correct choice from the following answers.
A) 423 cm 2
B) 122 cm 2
C) 420 cm 2
D) 251 cm 2
E) 288 cm 2 | <gadget id="calculator">18 * 16</gadget>
<output>288</output>
<result>E</result> | E | 288 | Find the area of a parallelogram with base 18 cm and height 16 cm? | {
"A": "423 cm 2",
"B": "122 cm 2",
"C": "420 cm 2",
"D": "251 cm 2",
"E": "288 cm 2"
} | multiply(18, 16) | multiply(n0,n1)| | "area of a parallelogram = base * height = 18 * 16 = 288 cm 2 answer : e" | geometry |
math_qa__NQ5kax0E3cBwYdrV | 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 24 girls Will take to construct? Answers:
A) 4 days
B) 14 days
C) 6 days
D) 8 days
E) 9 days | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) / 24</gadget>
<output>1/144 = around 0.006944</output>
<gadget id="calculator">24 * (1/144)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) / 16</gadget>
<output>1/96 = around 0.010417</output>
<gadget id="calculator">8 * (1/96)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/6) + (1/12)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / (1/4)</gadget>
<output>4</output>
<result>A</result> | A | 4 | 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 24 girls Will take to construct? | {
"A": "4 days",
"B": "14 days",
"C": "6 days",
"D": "8 days",
"E": "9 days"
} | divide(const_1, add(multiply(24, divide(divide(const_1, 6), 24)), multiply(8, divide(divide(const_1, 6), 16)))) | divide(const_1,n2)|divide(#0,n1)|divide(#0,n0)|multiply(n4,#1)|multiply(n3,#2)|add(#3,#4)|divide(const_1,#5)| | "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 24 girls = 8 ã — 6 / 4 + 12 = 12 + 24 = 36 girls 4 days to complete the work answer : option a" | physics |
math_qa__EOXMY7B6GTVsLcf9 | A certain country is divided into 6 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/9 the total number of Progressives in the entire country, what fraction of the country is Traditionalist? Pick.
A) 1 / 5 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 3 / 5 | <gadget id="calculator">6 / 9</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(2/3) / (5/3)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<result>E</result> | E | 0.6 | A certain country is divided into 6 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/9 the total number of Progressives in the entire country, what fraction of the country is Traditionalist? | {
"A": "1 / 5",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "3 / 5"
} | subtract(1, divide(divide(6, 9), add(divide(6, 9), 1))) | divide(n0,n2)|add(n1,#0)|divide(#0,#1)|subtract(n1,#2) | let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 9 the total number of traditionalists is 6 p / 9 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e . | general |
math_qa__VCIw1cdZEu4Z8PZS | A tradesman sold an article at a loss of 10%. If the selling price had been increased by $50, there would have been a gain of 10%. What was the cost price of the article ? Choose the correct choice from the following
A) $ 150
B) $ 200
C) $ 250
D) $ 120
E) $ 100 | <gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">50 / (1/5)</gadget>
<output>250</output>
<result>C</result> | C | 250 | A tradesman sold an article at a loss of 10%. If the selling price had been increased by $50, there would have been a gain of 10%. What was the cost price of the article ? | {
"A": "$ 150",
"B": "$ 200",
"C": "$ 250",
"D": "$ 120",
"E": "$ 100"
} | divide(50, divide(add(10, 10), const_100)) | add(n0,n2)|divide(#0,const_100)|divide(n1,#1)| | "let c . p . be $ x then 110 % of x - 90 % of x = 50 20 % of x = 50 x / 5 = 50 x = 250 answer is c" | gain |
math_qa__LoIzNtTNJtYDRHSY | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.20 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Choose the correct choice from the following options
A) 399 B) 272 C) 799.2 D) 277 E) 311 | <gadget id="calculator">3_136 ** (1/2)</gadget>
<output>56</output>
<gadget id="calculator">56 * 4</gadget>
<output>224</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">224 - 2</gadget>
<output>222</output>
<gadget id="calculator">222 * 1.2</gadget>
<output>266.4</output>
<gadget id="calculator">266.4 * 3</gadget>
<output>799.2</output>
<result>C</result> | C | 799.2 | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.20 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? | {
"A": "399",
"B": "272",
"C": "799.2",
"D": "277",
"E": "311"
} | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1.20), 3) | multiply(n3,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,n1)| | "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.2 = 799.2 answer : c" | physics |
math_qa__Q29RUDIvEASNadD3 | In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 2:3, If Rs 15,0000 was their profit, how much amount did B receive. Select the correct option: A) 12653 B) 14587 C) 36975 D) 75000 E) 12874 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 * 100</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 * 100</gadget>
<output>150_000</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">150_000 * (1/2)</gadget>
<output>75_000</output>
<result>D</result> | D | 75,000 | In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 2:3, If Rs 15,0000 was their profit, how much amount did B receive. | {
"A": "12653",
"B": "14587",
"C": "36975",
"D": "75000",
"E": "12874"
} | multiply(multiply(multiply(multiply(add(const_3, const_2), const_3), const_100), const_100), divide(3, add(add(1, 2), 3))) | add(n0,n1)|add(const_2,const_3)|add(n3,#0)|multiply(#1,const_3)|divide(n3,#2)|multiply(#3,const_100)|multiply(#5,const_100)|multiply(#4,#6) | explanation : a : b = 2 : 3 = 2 : 3 = > a : c = 2 : 1 = 2 : 1 = > a : b : c = 2 : 3 : 1 b share = ( 3 / 6 ) * 150000 = 75000 option d | gain |
math_qa__Vh39tgRDOKv1xhIW | If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2015) = ?
Choose one:
A) 2016 B) 2088 C) 270 D) 1881 E) 1781 | <gadget id="calculator">1 + 2_015</gadget>
<output>2_016</output>
<result>A</result> | A | 2,016 | If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2015) = ? | {
"A": "2016",
"B": "2088",
"C": "270",
"D": "1881",
"E": "1781"
} | add(1, 2015) | add(n3,n4)| | "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2015 ) = 2016 ans : a" | general |
math_qa__F1EOFHkj5NfFKJMN | A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Choose the correct choice from the following choices.
A) 3.6 B) 7.2 C) 8.4 D) 10 E) 8 | <gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">5 * 60</gadget>
<output>300</output>
<gadget id="calculator">300 / 3_600</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(3/5) / (1/12)</gadget>
<output>36/5 = around 7.2</output>
<result>B</result> | B | 7.2 | A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? | {
"A": "3.6",
"B": "7.2",
"C": "8.4",
"D": "10",
"E": "8"
} | divide(divide(600, const_1000), divide(multiply(5, const_60), const_3600)) | divide(n0,const_1000)|multiply(n1,const_60)|divide(#1,const_3600)|divide(#0,#2)| | "speed = 600 / ( 5 x 60 ) m / sec . = 2 m / sec . converting m / sec to km / hr = ( 2 x ( 18 / 5 ) ) km / hr = 7.2 km / hr . answer : b" | physics |
math_qa__wrEvNbwFzqFEF6gG | If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/8,
find P (not A and not B). Select the correct option
A) 1 / 9 B) 1 / 8 C) 1 / 11 D) 1 / 13 E) 2 / 5 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">3 + 7</gadget>
<output>10</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">lcm(4, 2)</gadget>
<output>4</output>
<gadget id="calculator">lcm(4, 8)</gadget>
<output>8</output>
<gadget id="calculator">9 - 8</gadget>
<output>1</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<result>B</result> | B | 0.125 | If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/8,
find P (not A and not B). | {
"A": "1 / 9",
"B": "1 / 8",
"C": "1 / 11",
"D": "1 / 13",
"E": "2 / 5"
} | divide(subtract(subtract(add(3, add(4, 3)), 1), lcm(lcm(4, 2), 8)), lcm(lcm(4, 2), 8)) | add(n0,n1)|lcm(n1,n3)|add(n0,#0)|lcm(n5,#1)|subtract(#2,n2)|subtract(#4,#3)|divide(#5,#3) | p ( not a and not b ) = 1 - ( p ( a ) + p ( b ) - p ( ab ) ) which you might find somewhere in your text . substituting in our probabilities we get : p ( not a and not b ) = 1 - ( 3 / 4 + 1 / 2 - 3 / 8 ) p ( not a and not b ) = 1 - ( 7 / 8 ) p ( not a and not b ) = 1 / 8 . b | general |
math_qa__KsyZKzIRDy3YR133 | When Sourav increases his speed from 20 Km/hr to 25 Km/hr, he takes one hour less than the usual time to cover a certain distance. What is the distance usually covered by him? Pick one:
A) 125 km
B) 100 km
C) 80 km
D) 120 km
E) 60 km | <gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">25 / 5</gadget>
<output>5</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<result>B</result> | B | 100 | When Sourav increases his speed from 20 Km/hr to 25 Km/hr, he takes one hour less than the usual time to cover a certain distance. What is the distance usually covered by him? | {
"A": "125 km",
"B": "100 km",
"C": "80 km",
"D": "120 km",
"E": "60 km"
} | multiply(20, divide(25, subtract(25, 20))) | subtract(n1,n0)|divide(n1,#0)|multiply(n0,#1) | detailed solution here , the distance travelled by sourav is constant in both the cases . so , 20 x t = 25 x ( t - 1 ) = d = ) 20 t = 25 t - 25 = ) 5 t = 25 = ) t = 5 hrs so , distance travelled = 20 x 5 = 100 km . correct answer b . | physics |
math_qa__0d85xhg1Z7QmzR9J | 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%? Choices
A) rs . 2500 B) rs . 2700 C) rs . 2800 D) rs . 5000 E) rs . 6000 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 4_000</gadget>
<output>200</output>
<gadget id="calculator">200 - 144</gadget>
<output>56</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(1/20) - (3/100)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">56 / (1/50)</gadget>
<output>2_800</output>
<result>C</result> | C | 2,800 | 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%? | {
