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stringlengths 7
6.48k
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stringlengths 8
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math_qa__55NIb4Gx1dHH8gUT | a is the product of each integer from 1 to 50, inclusive and b=100^k, where k is an integer . What is the greatest value of k for which y is a factor of a? Choose the correct option
A) 6 B) 7 C) 8 D) 9 E) 10 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>A</result> | A | 6 | a is the product of each integer from 1 to 50, inclusive and b=100^k, where k is an integer . What is the greatest value of k for which y is a factor of a? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | divide(add(divide(50, divide(const_10, const_2)), const_2), const_2) | divide(const_10,const_2)|divide(n1,#0)|add(#1,const_2)|divide(#2,const_2) | the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10 + 2 = 12 100 ^ k = 10 ^ 2 k → k = 12 / 2 = 6 a | general |
math_qa__B0YOkE9IxVrvPwVo | Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 432 as interest at the end of the loan period, what was the rate of interest? Answers: A) 3.6 B) 6 C) 18 D) can not be determined E) none of these | <gadget id="calculator">432 * 100</gadget>
<output>43_200</output>
<gadget id="calculator">43_200 / 1_200</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>B</result> | B | 6 | Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 432 as interest at the end of the loan period, what was the rate of interest? | {
"A": "3.6",
"B": "6",
"C": "18",
"D": "can not be determined",
"E": "none of these"
} | sqrt(divide(multiply(432, const_100), 1200)) | multiply(n1,const_100)|divide(#0,n0)|sqrt(#1)| | "let rate = r % and time = r years . then , 1200 x r x r / 100 = 432 12 r 2 = 432 r 2 = 36 r = 6 . answer : b" | gain |
math_qa__r6PABV5lyENHoYRn | If n is the greatest positive integer for which 4^n is a factor of 10!, then n =? Choose the correct choice from the following answers.
A) 2
B) 4
C) 6
D) 8
E) 10 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<result>B</result> | B | 4 | If n is the greatest positive integer for which 4^n is a factor of 10!, then n =? | {
"A": "2",
"B": "4",
"C": "6",
"D": "8",
"E": "10"
} | subtract(divide(10, const_2), const_1) | divide(n1,const_2)|subtract(#0,const_1) | 10 ! = 3628800 e . 4 ^ 10 = 1048576 ( 3628800 / 1048576 ) - this is not a factor of 10 ! d . 4 ^ 8 = 65536 ( 3628800 / 65536 ) - this is not a factor of 10 ! c . 4 ^ 6 = 4096 ( 3628800 / 4096 ) - this is not a factor of 10 ! b . 4 ^ 4 = 256 ( 3628800 / 256 ) - this is a factor of 10 ! b is answer | other |
math_qa__kN7TvUqzLLoIXLMJ | An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1400 sculptures are not on display, how many pieces of art does the gallery have? Choose one: A) 360 B) 3150 C) 540 D) 640 E) 720 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1_400 / (2/3)</gadget>
<output>2_100</output>
<gadget id="calculator">2_100 / (2/3)</gadget>
<output>3_150</output>
<result>B</result> | B | 3,150 | An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1400 sculptures are not on display, how many pieces of art does the gallery have? | {
"A": "360",
"B": "3150",
"C": "540",
"D": "640",
"E": "720"
} | divide(divide(1400, subtract(1, divide(1, 3))), subtract(1, divide(1, 3))) | divide(n0,n1)|subtract(n0,#0)|divide(n6,#1)|divide(#2,#1)| | "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1400 - - > { not on display } = 2100 . according to ( i ) 2 / 3 * { total } = 2100 - - > { total } = 3150 . answer : b ." | general |
math_qa__Cxt0Hysu3bXBPHLL | The grade point average of one third of the classroom is 60; the grade point average of the rest is 66. What is the grade point average of the whole class?
Choose the correct option.