"A": "rs . 2500",
"B": "rs . 2700",
"C": "rs . 2800",
"D": "rs . 5000",
"E": "rs . 6000"
} | divide(subtract(multiply(divide(5, const_100), 4000), 144), subtract(divide(5, const_100), divide(3, const_100))) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|subtract(#0,#1)|subtract(#2,n3)|divide(#4,#3) | explanation : ( x * 3 * 1 ) / 100 + [ ( 4000 - x ) * 5 * 1 ] / 100 = 144 3 x / 100 + 200 â € “ 5 x / 100 = 144 2 x / 100 = 56 ã ¨ x = 2800 answer is c | gain |
math_qa__eDFlW4HyW3kBHpZX | If 20% of a number = 200, then 120% of that number will be? Choose the correct option:
A) 20 B) 120 C) 360 D) 1200 E) 820 | <gadget id="calculator">120 * 200</gadget>
<output>24_000</output>
<gadget id="calculator">24_000 / 20</gadget>
<output>1_200</output>
<result>D</result> | D | 1,200 | If 20% of a number = 200, then 120% of that number will be? | {
"A": "20",
"B": "120",
"C": "360",
"D": "1200",
"E": "820"
} | divide(multiply(120, 200), 20) | multiply(n1,n2)|divide(#0,n0)| | "let the number x . then , 20 % of x = 200 x = ( 200 * 100 ) / 20 = 1000 120 % of x = ( 120 / 100 * 1000 ) = 1200 . answer : d" | gain |
math_qa__ITGwUQ2HuCCDv3Ni | Solve the equation for x : 14(-x + z) + 18 = -14(x - z) - 10 Choose the correct choice from the following options:
A) - 2 B) - 1 C) 0 D) 1 E) 2 | <gadget id="calculator">18 + 10</gadget>
<output>28</output>
<gadget id="calculator">14 + 14</gadget>
<output>28</output>
<gadget id="calculator">28 / 28</gadget>
<output>1</output>
<result>D</result> | D | 1 | Solve the equation for x : 14(-x + z) + 18 = -14(x - z) - 10 | {
"A": "- 2",
"B": "- 1",
"C": "0",
"D": "1",
"E": "2"
} | divide(add(18, 10), add(14, 14)) | add(n1,n3)|add(n0,n0)|divide(#0,#1) | d 1 - 14 x + 14 z + 18 = - 14 x + 14 z - 10 - 28 x + 28 = 0 - 28 x = - 28 = > x = 1 | general |
math_qa__FEjOnz8oIrkBsVkm | Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: Answers
A) rs . 169.50
B) rs . 170
C) rs . 175.50
D) rs . 180
E) rs . 190 | <gadget id="calculator">153 + 10</gadget>
<output>163</output>
<gadget id="calculator">163 + 10</gadget>
<output>173</output>
<gadget id="calculator">173 + 2</gadget>
<output>175</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">175 + (1/2)</gadget>
<output>351/2 = around 175.5</output>
<result>C</result> | C | 175.5 | Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be: | {
"A": "rs . 169.50",
"B": "rs . 170",
"C": "rs . 175.50",
"D": "rs . 180",
"E": "rs . 190"
} | add(add(add(add(153, const_10), const_10), 2), add(const_0_25, const_0_25)) | add(n5,const_10)|add(const_0_25,const_0_25)|add(#0,const_10)|add(n4,#2)|add(#3,#1) | explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . 126 + 135 = rs . 130.50 2 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 x - 153 = 22.50 x = 175.50 answer is c | other |
math_qa__YlgKeKLzEf1CrZro | If 1/3 of the passengers on a ship are from North America, 1/8 are Europeans, 1/5 are from Africa, 1/6 are from Asia and the remaining 42 people are citizens of other continents, then how many passengers are on board the ship? Choose the correct choice from the following options: A) 240 B) 250 C) 280 D) 300 E) 320 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/3) + (1/8)</gadget>
<output>11/24 = around 0.458333</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(11/24) + (1/5)</gadget>
<output>79/120 = around 0.658333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(79/120) + (1/6)</gadget>
<output>33/40 = around 0.825</output>
<gadget id="calculator">1 - (33/40)</gadget>
<output>7/40 = around 0.175</output>
<gadget id="calculator">42 / (7/40)</gadget>
<output>240</output>
<result>A</result> | A | 240 | If 1/3 of the passengers on a ship are from North America, 1/8 are Europeans, 1/5 are from Africa, 1/6 are from Asia and the remaining 42 people are citizens of other continents, then how many passengers are on board the ship? | {
"A": "240",
"B": "250",
"C": "280",
"D": "300",
"E": "320"
} | divide(42, subtract(1, add(add(add(divide(1, 3), divide(1, 8)), divide(1, 5)), divide(1, 6)))) | divide(n0,n1)|divide(n0,n3)|divide(n0,n5)|divide(n0,n7)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(n0,#6)|divide(n8,#7)| | "1 / 3 + 1 / 8 + 1 / 5 + 1 / 6 = ( 40 + 15 + 24 + 20 ) / 120 = 99 / 120 let x be the number of passengers on the ship . 42 = ( 21 / 120 ) x = 7 x / 40 x = 240 the answer is a ." | general |
math_qa__2HYvYoegfnEs4cRo | A room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor. Choose the correct choice from the following
A) 136 B) 146 C) 166 D) 176 E) 216 | <gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 + 44</gadget>
<output>544</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">300 + 74</gadget>
<output>374</output>
<gadget id="calculator">544 * 374</gadget>
<output>203_456</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">544 / 16</gadget>
<output>34</output>
<gadget id="calculator">34 ** 2</gadget>
<output>1_156</output>
<gadget id="calculator">203_456 / 1_156</gadget>
<output>176</output>
<result>D</result> | D | 176 | A room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor. | {
"A": "136",
"B": "146",
"C": "166",
"D": "176",
"E": "216"
} | divide(multiply(add(multiply(5, const_100), 44), add(multiply(3, const_100), 74)), power(divide(add(multiply(5, const_100), 44), power(const_2, const_4)), const_2)) | multiply(n0,const_100)|multiply(n2,const_100)|power(const_2,const_4)|add(n1,#0)|add(n3,#1)|divide(#3,#2)|multiply(#3,#4)|power(#5,const_2)|divide(#6,#7) | area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d | physics |
math_qa__l2KfinPp4A2OxvxD | Average expenditure of a person for the first 3 days of a week is Rs. 340 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: Options
A) 350 B) 370 C) 380 D) 430 E) none | <gadget id="calculator">420 - 340</gadget>
<output>80</output>
<gadget id="calculator">4 * 80</gadget>
<output>320</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">320 / 7</gadget>
<output>320/7 = around 45.714286</output>
<gadget id="calculator">340 + (320/7)</gadget>
<output>2_700/7 = around 385.714286</output>
<result>C</result> | C | 380 | Average expenditure of a person for the first 3 days of a week is Rs. 340 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: | {
"A": "350",
"B": "370",
"C": "380",
"D": "430",
"E": "none"
} | add(340, divide(multiply(4, subtract(420, 340)), add(3, 4))) | add(n0,n2)|subtract(n3,n1)|multiply(n2,#1)|divide(#2,#0)|add(n1,#3)| | "explanation : assumed mean = rs . 340 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 340 + rs . 40 = rs . 380 correct option : c" | general |
math_qa__gzi3RIheb1Ms9WeN | 400 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees Select the correct option: A) 10 B) 12 C) 14 D) 16 E) 18 | <gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">400 / 25</gadget>
<output>16</output>
<result>D</result> | D | 16 | 400 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees | {
"A": "10",
"B": "12",
"C": "14",
"D": "16",
"E": "18"
} | divide(400, add(subtract(26, 2), const_1)) | subtract(n1,n2)|add(#0,const_1)|divide(n0,#1)| | "26 trees have 25 gaps between them , required distance ( 400 / 25 ) = 16 d" | physics |
math_qa__ncXSFKdKcGK8iEO6 | A car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip? Choose the correct choice from the following options:
A) 8 B) 10 C) 12 D) 14 E) 16 | <gadget id="calculator">34 * 6</gadget>
<output>204</output>
<gadget id="calculator">30 * 6</gadget>
<output>180</output>
<gadget id="calculator">204 - 180</gadget>
<output>24</output>
<gadget id="calculator">46 - 34</gadget>
<output>12</output>
<gadget id="calculator">24 / 12</gadget>
<output>2</output>
<gadget id="calculator">2 + 6</gadget>
<output>8</output>
<result>A</result> | A | 8 | A car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip? | {
"A": "8",
"B": "10",
"C": "12",
"D": "14",
"E": "16"
} | add(divide(subtract(multiply(34, 6), multiply(30, 6)), subtract(46, 34)), 6) | multiply(n1,n3)|multiply(n0,n1)|subtract(n2,n3)|subtract(#0,#1)|divide(#3,#2)|add(n1,#4)| | "let t be the total time of the trip . 30 * 6 + 46 ( t - 6 ) = 34 t 12 t = 276 - 180 t = 8 the answer is a ." | physics |
math_qa__2ircf1hv7F0UtB1B | 5/8 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is Options
A) 28 %
B) 41 %
C) 45 %
D) 72 %
E) 68 % | <gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">8 - 5</gadget>
<output>3</output>
<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(7/10) * (3/8)</gadget>
<output>21/80 = around 0.2625</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(1/5) * (5/8)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) + (21/80)</gadget>
<output>31/80 = around 0.3875</output>
<gadget id="calculator">(21/80) / (31/80)</gadget>
<output>21/31 = around 0.677419</output>
<gadget id="calculator">(21/31) * 100</gadget>
<output>2_100/31 = around 67.741935</output>
<result>E</result> | E | 68 | 5/8 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is | {
"A": "28 %",
"B": "41 %",
"C": "45 %",
"D": "72 %",
"E": "68 %"
} | multiply(divide(multiply(divide(70, const_100), divide(subtract(8, 5), 8)), add(multiply(divide(subtract(const_100, 80), const_100), divide(5, 8)), multiply(divide(70, const_100), divide(subtract(8, 5), 8)))), const_100) | divide(n3,const_100)|divide(n0,n1)|subtract(n1,n0)|subtract(const_100,n2)|divide(#2,n1)|divide(#3,const_100)|multiply(#0,#4)|multiply(#5,#1)|add(#7,#6)|divide(#6,#8)|multiply(#9,const_100)| | "total population = 80 ( assume ) . 5 / 8 * 80 = 50 people from montague . 3 / 8 * 80 = 30 people from capulet . 0.2 * 50 = 10 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 10 + 21 ) = ~ 68 . answer : e" | gain |
math_qa__p3m3IbgkqEHVYveX | In a mayoral election, Candidate X received 1/2 more votes than candidate Y, and Candidate Y received 2/5 fewer votes than Z. If Z received 25,000 votes how many votes did candidate X received?