A) 55 B) 56 C) 64 D) 65 E) 66 | <gadget id="calculator">66 / 3</gadget>
<output>22</output>
<gadget id="calculator">22 * 2</gadget>
<output>44</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">44 + 20</gadget>
<output>64</output>
<result>C</result> | C | 64 | The grade point average of one third of the classroom is 60; the grade point average of the rest is 66. What is the grade point average of the whole class? | {
"A": "55",
"B": "56",
"C": "64",
"D": "65",
"E": "66"
} | add(multiply(divide(66, const_3), const_2), divide(60, const_3)) | divide(n0,const_3)|divide(n1,const_3)|multiply(#1,const_2)|add(#0,#2)| | "let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c" | general |
math_qa__jH3JtO7OlwKtuWfe | If the digits 33 in the decimal 0.00033 repeat indefinitely, what is the value of (10^5-10^3)(0.00033)? Options: A) 0.33 B) 33 C) 0.033 D) 0.0033 E) 3.3 e - 05 | <gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">100 * 99</gadget>
<output>9_900</output>
<gadget id="calculator">33 / 99</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">9_900 * (1/3)</gadget>
<output>3_300</output>
<gadget id="calculator">3_300 / 1_000</gadget>
<output>33/10 = around 3.3</output>
<gadget id="calculator">(33/10) * 10</gadget>
<output>33</output>
<result>B</result> | B | 33 | If the digits 33 in the decimal 0.00033 repeat indefinitely, what is the value of (10^5-10^3)(0.00033)? | {
"A": "0.33",
"B": "33",
"C": "0.033",
"D": "0.0033",
"E": "3.3 e - 05"
} | multiply(divide(multiply(multiply(multiply(10, 10), subtract(multiply(10, 10), const_1)), divide(33, subtract(multiply(10, 10), const_1))), const_1000), 10) | multiply(n2,n2)|subtract(#0,const_1)|divide(n0,#1)|multiply(#0,#1)|multiply(#2,#3)|divide(#4,const_1000)|multiply(n2,#5) | 99 * 0.33 = 32.67 approx . 33 answer : b | general |
math_qa__OZreeygEZWgpe93f | sum of two numbers is 10 . two times of the first exceeds by 5 from the 3 times of the other . then the numbers will be ? Choose one:
A) 7
B) 9
C) 11
D) 13
E) 15 | <gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">30 + 5</gadget>
<output>35</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">35 / 5</gadget>
<output>7</output>
<result>A</result> | A | 7 | sum of two numbers is 10 . two times of the first exceeds by 5 from the 3 times of the other . then the numbers will be ? | {
"A": "7",
"B": "9",
"C": "11",
"D": "13",
"E": "15"
} | divide(add(multiply(10, 3), 5), add(const_2, 3)) | add(n2,const_2)|multiply(n0,n2)|add(n1,#1)|divide(#2,#0) | explanation : x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a ) | general |
math_qa__Vod5Vv7r8jgReaZn | A group of men decided to do a work in 20days, but 2 of them became absent. If the rest of the group did the work in 22days, Find the original number of men?
Choose the correct choice.
A) 15 B) 22 C) 27 D) 29 E) 18 | <gadget id="calculator">2 * 22</gadget>
<output>44</output>
<gadget id="calculator">22 - 20</gadget>
<output>2</output>
<gadget id="calculator">44 / 2</gadget>
<output>22</output>
<result>B</result> | B | 22 | A group of men decided to do a work in 20days, but 2 of them became absent. If the rest of the group did the work in 22days, Find the original number of men? | {
"A": "15",
"B": "22",
"C": "27",
"D": "29",
"E": "18"
} | divide(multiply(2, 22), subtract(22, 20)) | multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | "original number of men = 2 * 22 / ( 22 - 20 ) = 22 answer is b" | physics |
math_qa__cGenJ1LflGNVK3kS | In how many no. between 10 and 30 exactly Two of the digits is 3? Choose the most appropriate option: A) 1 B) 20 C) 30 D) 40 E) 50 | <gadget id="calculator">30 / 10</gadget>
<output>3</output>
<gadget id="calculator">3 / 3</gadget>
<output>1</output>
<result>A</result> | A | 1 | In how many no. between 10 and 30 exactly Two of the digits is 3? | {
"A": "1",
"B": "20",
"C": "30",
"D": "40",
"E": "50"
} | divide(divide(30, 10), 3) | divide(n1,n0)|divide(#0,n2) | it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even de are large to have correct choice . ans : a | general |
math_qa__xLZ8o1U3XwCVDNsW | (208% of 1265) ÷ 6 = ?
Choices
A) 125 B) 439 C) 225 D) 375 E) 524 | <gadget id="calculator">208 / 100</gadget>
<output>52/25 = around 2.08</output>
<gadget id="calculator">(52/25) * 1_265</gadget>
<output>13_156/5 = around 2_631.2</output>
<gadget id="calculator">(13_156/5) / 6</gadget>
<output>6_578/15 = around 438.533333</output>
<result>B</result> | B | 439 | (208% of 1265) ÷ 6 = ? | {
"A": "125",
"B": "439",
"C": "225",
"D": "375",
"E": "524"
} | divide(multiply(divide(208, const_100), 1265), 6) | divide(n0,const_100)|multiply(n1,#0)|divide(#1,n2)| | "explanation : ? = ( 208 x 1265 / 100 ) ÷ 6 = 263120 / 600 = 439 answer : option b" | general |
math_qa__R9JxmPDI34wsVpmI | By selling an article at Rs.120, a profit of 25% is made. Find its cost price? Select the correct option:
A) s . 96 B) s . 45 C) s . 120 D) s . 180 E) s . 189 | <gadget id="calculator">120 * 100</gadget>
<output>12_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">12_000 / 125</gadget>
<output>96</output>
<result>A</result> | A | 96 | By selling an article at Rs.120, a profit of 25% is made. Find its cost price? | {
"A": "s . 96",
"B": "s . 45",
"C": "s . 120",
"D": "s . 180",
"E": "s . 189"
} | divide(multiply(120, const_100), add(const_100, 25)) | add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)| | "sp = 120 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 120 * [ 100 / ( 100 + 25 ) ] = 120 * [ 100 / 125 ] = rs . 96 answer : a" | gain |
math_qa__dKByMTelDNoPDfaa | The average score of a cricketer in 2 matches is 40 and in other 3 matches is 10. Then find the average score in all the 5 matches?