Pick.
A) 18000 B) 22500 C) 24000 D) 26000 E) 32000 | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">25 * 100</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 * 10</gadget>
<output>25_000</output>
<gadget id="calculator">(3/5) * 25_000</gadget>
<output>15_000</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">15_000 * (3/2)</gadget>
<output>22_500</output>
<result>B</result> | B | 22,500 | In a mayoral election, Candidate X received 1/2 more votes than candidate Y, and Candidate Y received 2/5 fewer votes than Z. If Z received 25,000 votes how many votes did candidate X received? | {
"A": "18000",
"B": "22500",
"C": "24000",
"D": "26000",
"E": "32000"
} | multiply(multiply(subtract(const_1, divide(2, 5)), multiply(multiply(multiply(const_0_25, const_100), const_100), const_10)), add(divide(1, 2), 1)) | divide(n0,n1)|divide(n1,n3)|multiply(const_0_25,const_100)|add(n0,#0)|multiply(#2,const_100)|subtract(const_1,#1)|multiply(#4,const_10)|multiply(#6,#5)|multiply(#3,#7) | z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b . | general |
math_qa__skKbR0gPy3keBLcF | A train 150 meters long completely crosses a 240 meters long bridge in 42 seconds. What is the speed of the train is? Choose the correct choice from the following answers
A) 32 B) 33 C) 88 D) 66 E) 09 | <gadget id="calculator">150 + 240</gadget>
<output>390</output>
<gadget id="calculator">390 / 1_000</gadget>
<output>39/100 = around 0.39</output>
<gadget id="calculator">42 / 3_600</gadget>
<output>7/600 = around 0.011667</output>
<gadget id="calculator">(39/100) / (7/600)</gadget>
<output>234/7 = around 33.428571</output>
<result>B</result> | B | 33 | A train 150 meters long completely crosses a 240 meters long bridge in 42 seconds. What is the speed of the train is? | {
"A": "32",
"B": "33",
"C": "88",
"D": "66",
"E": "09"
} | divide(divide(add(150, 240), const_1000), divide(42, const_3600)) | add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)| | "s = ( 150 + 240 ) / 42 = 390 / 42 * 18 / 5 = 33 answer : b" | physics |
math_qa__HDpRbKpZwXynrwCg | On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent T of thatbeforeJuly 1 last year? Choose the correct option
A) 90 % B) 99 % C) 100 % D) 101 % E) 110 % | <gadget id="calculator">10 * 10</gadget>
<output>100</output>
<result>B</result> | B | 99 | On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent T of thatbeforeJuly 1 last year? | {
"A": "90 %",
"B": "99 %",
"C": "100 %",
"D": "101 %",
"E": "110 %"
} | multiply(10, 10) | multiply(n1,n1)| | "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before t = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b" | general |
math_qa__NF7NdO1WOuikKChI | If 15 men, working 9 hours a day, can reap a field in 16 days, in how many
days will 18 men reap the field, working 8 hours a day?
Options:
A) 10 B) 15 C) 20 D) 25 E) none of them | <gadget id="calculator">15 * 9</gadget>
<output>135</output>
<gadget id="calculator">135 * 16</gadget>
<output>2_160</output>
<gadget id="calculator">18 * 8</gadget>
<output>144</output>
<gadget id="calculator">2_160 / 144</gadget>
<output>15</output>
<result>B</result> | B | 15 | If 15 men, working 9 hours a day, can reap a field in 16 days, in how many
days will 18 men reap the field, working 8 hours a day? | {
"A": "10",
"B": "15",
"C": "20",
"D": "25",
"E": "none of them"
} | divide(multiply(multiply(15, 9), 16), multiply(18, 8)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1) | let the required number of days be x . more men , less days ( indirect proportion ) less hours per day , more days ( indirect proportion ) men 18 : 15 hours per day 8 : 9 } : : 16 : x ( 18 x 8 x x ) = ( 15 x 9 x 16 ) = x = ( 44 x 15 ) 144 = 15 hence , required number of days = 15 . answer is b . | physics |
math_qa__lLYZihWKy9dTP2Bv | a small beaker is 1 / 2 filled with salt water . another beaker , which has 5 times the capacity of the small beaker , is 1 / 5 filled with fresh water . after dumping all of the salt water from the small beaker into the large beaker , to what fraction of its capacity will the large beaker be filled ? Choose the correct option: A) 2 / 3 B) 2 / 5 C) 3 / 5 D) 3 / 10 E) 7 / 20 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<result>D</result> | D | 0.3 | a small beaker is 1 / 2 filled with salt water . another beaker , which has 5 times the capacity of the small beaker , is 1 / 5 filled with fresh water . after dumping all of the salt water from the small beaker into the large beaker , to what fraction of its capacity will the large beaker be filled ? | {
"A": "2 / 3",
"B": "2 / 5",
"C": "3 / 5",
"D": "3 / 10",
"E": "7 / 20"
} | divide(add(1, 2), multiply(2, 5)) | add(n0,n1)|multiply(n1,n2)|divide(#0,#1) | 1 / 2 of the small beaker is 1 / 10 of the large beaker . 1 / 10 + 1 / 5 = 3 / 10 the answer is d . | general |
math_qa__5Vnrn90NiEqFmbKW | A football field is 9600 square yards. If 800 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards? Choose the correct choice from the following answers:
A) 450 B) 600 C) 750 D) 2400 E) 300 | <gadget id="calculator">800 / 9_600</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">3_600 * (1/12)</gadget>
<output>300</output>
<result>E</result> | E | 300 | A football field is 9600 square yards. If 800 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards? | {
"A": "450",
"B": "600",
"C": "750",
"D": "2400",
"E": "300"
} | multiply(3600, divide(800, 9600)) | divide(n1,n0)|multiply(n2,#0)| | "answer e ) 9600 yards need 1200 lbs 1 yard will need 800 / 9600 = 1 / 12 lbs 3600 yards will need 1 / 12 * 3600 yards = 300 lbs" | geometry |
math_qa__wrKyeDcmjO1AlenY | sum of the squares of 3 numbers is 222 and the sum of their products taken two at a time is 131 . find the sum ? Choose one
A) 22 B) 25 C) 26 D) 28 E) 29 | <gadget id="calculator">131 * 2</gadget>
<output>262</output>
<gadget id="calculator">262 + 222</gadget>
<output>484</output>
<gadget id="calculator">484 ** (1/2)</gadget>
<output>22</output>
<result>A</result> | A | 22 | sum of the squares of 3 numbers is 222 and the sum of their products taken two at a time is 131 . find the sum ? | {
"A": "22",
"B": "25",
"C": "26",
"D": "28",
"E": "29"
} | sqrt(add(multiply(131, const_2), 222)) | multiply(n2,const_2)|add(n1,#0)|sqrt(#1) | ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = √ 484 = 22 a | general |
math_qa__hFnSjYkafjPs0F1V | The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? Choose the correct choice from the following options: A) 1500 B) 1600 C) 1750 D) 1900 E) 2000 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 1_000</gadget>
<output>250</output>
<gadget id="calculator">250 * 10</gadget>
<output>2_500</output>
<gadget id="calculator">500 + 2_500</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 4</gadget>
<output>750</output>
<gadget id="calculator">2_500 - 750</gadget>
<output>1_750</output>
<result>C</result> | C | 1,750 | The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? | {
"A": "1500",
"B": "1600",
"C": "1750",
"D": "1900",
"E": "2000"
} | subtract(multiply(multiply(const_0_25, const_1000), const_10), divide(add(500, multiply(multiply(const_0_25, const_1000), const_10)), 4)) | multiply(const_0_25,const_1000)|multiply(#0,const_10)|add(n1,#1)|divide(#2,n3)|subtract(#1,#3)| | "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 4 of that new total price : p = 1 / 4 * $ 3,000 = $ 750 . plug this value in the first equation : c + 750 = $ 2,500 - - > c = $ 1,750 answer : c ." | general |
math_qa__GTEZZ0UsRMMnNY20 | n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =9? Choices
A) 16 B) 14 C) 18 D) 6 E) 9 | <gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">81 / 9</gadget>
<output>9</output>
<result>E</result> | E | 9 | n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =9? | {
"A": "16",
"B": "14",
"C": "18",
"D": "6",
"E": "9"
} | divide(power(9, 2), 9) | power(n4,n0)|divide(#0,n4)| | n ^ ( n / 2 ) = 9 apply log n / 2 logn = log 9 nlogn = 2 log 9 = log 9 ^ 2 = log 81 logn = log 81 now apply antilog n = 81 / n now n = 9 . answer : e | general |
math_qa__wdj21cKANQkBRYTE | Y and Z are in a relay race. Y runs the first leg of the course in 58 seconds. Z runs the second leg of the course in 26 seconds. What was the average time they took to run a leg of the course? Options: A) 39 B) 40 C) 41 D) 42 E) 43 | <gadget id="calculator">58 + 26</gadget>