Pick one: A) 25 B) 22 C) 30 D) 35 E) 42 | <gadget id="calculator">2 * 40</gadget>
<output>80</output>
<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">80 + 30</gadget>
<output>110</output>
<gadget id="calculator">110 / 5</gadget>
<output>22</output>
<result>B</result> | B | 22 | The average score of a cricketer in 2 matches is 40 and in other 3 matches is 10. Then find the average score in all the 5 matches? | {
"A": "25",
"B": "22",
"C": "30",
"D": "35",
"E": "42"
} | divide(add(multiply(2, 40), multiply(3, 10)), 5) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|divide(#2,n4)| | "average in 5 matches = ( 2 * 40 + 3 * 10 ) / 2 + 3 = 80 + 30 / 5 = 110 / 5 = 22 answer is b" | general |
math_qa__OFjzSDm8qfZFbIcy | Which number need to add to 8679921 to get a number exactly divisible by 330?
Choose the correct choice from the following answers:
A) 69 B) 62 C) 61 D) 63 E) 64 | <gadget id="calculator">8_679_921 / 330</gadget>
<output>2_893_307/110 = around 26_302.790909</output>
<gadget id="calculator">floor(2_893_307/110)</gadget>
<output>26_302</output>
<gadget id="calculator">26_302 + 1</gadget>
<output>26_303</output>
<gadget id="calculator">26_303 - (2_893_307/110)</gadget>
<output>23/110 = around 0.209091</output>
<gadget id="calculator">330 * (23/110)</gadget>
<output>69</output>
<result>A</result> | A | 69 | Which number need to add to 8679921 to get a number exactly divisible by 330? | {
"A": "69",
"B": "62",
"C": "61",
"D": "63",
"E": "64"
} | multiply(330, subtract(add(floor(divide(8679921, 330)), const_1), divide(8679921, 330))) | divide(n0,n1)|floor(#0)|add(#1,const_1)|subtract(#2,#0)|multiply(n1,#3) | 8679921 / 330 = 26302 and reminder = 261 . 330 - 261 = 69 so , the next number divisible by 339 is 69 places in front of 8679921 which means 69 + 8679921 = 8679990 69 should be added to 8679921 a | general |
math_qa__6PyC7XCZxIfjVme8 | At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? Choices
A) 4 % B) 8 % C) 4.2 % D) 4.8 % E) 5 % | <gadget id="calculator">60 * 40</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 100</gadget>
<output>24</output>
<gadget id="calculator">24 * 20</gadget>
<output>480</output>
<gadget id="calculator">480 / 100</gadget>
<output>24/5 = around 4.8</output>
<result>D</result> | D | 4.8 | At a certain college, 60 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts? | {
"A": "4 %",
"B": "8 %",
"C": "4.2 %",
"D": "4.8 %",
"E": "5 %"
} | divide(multiply(divide(multiply(60, 40), const_100), 20), const_100) | multiply(n0,n1)|divide(#0,const_100)|multiply(n2,#1)|divide(#2,const_100)| | "let ' s say there is a total of 100 students at this college . 60 percent of the total number of students are freshmen . # of freshmen = 60 % of 100 = 60 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 60 = 24 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 24 = 4.8 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4.8 / 100 = 4.8 % answer : d" | general |
math_qa__g2wHwvUeG9pNdK9g | What is the smallest integer k for which 64^k > 4^16?
Choose the correct choice from the following answers:
A) 4 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">16 / 3</gadget>
<output>16/3 = around 5.333333</output>
<gadget id="calculator">floor(16/3)</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<result>C</result> | C | 6 | What is the smallest integer k for which 64^k > 4^16? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | add(floor(divide(16, const_3)), const_1) | divide(n2,const_3)|floor(#0)|add(#1,const_1)| | "64 ^ k > 4 ^ 16 4 ^ ( 3 k ) > 4 ^ 16 3 k > 16 k = 6 the answer is c ." | general |
math_qa__flWfyZ5NdWzGmwbF | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 1000 m long? Pick:
A) 220 sec B) 190 sec C) 167 sec D) 197 sec E) 179 sec | <gadget id="calculator">1_200 + 1_000</gadget>
<output>2_200</output>
<gadget id="calculator">1_200 / 120</gadget>
<output>10</output>
<gadget id="calculator">2_200 / 10</gadget>
<output>220</output>
<result>A</result> | A | 220 | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 1000 m long? | {
"A": "220 sec",
"B": "190 sec",
"C": "167 sec",
"D": "197 sec",
"E": "179 sec"
} | divide(add(1200, 1000), divide(1200, 120)) | add(n0,n2)|divide(n0,n1)|divide(#0,#1)| | "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2200 m t = d / s t = 2200 / 10 t = 220 sec answer : a" | physics |
math_qa__Qtjeo5GHsmjpOurM | If T = 5/9 * (K - 32), and if T = 50, then what is the value of K? Select the correct option: A) 116 B) 119 C) 122 D) 125 E) 128 | <gadget id="calculator">50 * 9</gadget>
<output>450</output>
<gadget id="calculator">450 / 5</gadget>
<output>90</output>
<gadget id="calculator">90 + 32</gadget>
<output>122</output>
<result>C</result> | C | 122 | If T = 5/9 * (K - 32), and if T = 50, then what is the value of K? | {
"A": "116",
"B": "119",
"C": "122",
"D": "125",
"E": "128"
} | add(divide(multiply(50, 9), 5), 32) | multiply(n1,n3)|divide(#0,n0)|add(n2,#1)| | "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 50 ) / 5 + 32 = 122 the answer is c ." | general |
math_qa__Y5v3QGJfWeFDPIha | let q represent a set of 7 distinct prime numbers . if the sum of the numbers in q is even and x is a member of q , then what is the least possible value that x can be ? Options.
A) 1 B) 2 C) 3 D) 5 E) 7 | <gadget id="calculator">7 / 7</gadget>
<output>1</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<result>C</result> | C | 3 | let q represent a set of 7 distinct prime numbers . if the sum of the numbers in q is even and x is a member of q , then what is the least possible value that x can be ? | {
"A": "1",
"B": "2",
"C": "3",
"D": "5",
"E": "7"
} | add(divide(7, 7), const_2) | divide(n0,n0)|add(#0,const_2) | q = p 1 + p 2 + p 3 + p 4 + p 5 + p 6 + p 7 = even ( and all primes are distinct ) if the least prime is 2 then we have sum of q = even . ans . c . 3 | general |
math_qa__CLJ4IV51xe7dlG3e | How many digits are in the number 50^8 × 8^3 × 11^2 x 10^4?
Choose the most appropriate option
A) 22 B) 20 C) 19 D) 18 E) 17 | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 - 2</gadget>
<output>18</output>
<result>D</result> | D | 18 | How many digits are in the number 50^8 × 8^3 × 11^2 x 10^4? | {
"A": "22",
"B": "20",
"C": "19",
"D": "18",
"E": "17"
} | subtract(multiply(10, 2), const_2) | multiply(n5,n6)|subtract(#0,const_2) | whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 4 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 * 10 ^ 4 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 * 10 ^ 4 = 2 * 11 ^ 2 * 10 ^ 16 * 10 ^ 4 = 242 * 10 ^ 16 x 10 ^ 4 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 20 = 23 correct option : d | general |
math_qa__tDNQBe4ybwf0N6ox | Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $432 per week. How much does she earn in dollars per hour? Answers
A) 2 B) 8 C) 9 D) 11 E) 12 | <gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">432 / 36</gadget>
<output>12</output>
<result>E</result> | E | 12 | Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $432 per week. How much does she earn in dollars per hour? | {
"A": "2",
"B": "8",
"C": "9",
"D": "11",
"E": "12"
} | divide(432, add(multiply(8, const_3), multiply(6, const_2))) | multiply(n0,const_3)|multiply(n1,const_2)|add(#0,#1)|divide(n2,#2)| | "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 432 . hourly wage = 432 / 36 = 12 answer : e" | physics |
math_qa__XdpK2gOgoAD0vp7n | X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 11. What is the value of Z?
Choose one:
A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">8 - 6</gadget>
<output>2</output>
<gadget id="calculator">11 - 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<result>B</result> | B | 3 | X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 11. What is the value of Z? | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | divide(subtract(11, subtract(multiply(const_4, 2), multiply(2, 3))), 3) | multiply(n0,const_4)|multiply(n0,n1)|subtract(#0,#1)|subtract(n4,#2)|divide(#3,n1)| | "if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 11 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 11 3 z = 9 z = 3 the answer is b ." | general |
math_qa__7Yun9sCWYJ0OAbXM | A and B are two circles. The radius of A is 5 times as large as the radius of B. What is the ratio between the areas of the circles? Choose the correct choice from the following answers.
A) 1 : 8 .