<output>84</output>
<gadget id="calculator">84 / 2</gadget>
<output>42</output>
<result>D</result> | D | 42 | Y and Z are in a relay race. Y runs the first leg of the course in 58 seconds. Z runs the second leg of the course in 26 seconds. What was the average time they took to run a leg of the course? | {
"A": "39",
"B": "40",
"C": "41",
"D": "42",
"E": "43"
} | divide(add(58, 26), const_2) | add(n0,n1)|divide(#0,const_2) | ( 58 seconds + 26 seconds ) / 2 = 42 seconds correct option is : d | general |
math_qa__aKXwMvp2XxXXBJwp | a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R? Choose the correct choice from the following choices: A) 3 / 8 B) 1 / 2 C) 9 / 16 D) 5 / 7 E) 3 / 4 | <gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(5/8) * 2</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) - 1</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / (1/2)</gadget>
<output>2</output>
<gadget id="calculator">(1/4) / 2</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 + (1/8)</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">(9/8) / 2</gadget>
<output>9/16 = around 0.5625</output>
<result>C</result> | C | 0.5625 | a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R? | {
"A": "3 / 8",
"B": "1 / 2",
"C": "9 / 16",
"D": "5 / 7",
"E": "3 / 4"
} | divide(add(const_1, divide(subtract(multiply(divide(5, 8), const_2), const_1), divide(const_1, subtract(multiply(divide(3, 4), const_2), const_1)))), const_2) | divide(n2,n3)|divide(n0,n1)|multiply(#0,const_2)|multiply(#1,const_2)|subtract(#2,const_1)|subtract(#3,const_1)|divide(const_1,#5)|divide(#4,#6)|add(#7,const_1)|divide(#8,const_2) | the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 5 / 8 * c : ( b + c ) / 2 = ( 5 / 8 ) * c b = ( 1 / 4 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 4 * c ) / 2 = ( 1 / 8 ) * c median = ( a + c ) / 2 = ( 1 / 8 * c + c ) / 2 = ( 9 / 8 ) * c / 2 = ( 9 / 16 ) * c ( answer c ) | general |
math_qa__Bgtx8LKGq1IKWtvp | The mean of 30 values was 180. It was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean. Find the correct mean. Pick one
A) 151
B) 149
C) 152
D) 148
E) 180.67 | <gadget id="calculator">30 * 180</gadget>
<output>5_400</output>
<gadget id="calculator">155 - 135</gadget>
<output>20</output>
<gadget id="calculator">5_400 + 20</gadget>
<output>5_420</output>
<gadget id="calculator">5_420 / 30</gadget>
<output>542/3 = around 180.666667</output>
<result>E</result> | E | 180.67 | The mean of 30 values was 180. It was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean. Find the correct mean. | {
"A": "151",
"B": "149",
"C": "152",
"D": "148",
"E": "180.67"
} | divide(add(multiply(30, 180), subtract(155, 135)), 30) | multiply(n0,n1)|subtract(n2,n3)|add(#0,#1)|divide(#2,n0)| | "corrected mean = 180 × 30 − 135 + 155 / 30 = 5400 − 135 + 155 / 30 = 5420 / 30 = 180.67 answer e" | general |
math_qa__f79PnIqKnY6vaHBX | A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 6480 interest. The principal amount borrowed by him was. Pick
A) rs 14000 B) rs 15000 C) rs 16000 D) rs 18000 E) none of these | <gadget id="calculator">6_480 * 100</gadget>
<output>648_000</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">648_000 / 36</gadget>
<output>18_000</output>
<result>D</result> | D | 18,000 | A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 6480 interest. The principal amount borrowed by him was. | {
"A": "rs 14000",
"B": "rs 15000",
"C": "rs 16000",
"D": "rs 18000",
"E": "none of these"
} | divide(multiply(6480, const_100), multiply(12, 3)) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)| | "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 6480 â ˆ — 100 / 12 â ˆ — 3 = rs 18000 option d" | gain |
math_qa__TVLCfW85TeB0e5Ki | How long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak, but due to the leak it will take one additional hour to be filled? Choose the correct choice from the following answers
A) 12 hours
B) 111 hours
C) 15 hours
D) 14 hours
E) 11 hours | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>A</result> | A | 12 | How long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak, but due to the leak it will take one additional hour to be filled? | {
"A": "12 hours",
"B": "111 hours",
"C": "15 hours",
"D": "14 hours",
"E": "11 hours"
} | inverse(subtract(inverse(3), inverse(add(3, const_1)))) | add(n0,const_1)|inverse(n0)|inverse(#0)|subtract(#1,#2)|inverse(#3) | part filled without leak in 1 hour = 1 / 3 part filled with leak in 1 hour = 1 / 4 work done by leak in 1 hour = 1 / 3 â ˆ ’ 1 / 4 = 12 hours answer : a | physics |
math_qa__SE21RWXECp06lBcc | the security gate at a storage facility requires a 5 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be even , how many lock codes are possible ? Choose the most appropriate option
A) 120
B) 240
C) 360
D) 720
E) 1440 | <gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">6 * 60</gadget>
<output>360</output>
<result>C</result> | C | 360 | the security gate at a storage facility requires a 5 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be even , how many lock codes are possible ? | {
"A": "120",
"B": "240",
"C": "360",
"D": "720",
"E": "1440"
} | multiply(factorial(const_3), divide(factorial(5), const_2)) | factorial(n0)|factorial(const_3)|divide(#0,const_2)|multiply(#2,#1) | x - x - x - x - x - - > there are 3 even digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 3 - x - x - x - 2 . other x ' s can take following values : 3 - 5 - 4 - 3 - 2 - - > 3 * 5 * 4 * 3 * 2 = 360 . answer : c . | general |
math_qa__ZfR0liyTWgYolY3D | The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: Select: A) 678 B) 944 C) 456 D) 323 E) 899 | <gadget id="calculator">59 * 16</gadget>
<output>944</output>
<result>B</result> | B | 944 | The H.C.F. of two numbers is 59 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: | {
"A": "678",
"B": "944",
"C": "456",
"D": "323",
"E": "899"
} | multiply(59, 16) | multiply(n0,n2) | : explanation : clearly , the numbers are ( 59 x 13 ) and ( 59 x 16 ) . { \ color { blue } \ therefore } larger number = ( 59 x 16 ) = 944 . answer : b ) 944 | other |
math_qa__SWYdo4LSJ72enVJC | The difference between simple and compound interest on Rs. 1700 for one year at 10% per annum reckoned half-yearly is? Choose one:
A) 8.25
B) 4.25
C) 9.25
D) 3.25
E) 2.25 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(441/400) - (11/10)</gadget>
<output>1/400 = around 0.0025</output>
<gadget id="calculator">(1/400) * 1_700</gadget>
<output>17/4 = around 4.25</output>
<result>B</result> | B | 4.25 | The difference between simple and compound interest on Rs. 1700 for one year at 10% per annum reckoned half-yearly is? | {
"A": "8.25",
"B": "4.25",
"C": "9.25",
"D": "3.25",
"E": "2.25"
} | multiply(subtract(power(add(divide(divide(10, const_2), const_100), const_1), const_2), add(divide(10, const_100), const_1)), 1700) | divide(n1,const_2)|divide(n1,const_100)|add(#1,const_1)|divide(#0,const_100)|add(#3,const_1)|power(#4,const_2)|subtract(#5,#2)|multiply(n0,#6)| | "s . i . = ( 1700 * 10 * 1 ) / 100 = rs . 170 c . i . = [ 1700 * ( 1 + 5 / 100 ) 2 - 1700 ] = rs . 174.25 difference = ( 174.25 - 174 ) = rs . 4.25 . answer : b" | gain |
math_qa__HOxXqIVaHgy1NTK1 | Vijay sells a cupboard at 16% below cost price. Had he got Rs.1800 more, he would have made a profit of 16%. What is the cost price of the cupboard? Options:
A) 7450
B) 14900
C) 5625
D) 7500
E) none of these | <gadget id="calculator">100 + 16</gadget>
<output>116</output>
<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<gadget id="calculator">116 - 84</gadget>
<output>32</output>
<gadget id="calculator">32 / 100</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">1_800 / (8/25)</gadget>
<output>5_625</output>
<result>C</result> | C | 5,625 | Vijay sells a cupboard at 16% below cost price. Had he got Rs.1800 more, he would have made a profit of 16%. What is the cost price of the cupboard? | {
"A": "7450",
"B": "14900",
"C": "5625",
"D": "7500",
"E": "none of these"
} | divide(1800, divide(subtract(add(const_100, 16), subtract(const_100, 16)), const_100)) | add(n0,const_100)|subtract(const_100,n0)|subtract(#0,#1)|divide(#2,const_100)|divide(n1,#3) | explanation : cost price = 1800 / ( 0.16 + 0.16 ) = 1800 / 0.32 = rs . 5625 answer c | gain |
math_qa__h6Vgdlr1zGuuF9v4 | If A:B=4:7 AND B:C=5:9,THEN A:C=? Choose the correct choice from the following options.