B) 1 : 2 .
C) 1 : 4 .
D) 1 : 25 .
E) 1 : 6 . | <gadget id="calculator">pi * 1</gadget>
<output>pi = around 3.141593</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">pi * 25</gadget>
<output>25*pi = around 78.539816</output>
<gadget id="calculator">pi / (25*pi)</gadget>
<output>1/25 = around 0.04</output>
<result>D</result> | D | 0.04 | A and B are two circles. The radius of A is 5 times as large as the radius of B. What is the ratio between the areas of the circles? | {
"A": "1 : 8 .",
"B": "1 : 2 .",
"C": "1 : 4 .",
"D": "1 : 25 .",
"E": "1 : 6 ."
} | divide(multiply(const_pi, const_1), multiply(const_pi, power(5, const_2))) | multiply(const_1,const_pi)|power(n0,const_2)|multiply(#1,const_pi)|divide(#0,#2) | given : the radius of a is 5 times as large as the radius of b . = > r ( a ) = 5 r ( b ) . the radius are in ratio of 1 : 5 thus the area will be in the ratio of square of radius . 1 : 25 . hence d . | geometry |
math_qa__ISy1GRpst66SCSIm | [( 3.242 x 10 ) / 100] = ? Choices
A) 0.045388 B) 4.5388 C) 0.03242 D) 473.88 E) none of these | <gadget id="calculator">3.242 * 10</gadget>
<output>32.42</output>
<gadget id="calculator">32.42 / 100</gadget>
<output>0.3242</output>
<gadget id="calculator">0.3242 / 10</gadget>
<output>0.03242</output>
<result>C</result> | C | 0.03242 | [( 3.242 x 10 ) / 100] = ? | {
"A": "0.045388",
"B": "4.5388",
"C": "0.03242",
"D": "473.88",
"E": "none of these"
} | divide(divide(multiply(3.242, 10), 100), const_10) | multiply(n0,n1)|divide(#0,n2)|divide(#1,const_10)| | "answer multiplying 3.242 x 10 = 3.242 now divide 3.242 by 100 so , 3.242 ÷ 100 = 0.03242 ∴ shift the decimal two places to the left as 100 correct option : c" | general |
math_qa__aQIfi2ktYDCxcM4M | Pipe A can fill a pool in 12 hours at a constant rate. If Pipe A does the job for 8 hours and Pipe B does the rest of the job, which works at 1/3 constant rate of Pipe A. How long will it take for Pipe B alone to do the rest of the job? Choose the correct choice from the following answers.
A) 12 hrs B) 6 hrs C) 8 hrs D) 10 hrs E) 24 hrs | <gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">4 / (1/3)</gadget>
<output>12</output>
<result>A</result> | A | 12 | Pipe A can fill a pool in 12 hours at a constant rate. If Pipe A does the job for 8 hours and Pipe B does the rest of the job, which works at 1/3 constant rate of Pipe A. How long will it take for Pipe B alone to do the rest of the job? | {
"A": "12 hrs",
"B": "6 hrs",
"C": "8 hrs",
"D": "10 hrs",
"E": "24 hrs"
} | divide(subtract(12, 8), inverse(3)) | inverse(n3)|subtract(n0,n1)|divide(#1,#0) | pipe a will do 8 / 12 in 8 hrs , so a does 2 / 3 of the work . . therefore , b will do the remaining 1 / 3 rd work alone . . as the speed of b is 1 / 3 rate of a , b will do the 1 / 3 rd work in same time that a takes to complete full job . . . ans 12 a | physics |
math_qa__TU4dPIxDzb9HuAD7 | Rs.1210 were divided among A,B,C so that A : B = 5 : 4 and B : C = 9 : 10.Then,C gets : Choose the correct choice: A) rs . 340 B) rs . 400 C) rs . 450 D) rs . 475 E) none | <gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">1_210 - 14</gadget>
<output>1_196</output>
<gadget id="calculator">1_196 / 3</gadget>
<output>1_196/3 = around 398.666667</output>
<gadget id="calculator">(1_196/3) + 4</gadget>
<output>1_208/3 = around 402.666667</output>
<gadget id="calculator">(1_208/3) + 5</gadget>
<output>1_223/3 = around 407.666667</output>
<result>B</result> | B | 400 | Rs.1210 were divided among A,B,C so that A : B = 5 : 4 and B : C = 9 : 10.Then,C gets : | {
"A": "rs . 340",
"B": "rs . 400",
"C": "rs . 450",
"D": "rs . 475",
"E": "none"
} | add(add(divide(subtract(1210, add(add(5, 5), 4)), const_3), 4), 5) | add(n1,n1)|add(n2,#0)|subtract(n0,#1)|divide(#2,const_3)|add(n2,#3)|add(n1,#4)| | "solution a : b = 5 : 4 , b : c = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 90 = 4 : 40 / 9 ∴ a : b : c = 5 : 4 : 40 / 9 = 45 : 36 : 40 . sum of ratio terms = ( 45 + 36 + 40 ) = 121 ∴ c ’ s share = rs . ( 1210 x 40 / 121 ) = rs . 400 . answer b" | general |