A) 28 : 37 B) 18 : 37 C) 16 : 53 D) 20 : 63 E) 15 : 48 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">7 * 9</gadget>
<output>63</output>
<gadget id="calculator">20 / 63</gadget>
<output>20/63 = around 0.31746</output>
<result>D</result> | D | 0.31746 | If A:B=4:7 AND B:C=5:9,THEN A:C=? | {
"A": "28 : 37",
"B": "18 : 37",
"C": "16 : 53",
"D": "20 : 63",
"E": "15 : 48"
} | divide(multiply(4, 5), multiply(7, 9)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1) | a / b = 4 / 7 and b / c = 5 / 9 a / b * b / c = 4 / 7 * 5 / 9 = 20 / 63 so a / c = 20 / 63 20 : 63 answer d | general |
math_qa__y7L8ubnumY2sp6Lw | On the first of the year, James invested x dollars at Proudstar bank in an account that yields 3% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? Select:
A) 22.04 % B) 16.12 % C) 12.5 % D) 18.25 % E) 10 % | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<result>C</result> | C | 12.5 | On the first of the year, James invested x dollars at Proudstar bank in an account that yields 3% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? | {
"A": "22.04 %",
"B": "16.12 %",
"C": "12.5 %",
"D": "18.25 %",
"E": "10 %"
} | multiply(3, const_4) | multiply(n0,const_4)| | per quarter , interest = 3 % so for a year , interest = 12 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 12 % answer = 12.5 % = answer : c | gain |
math_qa__NpjdxWLKMeeGB16M | The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 800 per sq. meter. Pick:
A) rs . 12000
B) rs . 19500
C) rs . 18000
D) rs . 16500
E) rs . 17500 | <gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">800 * 20.625</gadget>
<output>16_500</output>
<result>D</result> | D | 16,500 | The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 800 per sq. meter. | {
"A": "rs . 12000",
"B": "rs . 19500",
"C": "rs . 18000",
"D": "rs . 16500",
"E": "rs . 17500"
} | multiply(800, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | "explanation : area = 5.5 × 3.75 sq . metre . cost for 11 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : option d" | physics |
math_qa__vK3aZUi2MQik5mag | A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over. What is the sum of the two smallest possible values of n? Choose the correct choice from the following choices:
A) 42 . B) 46 . C) 50 . D) 54 . E) 58 . | <gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">14 + 2</gadget>
<output>16</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">7 * 4</gadget>
<output>28</output>
<gadget id="calculator">28 + 2</gadget>
<output>30</output>
<gadget id="calculator">16 + 30</gadget>
<output>46</output>
<result>B</result> | B | 46 | A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over. What is the sum of the two smallest possible values of n? | {
"A": "42 .",
"B": "46 .",
"C": "50 .",
"D": "54 .",
"E": "58 ."
} | add(add(multiply(7, const_2), 2), add(multiply(7, multiply(const_2, 2)), 2)) | multiply(n2,const_2)|multiply(const_2,n3)|add(n3,#0)|multiply(n2,#1)|add(n3,#3)|add(#2,#4)| | "n = 4 k + 1 = 7 j + 2 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 2 . 1 , 5 , 9 = 7 ( 1 ) + 2 the next such number is 9 + 4 * 7 = 37 . 9 + 37 = 46 the answer is b ." | general |
math_qa__184StaiOBoeMQ3kd | The breath of a rectangular landscape is 8 times its length. There is a playground in it whose area is 3200 square mtr & which is 1/9 rd of the total landscape. What is the breath of the landscape?
Choose the correct choice from the following choices: A) 420 B) 430 C) 280 D) 360 E) 480 | <gadget id="calculator">3_200 * 9</gadget>
<output>28_800</output>
<gadget id="calculator">28_800 / 8</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 ** (1/2)</gadget>
<output>60</output>
<gadget id="calculator">60 * 8</gadget>
<output>480</output>
<result>E</result> | E | 480 | The breath of a rectangular landscape is 8 times its length. There is a playground in it whose area is 3200 square mtr & which is 1/9 rd of the total landscape. What is the breath of the landscape? | {
"A": "420",
"B": "430",
"C": "280",
"D": "360",
"E": "480"
} | multiply(sqrt(divide(multiply(3200, 9), 8)), 8) | multiply(n1,n3)|divide(#0,n0)|sqrt(#1)|multiply(n0,#2) | sol . 8 x * x = 9 * 3200 x = 60 length = 8 * 60 = 480 e | geometry |
math_qa__P812aMdIfj5mzr54 | Machine C takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine C to make 40 widgets? Select the correct option
A) 5 B) 6 C) 8 D) 10 E) 12 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 40</gadget>
<output>240</output>
<gadget id="calculator">240 / 20</gadget>
<output>12</output>
<result>E</result> | E | 12 | Machine C takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine C to make 40 widgets? | {
"A": "5",
"B": "6",
"C": "8",
"D": "10",
"E": "12"
} | divide(multiply(add(const_4, 2), 40), 20) | add(n0,const_4)|multiply(n4,#0)|divide(#1,n1) | i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of c is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and c reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of c . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer | physics |
math_qa__8Y8C2HahJd7nmzO3 | Jim is able to sell a hand-carved statue for $670 which was a 25% profit over his cost. How much did the statue originally cost him? Choose the correct choice from the following options.
A) $ 496.30 B) $ 536.00 C) $ 555.40 D) $ 574.90 E) $ 588.20 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">670 / (5/4)</gadget>
<output>536</output>
<result>B</result> | B | 536 | Jim is able to sell a hand-carved statue for $670 which was a 25% profit over his cost. How much did the statue originally cost him? | {
"A": "$ 496.30",
"B": "$ 536.00",
"C": "$ 555.40",
"D": "$ 574.90",
"E": "$ 588.20"
} | divide(670, add(divide(25, const_100), const_1)) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | "670 = 1.25 * x x = 670 / 1.25 = 536 $ 536 , which is ( b ) ." | gain |
math_qa__85yPPrXmBr9w5TwJ | Sandy had $224 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?
Choose the correct choice from the following: A) $ 260 B) $ 290 C) $ 320 D) $ 350 E) $ 380 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">224 / (7/10)</gadget>
<output>320</output>
<result>C</result> | C | 320 | Sandy had $224 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? | {
"A": "$ 260",
"B": "$ 290",
"C": "$ 320",
"D": "$ 350",
"E": "$ 380"
} | divide(224, divide(subtract(const_100, 30), const_100)) | subtract(const_100,n1)|divide(#0,const_100)|divide(n0,#1)| | "let the money sandy took for shopping be x . 0.7 x = 224 x = 320 the answer is c ." | gain |
math_qa__GS1PKUij5EmD0aUZ | Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 72 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent? Choose the correct answer.
A) 24 % B) 16 % C) 11 % D) 7 % E) 5 % | <gadget id="calculator">100 - 72</gadget>
<output>28</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">2 / (1/4)</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">28 * 40</gadget>
<output>1_120</output>
<gadget id="calculator">1_120 / 100</gadget>
<output>56/5 = around 11.2</output>
<result>C</result> | C | 11 | Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 72 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent? | {
"A": "24 %",
"B": "16 %",
"C": "11 %",
"D": "7 %",
"E": "5 %"
} | divide(multiply(subtract(const_100, 72), multiply(add(divide(const_2, const_0_25), const_2), const_4)), const_100) | divide(const_2,const_0_25)|subtract(const_100,n0)|add(#0,const_2)|multiply(#2,const_4)|multiply(#3,#1)|divide(#4,const_100) | let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.72 ( i + f ) 0.08 f = 0.32 i f = 4 i this means that for every 1 incandescent bulb , there are 4 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 4 i ) = 0.4 i / 3.6 i = 1 / 9 which is about 11 % . the answer is c . | gain |
math_qa__VAbMczveQyZQ0LKg | A motorcyclist goes from Bombay to Pune, a distance of 224 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? Choose the most appropriate option.
A) 1 : 2
B) 1 : 5
C) 4 : 7
D) 1 : 1
E) 1 : 8 | <gadget id="calculator">224 / 32</gadget>
<output>7</output>
<gadget id="calculator">224 / 7</gadget>
<output>32</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<gadget id="calculator">224 / 4</gadget>
<output>56</output>
<gadget id="calculator">32 / 56</gadget>
<output>4/7 = around 0.571429</output>
<result>C</result> | C | 0.571429 | A motorcyclist goes from Bombay to Pune, a distance of 224 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? | {
"A": "1 : 2",
"B": "1 : 5",
"C": "4 : 7",
"D": "1 : 1",
"E": "1 : 8"
} | divide(divide(224, divide(224, 32)), divide(224, subtract(divide(224, 32), const_3))) | divide(n0,n1)|divide(n0,#0)|subtract(#0,const_3)|divide(n0,#2)|divide(#1,#3)| | "t = 224 / 32 = 7 h t = 7 - 3 = 4 time ratio = 7 : 4 speed ratio = 4 : 7 answer : c" | physics |
math_qa__uYbdetJtVfW6k2RS | If A is thrice as fast as B and together can do a work in 12 days. In how many days A alone can do the work? Options
A) 16 B) 42 C) 28 D) 54 E) 45 | <gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">3 / 48</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 / (1/16)</gadget>
<output>16</output>
<result>A</result> | A | 16 | If A is thrice as fast as B and together can do a work in 12 days. In how many days A alone can do the work? | {
"A": "16",
"B": "42",
"C": "28",
"D": "54",
"E": "45"
} | inverse(divide(const_3, multiply(12, const_4))) | multiply(n0,const_4)|divide(const_3,#0)|inverse(#1)| | "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 12 = 3 + 1 / 3 x = 4 / 3 x = 1 / 12 x = 12 * 4 / 3 = 16 answer : a" | physics |
math_qa__07rsgF1ZOaa4B1rA | In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−6, −5)? Pick one.