math_qa__PagVpJJd8B5RFTbo | Two sacks together contained 40 kilograms of sugar. If after 1 kilogram of sugar was taken from the first sack and poured into the second the weight of the sugar in the first sack became 60% the weight of the sugar in the second, what was the original difference in the weights of the sacks? Pick one:
A) 4 B) 6 C) 8 D) 10 E) 12 | <gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">40 / (8/5)</gadget>
<output>25</output>
<gadget id="calculator">25 - 1</gadget>
<output>24</output>
<gadget id="calculator">40 - 24</gadget>
<output>16</output>
<gadget id="calculator">24 - 16</gadget>
<output>8</output>
<result>C</result> | C | 8 | Two sacks together contained 40 kilograms of sugar. If after 1 kilogram of sugar was taken from the first sack and poured into the second the weight of the sugar in the first sack became 60% the weight of the sugar in the second, what was the original difference in the weights of the sacks? | {
"A": "4",
"B": "6",
"C": "8",
"D": "10",
"E": "12"
} | subtract(subtract(divide(40, add(const_1, divide(60, const_100))), 1), subtract(40, subtract(divide(40, add(const_1, divide(60, const_100))), 1))) | divide(n2,const_100)|add(#0,const_1)|divide(n0,#1)|subtract(#2,n1)|subtract(n0,#3)|subtract(#3,#4) | say the weight of the second sack after change is x kilograms , then the weight of the first sack after change would be 0.6 x . since the total weight of sugar in both sacks remained the same then x + 0.6 x = 40 , which gives x = 25 . now , if the weight of the second sack after change is 25 kilograms then initially it was 25 − 1 = 24 kilograms and the initial weight of the first sack was 40 − 24 = 16 kilograms , so the difference was 24 − 16 = 8 kilograms . answer : c | other |
math_qa__pyJi9ifzOOGqwbQ0 | Find a positive number, which when increased by 8 is equal to 128 times reciprocal of the number. Answers: A) 5 B) 6 C) 8 D) 7 E) 9 | <gadget id="calculator">128 * 4</gadget>
<output>512</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">512 + 64</gadget>
<output>576</output>
<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<gadget id="calculator">24 - 8</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>C</result> | C | 8 | Find a positive number, which when increased by 8 is equal to 128 times reciprocal of the number. | {
"A": "5",
"B": "6",
"C": "8",
"D": "7",
"E": "9"
} | divide(subtract(sqrt(add(multiply(128, const_4), power(8, const_2))), 8), const_2) | multiply(n1,const_4)|power(n0,const_2)|add(#0,#1)|sqrt(#2)|subtract(#3,n0)|divide(#4,const_2) | explanation : let the number be x . then , x + 8 = 128 x ( 1 / x ) = > x < sup > 2 < / sup > + 8 x - 128 = 0 = > ( x + 16 ) ( x - 8 ) = 0 = > x = 8 answer : option c | general |
math_qa__92fpf2fCJlrxc4Y5 | Sheela deposits Rs. 3400 in bank savings account. If this is 15% of her monthly income. What is her monthly income in?
Options: A) 22666 B) 20000 C) 25000 D) 22235 E) none of these | <gadget id="calculator">3_400 * 100</gadget>
<output>340_000</output>
<gadget id="calculator">340_000 / 15</gadget>
<output>68_000/3 = around 22_666.666667</output>
<result>A</result> | A | 22,666 | Sheela deposits Rs. 3400 in bank savings account. If this is 15% of her monthly income. What is her monthly income in? | {
"A": "22666",
"B": "20000",
"C": "25000",
"D": "22235",
"E": "none of these"
} | divide(multiply(3400, const_100), 15) | multiply(n0,const_100)|divide(#0,n1)| | "explanation : 15 % of income = rs . 3400 100 % of income = 3400 x 100 / 15 = rs . 22666 answer : a" | gain |
math_qa__XuMCR6IMI2emuh7R | When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of R? Choose the correct answer.
A) 7
B) 8
C) 9
D) 10
E) 11 | <gadget id="calculator">39 - 15</gadget>
<output>24</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<result>A</result> | A | 7 | When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of R? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | subtract(divide(subtract(39, 15), add(2, 1)), 1) | add(n1,n3)|subtract(n0,n2)|divide(#1,#0)|subtract(#2,n3)| | "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . r * 23 + 39 = 25 * ( r + 1 ) r = 7 ans . ( a )" | general |
math_qa__r6t7WOz4biISzstN | A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 is 108. What is the original number?