A) 4 B) 2 C) 0 D) − 2 E) − 4 | <gadget id="calculator">-5</gadget>
<output>-5</output>
<gadget id="calculator">(-5) - 3</gadget>
<output>-8</output>
<gadget id="calculator">-6</gadget>
<output>-6</output>
<gadget id="calculator">(-6) - 10</gadget>
<output>-16</output>
<gadget id="calculator">(-8) / (-16)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 10</gadget>
<output>5</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">2 / (1/2)</gadget>
<output>4</output>
<result>A</result> | A | 4 | In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−6, −5)? | {
"A": "4",
"B": "2",
"C": "0",
"D": "− 2",
"E": "− 4"
} | divide(subtract(multiply(divide(subtract(negate(5), 3), subtract(negate(6), 10)), 10), 3), divide(subtract(negate(5), 3), subtract(negate(6), 10))) | negate(n3)|negate(n2)|subtract(#0,n1)|subtract(#1,n0)|divide(#2,#3)|multiply(n0,#4)|subtract(#5,n1)|divide(#6,#4) | first , solve for the slope , m : m = ( y 2 - y 1 ) / ( x 2 - x 1 ) = ( - 5 - 3 ) / ( - 6 - 10 ) = - 8 / - 16 or 1 / 2 then you can re - write the equation as y = ( 1 / 2 ) x + b and plug in one of the points to find b , the y intercept . using point ( 10 , 3 ) : 3 = ( 1 / 2 ) ( 10 ) + b , which can be simplified to 3 = 5 + b . solve for b and you get b = - 2 . the equation now reads : y = ( 1 / 2 ) x - 2 . to find the x intercept , plug in 0 for y : 0 = ( 1 / 2 ) x - 2 , which simplifies to 2 = ( 1 / 2 ) x . from this , we can see that the x intercept = 4 . answer is a . | general |
math_qa__7ResPbQuV2yMZNGW | In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water?
Choose the correct choice from the following options.
A) 5 : 2 B) 4 : 3 C) 3 : 2 D) 2 : 1 E) 4 : 1 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">7 - 6</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<result>D</result> | D | 2 | In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? | {
"A": "5 : 2",
"B": "4 : 3",
"C": "3 : 2",
"D": "2 : 1",
"E": "4 : 1"
} | add(subtract(add(const_4.0, 3), add(5, 1)), const_1) | add(const_4.0,n3)|add(n0,n2)|subtract(#0,#1)|add(#2,const_1)| | "( 5 / 8 ) * p + ( 1 / 4 ) * q = ( 3 / 8 ) * p + ( 3 / 4 ) * q 2 p = 4 q p / q = 2 / 1 the answer is d ." | general |
math_qa__rwCbP9V54mTue56f | A person travels from P to Q a speed of 80 km/hr and returns by increasing his speed by 10%. What is his average speed for both the trips? Choices.
A) 33 B) 77 C) 48 D) 84 E) 21 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">80 * (11/10)</gadget>
<output>88</output>
<gadget id="calculator">88 + 80</gadget>
<output>168</output>
<gadget id="calculator">168 / 2</gadget>
<output>84</output>
<result>D</result> | D | 84 | A person travels from P to Q a speed of 80 km/hr and returns by increasing his speed by 10%. What is his average speed for both the trips? | {
"A": "33",
"B": "77",
"C": "48",
"D": "84",
"E": "21"
} | divide(add(multiply(80, add(const_1, divide(10, const_100))), 80), const_2) | divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|add(n0,#2)|divide(#3,const_2)| | "speed on return trip = 110 % of 80 = 88 km / hr . average speed of trip = 80 + 88 / 2 = 168 / 2 = 84 km / hr answer : d" | general |
math_qa__PQF83QOg7DiJrmsW | A tempo is insured to an extent of 4/5 of its original value. If the premium on it at the rate of 1.3% amounts to $910, The original value of the tempo is? Choose the correct choice from the following choices
A) 92500 B) 75230 C) 65990 D) 45280 E) 87500 | <gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 1.3</gadget>
<output>1.04</output>
<gadget id="calculator">1.04 / 100</gadget>
<output>0.0104</output>
<gadget id="calculator">910 / 0.0104</gadget>
<output>87_500</output>
<result>E</result> | E | 87,500 | A tempo is insured to an extent of 4/5 of its original value. If the premium on it at the rate of 1.3% amounts to $910, The original value of the tempo is? | {
"A": "92500",
"B": "75230",
"C": "65990",
"D": "45280",
"E": "87500"
} | divide(910, divide(multiply(divide(4, 5), 1.3), const_100)) | divide(n0,n1)|multiply(n2,#0)|divide(#1,const_100)|divide(n3,#2) | let the original value of the tempo is $ x 1.3 % of 4 / 5 of x = 910 ( 13 / 10 ) * ( 1 / 100 ) * ( 4 / 5 ) x = 910 x = $ 87500 answer is e | gain |
math_qa__HA0NVOQDH3lqNuO2 | A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 60 meters, what is the height of the building (in meters)? Choose the correct choice from the following: A) 20 B) 24 C) 28 D) 32 E) 36 | <gadget id="calculator">18 / 45</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">60 * (2/5)</gadget>
<output>24</output>
<result>B</result> | B | 24 | A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 60 meters, what is the height of the building (in meters)? | {
"A": "20",
"B": "24",
"C": "28",
"D": "32",
"E": "36"
} | multiply(60, divide(18, 45)) | divide(n0,n1)|multiply(n2,#0) | the height : length ratio will be equal in both cases . 18 / 45 = x / 60 x = 24 the answer is b . | physics |
math_qa__WAljEPh5lBk68Vbr | In a class of 38 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Select:
A) 3
B) 5
C) 8
D) 13
E) 15 | <gadget id="calculator">38 * 2</gadget>
<output>76</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">12 + 10</gadget>
<output>22</output>
<gadget id="calculator">22 + 2</gadget>
<output>24</output>
<gadget id="calculator">38 - 24</gadget>
<output>14</output>
<gadget id="calculator">14 - 1</gadget>
<output>13</output>
<gadget id="calculator">13 * 3</gadget>
<output>39</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">12 + 20</gadget>
<output>32</output>
<gadget id="calculator">39 + 32</gadget>
<output>71</output>
<gadget id="calculator">76 - 71</gadget>
<output>5</output>
<result>B</result> | B | 5 | In a class of 38 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? | {
"A": "3",
"B": "5",
"C": "8",
"D": "13",
"E": "15"
} | subtract(multiply(38, 2), add(multiply(subtract(subtract(38, add(add(multiply(12, 1), 10), 2)), 1), 3), add(multiply(12, 1), multiply(10, 2)))) | multiply(n0,n1)|multiply(n2,n3)|multiply(n1,n4)|add(#1,#2)|add(n4,#1)|add(n1,#4)|subtract(n0,#5)|subtract(#6,n3)|multiply(n6,#7)|add(#3,#8)|subtract(#0,#9)| | "total # of students = 38 avg # of books per student = 2 total # of books = 38 * 2 = 76 # of student borrowed at least 3 books = 38 - 2 - 12 - 10 = 14 # of books borrowed by above 14 students = 76 - ( 12 * 1 ) + ( 10 * 2 ) = 44 considering that 13 out of above 14 students borrowed only 3 books , # of books borrowed = 13 * 3 = 39 so maximum # of books borrowed by any single student = 44 - 39 = 5 option b" | general |
math_qa__U0FQIKTqHr4EVfnz | 8 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days? Options
A) 6 B) 7 C) 8 D) 9 E) 10 | <gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">56 * 18</gadget>
<output>1_008</output>
<gadget id="calculator">12 * 12</gadget>
<output>144</output>
<gadget id="calculator">1_008 / 144</gadget>
<output>7</output>
<result>B</result> | B | 7 | 8 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 12 men work to complete the same work in 12 days? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | divide(multiply(multiply(8, 7), 18), multiply(12, 12)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | "the number of hours required to complete the work is 8 * 7 * 18 = 1008 12 × 12 × ( x ) = 1008 x = 7 the answer is b ." | physics |
math_qa__nRImjSUIKg8NcpOW | (5)1.25 × (12)0.25 × (60)0.75 = ?
Choose the correct choice from the following choices: A) 420 B) 260 C) 200 D) 300 E) 400 | <gadget id="calculator">60 ** 0.75</gadget>
<output>21.558247</output>
<gadget id="calculator">5 ** 1.25</gadget>
<output>7.476744</output>
<gadget id="calculator">12 ** 0.25</gadget>
<output>1.86121</output>
<gadget id="calculator">7.476744 * 1.86121</gadget>
<output>13.915791</output>
<gadget id="calculator">21.558247 * 13.915791</gadget>
<output>300.00006</output>
<result>D</result> | D | 300 | (5)1.25 × (12)0.25 × (60)0.75 = ? | {
"A": "420",
"B": "260",
"C": "200",
"D": "300",
"E": "400"
} | multiply(power(60, 0.75), multiply(power(5, 1.25), power(12, 0.25))) | power(n0,n1)|power(n2,n3)|power(n4,n5)|multiply(#0,#1)|multiply(#3,#2) | explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d | general |
math_qa__bkDwuLGU7ckxWzX3 | A computer factory produces 4200 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month? Choose the most appropriate option.
A) 2.25 B) 3.125 . C) 4.5 D) 5.225 E) 6.25 | <gadget id="calculator">4_200 / 28</gadget>
<output>150</output>
<gadget id="calculator">28 - 4</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">150 / 48</gadget>
<output>25/8 = around 3.125</output>
<result>B</result> | B | 3.125 | A computer factory produces 4200 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month? | {
"A": "2.25",
"B": "3.125 .",
"C": "4.5",
"D": "5.225",
"E": "6.25"
} | divide(divide(4200, 28), multiply(subtract(28, const_4), const_2)) | divide(n0,n2)|subtract(n2,const_4)|multiply(#1,const_2)|divide(#0,#2)| | "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4200 / ( 28 * 24 * 2 ) = 3.125 answer b" | physics |
math_qa__3RXVja1vA7sOIJ6p | A bowl of fruit contains 14 apples and 20 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples? Options.