Choose the correct choice.
A) 10 B) 18 C) 13 D) 21 E) 27 | <gadget id="calculator">108 / 4</gadget>
<output>27</output>
<result>E</result> | E | 27 | A number when multiplied by 3 is odd and divisible by 9. This number when multiplied by 4 is 108. What is the original number? | {
"A": "10",
"B": "18",
"C": "13",
"D": "21",
"E": "27"
} | divide(108, 4) | divide(n3,n2) | working backward , 108 divided by 4 is 27 . this number fits the rules of three and nine , where the digits add up to a sum divisible by nine . answer is e . | general |
math_qa__HfkV9YcAt5oGgogF | if there is one larger cube with surface area 600 and no. of smaller cubes with surface area 24.then how many small cubes are required to make a larger cube with surface area of 600? Choose the correct choice from the following options
A) 5 B) 125 C) 4 D) 100 E) 24 | <gadget id="calculator">600 / 100</gadget>
<output>6</output>
<gadget id="calculator">600 / 6</gadget>
<output>100</output>
<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">24 / 6</gadget>
<output>4</output>
<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<result>B</result> | B | 125 | if there is one larger cube with surface area 600 and no. of smaller cubes with surface area 24.then how many small cubes are required to make a larger cube with surface area of 600? | {
"A": "5",
"B": "125",
"C": "4",
"D": "100",
"E": "24"
} | volume_cube(divide(sqrt(divide(600, divide(600, const_100))), sqrt(divide(24, divide(600, const_100))))) | divide(n0,const_100)|divide(n0,#0)|divide(n1,#0)|sqrt(#1)|sqrt(#2)|divide(#3,#4)|volume_cube(#5) | the ratio between larger and smaller is 6 a 12 : 6 a 22 = 600 : 24 a 12 : a 22 = 100 : 4 a 1 : a 2 = 10 : 2 then length of cube is 10 and 2 so make a cube with length 10 , we have to 5 small cubes each in length , breadth and height . so total 125 cubes are required . then the answer is b | geometry |
math_qa__mVSBcz8jJXFlpGAm | The interest on a certain deposit at 4.5% p.a. is Rs. 405 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ? Choose the correct option.
A) rs . 50 B) rs . 45 C) rs . 40.5 D) rs . 48.5 E) rs . 49.5 | <gadget id="calculator">4.5 / 100</gadget>
<output>0.045</output>
<gadget id="calculator">405 / 0.045</gadget>
<output>9_000</output>
<gadget id="calculator">9_000 * 5</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 100</gadget>
<output>450</output>
<gadget id="calculator">450 - 405</gadget>
<output>45</output>
<result>B</result> | B | 45 | The interest on a certain deposit at 4.5% p.a. is Rs. 405 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ? | {
"A": "rs . 50",
"B": "rs . 45",
"C": "rs . 40.5",
"D": "rs . 48.5",
"E": "rs . 49.5"
} | subtract(divide(multiply(divide(405, divide(4.5, const_100)), 5), const_100), 405) | divide(n0,const_100)|divide(n1,#0)|multiply(n2,#1)|divide(#2,const_100)|subtract(#3,n1) | s . i . = rs . 405 r = 4.5 % t = 1 year principal = ( 100 * 405 ) / ( 4.5 * 1 ) = rs . 9000 s . i at 5 % interest = ( 9000 * 5 * 1 ) / 100 = rs . 450 difference in interest = 450 – 405 = rs . 45 answer : b | gain |
math_qa__t31dCcHndbn51WOL | Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 100 feet across and 4 feet deep? Choose the correct answer:
A) 15000 B) 30000 C) 50000 D) 70000 E) 90000 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">pi * (50 ** 2) * 4</gadget>
<output>10000*pi = around 31_415.926536</output>
<result>B</result> | B | 30,000 | Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 100 feet across and 4 feet deep? | {
"A": "15000",
"B": "30000",
"C": "50000",
"D": "70000",
"E": "90000"
} | volume_cylinder(divide(100, const_2), 4) | divide(n0,const_2)|volume_cylinder(#0,n1)| | "answer should be b . v = \ pir ^ 2 h = \ pi * 50 ^ 2 * 4 = approximately 30000" | geometry |
math_qa__ouYzMQcqtu2d1zcA | Two friends plan to walk along a 33-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other? Choose the correct option:
A) 15 B) 16 C) 17 D) 18 E) 19 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) + 1</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">33 / (11/5)</gadget>
<output>15</output>
<gadget id="calculator">15 * (6/5)</gadget>
<output>18</output>
<result>D</result> | D | 18 | Two friends plan to walk along a 33-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other? | {
"A": "15",
"B": "16",
"C": "17",
"D": "18",
"E": "19"