A) 3 B) 6 C) 14 D) 17 E) 20 | <gadget id="calculator">14 + 20</gadget>
<output>34</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">34 * (7/10)</gadget>
<output>119/5 = around 23.8</output>
<gadget id="calculator">(119/5) - 14</gadget>
<output>49/5 = around 9.8</output>
<gadget id="calculator">(49/5) / (7/10)</gadget>
<output>14</output>
<result>C</result> | C | 14 | A bowl of fruit contains 14 apples and 20 oranges. How many oranges must be removed so that 70% of the pieces of fruit in the bowl will be apples? | {
"A": "3",
"B": "6",
"C": "14",
"D": "17",
"E": "20"
} | divide(subtract(multiply(add(14, 20), divide(70, const_100)), 14), divide(70, const_100)) | add(n0,n1)|divide(n2,const_100)|multiply(#0,#1)|subtract(#2,n0)|divide(#3,#1)| | "number of apples = 14 number of oranges = 20 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 20 - x ) = 34 - x 14 / ( 34 - x ) = 7 / 10 = > 20 = 34 - x = > x = 14 answer c" | gain |
math_qa__JCAD0g2J0O2dsVPl | The area of a square field is 1225 km2. How long will it take for a horse to run around at the speed of 20 km/h ? Pick one
A) 7 h B) 10 h C) 8 h D) 6 h E) none of these | <gadget id="calculator">1_225 ** (1/2)</gadget>
<output>35</output>
<gadget id="calculator">4 * 35</gadget>
<output>140</output>
<gadget id="calculator">140 / 20</gadget>
<output>7</output>
<result>A</result> | A | 7 | The area of a square field is 1225 km2. How long will it take for a horse to run around at the speed of 20 km/h ? | {
"A": "7 h",
"B": "10 h",
"C": "8 h",
"D": "6 h",
"E": "none of these"
} | divide(multiply(const_4, sqrt(1225)), 20) | sqrt(n0)|multiply(#0,const_4)|divide(#1,n2)| | explanation area of field = 1225 km 2 . then , each side of field = √ 1225 = 35 km distance covered by the horse = perimeter of square field = 35 × 4 = 140 km ∴ time taken by horse = distances / peed = 140 / 20 = 7 h answer a | geometry |
math_qa__mOd7iib8WkfW6USw | Xavier starts from P towards Q at a speed of 50 kmph and after every 12 mins increases his speed by 10 kmph. If the distance between P and Q is 52km, then how much time does he take to cover the distance? Choose the correct choice from the following.
A) 40 B) 60 C) 48 D) 70 E) 80 | <gadget id="calculator">12 + 12</gadget>
<output>24</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">36 + 12</gadget>
<output>48</output>
<result>C</result> | C | 48 | Xavier starts from P towards Q at a speed of 50 kmph and after every 12 mins increases his speed by 10 kmph. If the distance between P and Q is 52km, then how much time does he take to cover the distance? | {
"A": "40",
"B": "60",
"C": "48",
"D": "70",
"E": "80"
} | add(add(add(12, 12), 12), 12) | add(n1,n1)|add(n1,#0)|add(n1,#1) | first 12 min = 50 * 12 / 60 = 10 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 70 * 12 / 60 = 14 km 4 th 12 min = 80 * 12 / 60 = 16 km total time 12.4 = 48 min c | physics |
math_qa__XVM5wCcqZkub7euI | A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition? Choose the correct choice from the following choices.
A) 92.5 % B) 89.0 % C) 85.2 % D) 96.8 % E) 78.9 % | <gadget id="calculator">600 + 400</gadget>
<output>1_000</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">600 * (3/20)</gadget>
<output>90</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">400 * (1/20)</gadget>
<output>20</output>
<gadget id="calculator">90 + 20</gadget>
<output>110</output>
<gadget id="calculator">1_000 - 110</gadget>
<output>890</output>
<gadget id="calculator">890 / 1_000</gadget>
<output>89/100 = around 0.89</output>
<gadget id="calculator">(89/100) * 100</gadget>
<output>89</output>
<result>B</result> | B | 89 | A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition? | {
"A": "92.5 %",
"B": "89.0 %",
"C": "85.2 %",
"D": "96.8 %",
"E": "78.9 %"
} | multiply(divide(subtract(add(600, 400), add(multiply(600, divide(15, const_100)), multiply(400, divide(5, const_100)))), add(600, 400)), const_100) | add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|subtract(#0,#5)|divide(#6,#0)|multiply(#7,const_100)| | "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 5 % of 400 = 20 therefore , total number of rotten fruits = 90 + 20 = 110 therefore number of fruits in good condition = 1000 - 110 = 890 therefore percentage of fruits in good condition = ( 890 / 1000 × 100 ) % = ( 89000 / 1000 ) % = 89.0 % answer : b" | gain |
math_qa__C8BVZmU25AxxDM2J | On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course? Pick one.
A) 75 B) 105 C) 117 D) 150 E) 162 | <gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">30 * (1/5)</gadget>
<output>6</output>
<gadget id="calculator">20 - 6</gadget>
<output>14</output>
<gadget id="calculator">14 / 8</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">(7/4) * 60</gadget>
<output>105</output>
<gadget id="calculator">105 + 12</gadget>
<output>117</output>
<result>C</result> | C | 117 | On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course? | {
"A": "75",
"B": "105",
"C": "117",
"D": "150",
"E": "162"
} | add(multiply(divide(subtract(20, multiply(30, divide(12, const_60))), 8), const_60), 12) | divide(n2,const_60)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n3)|multiply(#3,const_60)|add(n2,#4) | at an average rate of 30 miles per hour in 12 minute ( 1 / 5 hours ) pat covers ( distance ) = ( time ) * ( rate ) = 1 / 5 * 30 = 6 miles , thus she should cover the remaining distance of 20 - 6 = 14 miles at an average rate of 8 miles per hour . to cover 14 miles at an average rate of 8 miles per hour pat needs ( time ) = ( distance ) / ( rate ) = 14 / 8 = 1.75 hours = 105 minutes . therefore pat needs total of 12 + 105 = 117 minutes to cover the entire course . answer : c . | physics |
math_qa__2CxCMhx4gTUX6KR5 | The sum of all the integers k such that –25 < k < 24 is Choose the correct choice from the following options:
A) 0
B) - 2
C) - 25
D) - 49
E) - 47 | <gadget id="calculator">-25</gadget>
<output>-25</output>
<gadget id="calculator">(-25) + 1</gadget>
<output>-24</output>
<gadget id="calculator">(-24) + 1</gadget>
<output>-23</output>
<gadget id="calculator">(-24) + (-23)</gadget>
<output>-47</output>
<result>E</result> | E | -47 | The sum of all the integers k such that –25 < k < 24 is | {
"A": "0",
"B": "- 2",
"C": "- 25",
"D": "- 49",
"E": "- 47"
} | add(add(negate(25), const_1), add(add(negate(25), const_1), const_1)) | negate(n0)|add(#0,const_1)|add(#1,const_1)|add(#1,#2)| | "- 24 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 24 - 23 sum of which is - 47 . hence option d . e" | general |
math_qa__FQaAYfAbAiFE5m7A | Sonika deposited Rs.14500 which amounted to Rs.12200 after 3 years at simple interest. Had the interest been 3% more. She would get how much? Choose the most appropriate option:
A) 13505 B) 12004 C) 15003 D) 14500 E) 16400 | <gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">12_200 - 14_500</gadget>
<output>-2_300</output>
<gadget id="calculator">(-2_300) / 3</gadget>
<output>-2_300/3 = around -766.666667</output>
<gadget id="calculator">(-2_300/3) / 14_500</gadget>
<output>-23/435 = around -0.052874</output>
<gadget id="calculator">(3/100) + (-23/435)</gadget>
<output>-199/8_700 = around -0.022874</output>
<gadget id="calculator">(-199/8_700) * 14_500</gadget>
<output>-995/3 = around -331.666667</output>
<gadget id="calculator">(-995/3) * 3</gadget>
<output>-995</output>
<gadget id="calculator">(-995) + 14_500</gadget>
<output>13_505</output>
<result>A</result> | A | 13,505 | Sonika deposited Rs.14500 which amounted to Rs.12200 after 3 years at simple interest. Had the interest been 3% more. She would get how much? | {
"A": "13505",
"B": "12004",
"C": "15003",
"D": "14500",
"E": "16400"
} | add(multiply(multiply(add(divide(3, const_100), divide(divide(subtract(12200, 14500), 3), 14500)), 14500), 3), 14500) | divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)| | "( 14500 * 3 * 3 ) / 100 = 1305 12200 - - - - - - - - 13505 answer : a" | gain |
math_qa__FKoUEGPWHVswevZa | The sale price sarees listed for Rs.298 after successive discount is 12% and 15% is?
Select:
A) 321 B) 223 C) 245 D) 265 E) 162 | <gadget id="calculator">298 * 12</gadget>
<output>3_576</output>
<gadget id="calculator">3_576 / 100</gadget>
<output>894/25 = around 35.76</output>
<gadget id="calculator">298 - (894/25)</gadget>
<output>6_556/25 = around 262.24</output>
<gadget id="calculator">(6_556/25) * 15</gadget>
<output>19_668/5 = around 3_933.6</output>
<gadget id="calculator">(19_668/5) / 100</gadget>
<output>4_917/125 = around 39.336</output>
<gadget id="calculator">(6_556/25) - (4_917/125)</gadget>
<output>27_863/125 = around 222.904</output>
<result>B</result> | B | 223 | The sale price sarees listed for Rs.298 after successive discount is 12% and 15% is? | {
"A": "321",
"B": "223",
"C": "245",
"D": "265",
"E": "162"
} | subtract(subtract(298, divide(multiply(298, 12), const_100)), divide(multiply(subtract(298, divide(multiply(298, 12), const_100)), 15), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | "explanation : 298 * ( 88 / 100 ) * ( 85 / 100 ) = 223 answer : b" | gain |
math_qa__NccVI32v8QnDOOsN | 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 170kg then find the average weight of all the 7 rounds? Options: A) 97.1 kgs B) 88.5 kgs C) 86.5 kgs D) 67.5 kgs E) 88.2 kgs | <gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">4 * 170</gadget>
<output>680</output>
<gadget id="calculator">680 / 7</gadget>
<output>680/7 = around 97.142857</output>
<result>A</result> | A | 97.1 | 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 170kg then find the average weight of all the 7 rounds? | {
"A": "97.1 kgs",
"B": "88.5 kgs",
"C": "86.5 kgs",
"D": "67.5 kgs",
"E": "88.2 kgs"
} | divide(multiply(add(const_1, 3), 170), 7) | add(const_1,n0)|multiply(n2,#0)|divide(#1,n1)| | "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 170 / 7 = 97.1 kgs answer : a" | general |
math_qa__XxdZoVZTsVAlwTEX | A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 20 percent of the drive from the center, what percent of the round-trip has the technician completed? Choose the correct option:
A) 60 B) 50 C) 40 D) 70 E) 45 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">20 * 50</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 100</gadget>
<output>10</output>
<gadget id="calculator">50 + 10</gadget>
<output>60</output>
<result>A</result> | A | 60 | A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 20 percent of the drive from the center, what percent of the round-trip has the technician completed? | {
"A": "60",
"B": "50",
"C": "40",
"D": "70",
"E": "45"
} | add(divide(const_100, const_2), divide(multiply(20, divide(const_100, const_2)), const_100)) | divide(const_100,const_2)|multiply(n0,#0)|divide(#1,const_100)|add(#0,#2)| | "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 20 % of 50 % i . e 10 % . so he completed 50 + 10 = 60 % of total trip a" | gain |
math_qa__5b5cMlzyBiEWcqq3 | It has been raining at the rate of 5 centimeters per hour. If the rain filled a cylindrical drum with a depth of 15 centimeters, and area 300 square centimeters, how long did it take to fill the drum completely? Choose the correct choice
A) 3 hours B) 4 hours 15 minutes C) 6 hours D) 2 hours 5 minutes E) 8 hours | <gadget id="calculator">15 / 5</gadget>
<output>3</output>
<result>A</result> | A | 3 | It has been raining at the rate of 5 centimeters per hour. If the rain filled a cylindrical drum with a depth of 15 centimeters, and area 300 square centimeters, how long did it take to fill the drum completely? | {
"A": "3 hours",
"B": "4 hours 15 minutes",
"C": "6 hours",
"D": "2 hours 5 minutes",
"E": "8 hours"
} | divide(15, 5) | divide(n1,n0) | answer is : a , 3 hours the volume of the drum is irrelevant and only height matters since rain fell all over the city . thus , it takes only 15 / 5 = 3 hours of rain to fill the drum | geometry |
math_qa__UzAS4vPss9AjOaie | In digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be? Choose one: A) 3387 B) 1000 C) 2866 D) 2787 E) 1400 | <gadget id="calculator">28 * 10</gadget>
<output>280</output>
<gadget id="calculator">280 * 5</gadget>
<output>1_400</output>
<result>E</result> | E | 1,400 | In digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be? | {
"A": "3387",
"B": "1000",
"C": "2866",
"D": "2787",
"E": "1400"
} | multiply(multiply(28, 10), 5) | multiply(n0,n1)|multiply(n2,#0)| | "28 * 10 * 5 = 1400 answer : e" | general |
math_qa__Xbp1Hi75dirXi5AH | The diameter of a cylindrical tin is 10 cm and height is 5 cm. Find the volume of the cylinder? Choose the correct choice.
A) 125 B) 155 C) 130 D) 120 E) 100 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">pi * (5 ** 2) * 5</gadget>
<output>125*pi = around 392.699082</output>
<gadget id="calculator">(125*pi) / pi</gadget>
<output>125</output>
<result>A</result> | A | 125 | The diameter of a cylindrical tin is 10 cm and height is 5 cm. Find the volume of the cylinder? | {
"A": "125",
"B": "155",
"C": "130",
"D": "120",
"E": "100"
} | divide(volume_cylinder(divide(10, const_2), 5), const_pi) | divide(n0,const_2)|volume_cylinder(#0,n1)|divide(#1,const_pi)| | "r = 5 h = 5 π * 5 * 5 * 5 = 125 π cc answer : a" | geometry |
math_qa__SIuTs81KCMt04P7s | (150% of 1265) ÷ 7 = ? Choose the most appropriate option
A) 125 B) 175 C) 271 D) 375 E) 524 | <gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 1_265</gadget>
<output>3_795/2 = around 1_897.5</output>
<gadget id="calculator">(3_795/2) / 7</gadget>
<output>3_795/14 = around 271.071429</output>
<result>C</result> | C | 271 | (150% of 1265) ÷ 7 = ? | {
"A": "125",
"B": "175",
"C": "271",
"D": "375",
"E": "524"
} | divide(multiply(divide(150, const_100), 1265), 7) | divide(n0,const_100)|multiply(n1,#0)|divide(#1,n2)| | "explanation : ? = ( 150 x 1265 / 100 ) ÷ 7 = 189750 / 700 = 271 answer : option c" | general |
math_qa__0rxUlXJdUqUQzg2f | Two vessels contains equal number of mixtures milk and water in the ratio 7:2 and 8:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained? Answers
A) 1 : 3 B) 9 : 13 C) 5 : 1 D) 11 : 3 E) 15 : 4 | <gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 9</gadget>
<output>1</output>
<gadget id="calculator">7 * 1</gadget>
<output>7</output>
<gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<result>C</result> | C | 5 | Two vessels contains equal number of mixtures milk and water in the ratio 7:2 and 8:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained? | {
"A": "1 : 3",
"B": "9 : 13",
"C": "5 : 1",
"D": "11 : 3",
"E": "15 : 4"
} | divide(add(multiply(7, divide(add(8, 1), add(7, 2))), 8), add(multiply(2, divide(add(8, 1), add(7, 2))), 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(n0,#2)|multiply(n1,#2)|add(n2,#3)|add(n3,#4)|divide(#5,#6)| | "the ratio of milk and water in the new vessel is = ( 7 / 9 + 8 / 9 ) : ( 2 / 9 + 1 / 9 ) = 15 / 9 : 3 / 9 = 5 : 1 answer is c" | other |
math_qa__TUpOKz2qNpzGXrfK | A 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
Select the correct option: A) 1 / 4 B) 2 / 5 C) 1 / 2 D) 3 / 5 E) 2 / 3 | <gadget id="calculator">0.375 / 5</gadget>
<output>0.075</output>
<gadget id="calculator">0.075 * 30</gadget>
<output>2.25</output>
<gadget id="calculator">3 - 2.25</gadget>
<output>0.75</output>
<gadget id="calculator">1.375 / 10</gadget>
<output>0.1375</output>
<gadget id="calculator">0.1375 - 0.075</gadget>
<output>0.0625</output>
<gadget id="calculator">0.75 / 0.0625</gadget>
<output>12</output>
<gadget id="calculator">30 - 12</gadget>
<output>18</output>
<gadget id="calculator">12 / 18</gadget>
<output>2/3 = around 0.666667</output>
<result>E</result> | E | 0.666667 | A 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar? | {
"A": "1 / 4",
"B": "2 / 5",
"C": "1 / 2",
"D": "3 / 5",
"E": "2 / 3"
} | divide(divide(subtract(3, multiply(divide(0.375, 5), 30)), subtract(divide(1.375, 10), divide(0.375, 5))), subtract(30, divide(subtract(3, multiply(divide(0.375, 5), 30)), subtract(divide(1.375, 10), divide(0.375, 5))))) | divide(n5,n4)|divide(n3,n2)|multiply(n0,#0)|subtract(#1,#0)|subtract(n1,#2)|divide(#4,#3)|subtract(n0,#5)|divide(#5,#6)| | "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 3 kg when 30 kg alloy is immersed . this is a loss of ( 3 / 30 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e" | other |
math_qa__YzRYh7XMAqKefegB | The diameter of a cylindrical tin is 14 cm and height is 2 cm. Find the volume of the cylinder? Choose the correct answer:
A) 33 B) 45 C) 66 D) 77 E) 98 | <gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">pi * (7 ** 2) * 2</gadget>
<output>98*pi = around 307.87608</output>
<gadget id="calculator">(98*pi) / pi</gadget>
<output>98</output>
<result>E</result> | E | 98 | The diameter of a cylindrical tin is 14 cm and height is 2 cm. Find the volume of the cylinder? | {
"A": "33",
"B": "45",
"C": "66",
"D": "77",
"E": "98"
} | divide(volume_cylinder(divide(14, const_2), 2), const_pi) | divide(n0,const_2)|volume_cylinder(#0,n1)|divide(#1,const_pi)| | "r = 7 h = 5 π * 7 * 7 * 5 = 98 π cc answer : e" | geometry |
math_qa__BV8CobOGRqrKWOE5 | A shopkeeper sold an article for Rs 2552.36. Approximately what was his profit percent if the cost price of the article was Rs 2400
Choose the correct choice: A) 4 % B) 5 % C) 6 % D) 7 % E) 8 % | <gadget id="calculator">2_552.36 - 2_400</gadget>
<output>152.36</output>
<gadget id="calculator">152.36 / 2_400</gadget>
<output>0.063483</output>
<gadget id="calculator">100 * 0.063483</gadget>
<output>6.3483</output>
<gadget id="calculator">floor(6.3483)</gadget>
<output>6</output>
<result>C</result> | C | 6 | A shopkeeper sold an article for Rs 2552.36. Approximately what was his profit percent if the cost price of the article was Rs 2400 | {
"A": "4 %",
"B": "5 %",
"C": "6 %",
"D": "7 %",
"E": "8 %"
} | floor(multiply(const_100, divide(subtract(2552.36, 2400), 2400))) | subtract(n0,n1)|divide(#0,n1)|multiply(#1,const_100)|floor(#2) | explanation : gain % = ( 152.36 * 100 / 2400 ) = 6.34 % = 6 % approx option c | gain |
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