} | multiply(divide(33, add(add(divide(20, const_100), const_1), const_1)), add(divide(20, const_100), const_1)) | divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|divide(n0,#2)|multiply(#1,#3)| | "if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 33 2.2 x = 33 x = 15 then p will have have walked 1.2 * 15 = 18 km . the answer is d ." | gain |
math_qa__YvbJcfgelJTYwjdi | The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is Answers: A) 720 B) 180 C) 75 D) 65 E) none of these | <gadget id="calculator">floor(2.3)</gadget>
<output>2</output>
<gadget id="calculator">2.3 - 2</gadget>
<output>0.3</output>
<gadget id="calculator">0.3 / 60</gadget>
<output>0.005</output>
<gadget id="calculator">0.005 * 100</gadget>
<output>0.5</output>
<gadget id="calculator">2 + 0.5</gadget>
<output>2.5</output>
<gadget id="calculator">2.5 * 3</gadget>
<output>7.5</output>
<gadget id="calculator">7.5 * 10</gadget>
<output>75</output>
<result>C</result> | C | 75 | The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is | {
"A": "720",
"B": "180",
"C": "75",
"D": "65",
"E": "none of these"
} | multiply(multiply(add(floor(2.30), multiply(divide(subtract(2.30, floor(2.30)), const_60), const_100)), const_3), const_10) | floor(n0)|subtract(n0,#0)|divide(#1,const_60)|multiply(#2,const_100)|add(#0,#3)|multiply(#4,const_3)|multiply(#5,const_10)| | "explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c" | physics |
math_qa__5XdKbh7cX1ewXVNd | A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train?
Select the correct option.
A) 325 B) 350 C) 375 D) 400 E) 425 | <gadget id="calculator">90 * 1_000</gadget>
<output>90_000</output>
<gadget id="calculator">90_000 / 3_600</gadget>
<output>25</output>
<gadget id="calculator">25 * 15</gadget>
<output>375</output>
<result>C</result> | C | 375 | A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train? | {
"A": "325",
"B": "350",
"C": "375",
"D": "400",
"E": "425"
} | multiply(divide(multiply(90, const_1000), const_3600), 15) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = ( 90 x ( 5 / 18 ) m / sec = ( 25 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 ) x 15 ) m = 375 m c" | physics |
math_qa__SMCxzOMMPrJotIuz | Five machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? Choose one:
A) 4 B) 6 C) 8 D) 5 E) 10 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<result>D</result> | D | 5 | Five machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days? | {
"A": "4",
"B": "6",
"C": "8",
"D": "5",
"E": "10"
} | subtract(divide(multiply(20, add(const_4, const_1)), 10), add(const_4, const_1)) | add(const_1,const_4)|multiply(n0,#0)|divide(#1,n1)|subtract(#2,#0) | rate of one machine = 1 job / ( 20 * 5 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 5 * 20 ) * 10 * x = 1 job x = 10 10 - 5 = 5 answer : d | physics |
math_qa__MXmhtVbNOVzKP8ej | Find (7x + 4y ) / (x-2y) if x/2y = 5/2 ? Choose the correct choice from the following answers
A) 13 B) 25 C) 26 D) 27 E) 29 | <gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) * 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">35 + 4</gadget>
<output>39</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">39 / 3</gadget>
<output>13</output>
<result>A</result> | A | 13 | Find (7x + 4y ) / (x-2y) if x/2y = 5/2 ? | {
"A": "13",
"B": "25",
"C": "26",
"D": "27",
"E": "29"
} | divide(add(multiply(multiply(divide(5, 2), 2), 7), 4), subtract(multiply(divide(5, 2), 2), 2)) | divide(n4,n2)|multiply(n2,#0)|multiply(n0,#1)|subtract(#1,n2)|add(n1,#2)|divide(#4,#3)| | "x / 2 y = 3 / 2 = > x = 10 y / 2 = 5 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 5 y ) ) + 4 y ) / ( 5 y - 2 y ) = > 39 y / 3 y = 13 answer : a" | general |
math_qa__24TqhOkWjIPXF4XK | A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 40 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany? Choose the correct choice from the following answers:
A) 45
B) 20
C) 30
D) 40
E) 50 | <gadget id="calculator">24 / 60</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">5 + (2/5)</gadget>
<output>27/5 = around 5.4</output>
<gadget id="calculator">120 / 40</gadget>
<output>3</output>
<gadget id="calculator">(27/5) - 3</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">120 / (12/5)</gadget>
<output>50</output>
<result>E</result> | E | 50 | A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 40 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany? | {
"A": "45",
"B": "20",
"C": "30",
"D": "40",
"E": "50"
} | speed(120, subtract(add(5, divide(24, const_60)), divide(120, 40))) | divide(n3,const_60)|divide(n0,n1)|add(n2,#0)|subtract(#2,#1)|speed(n0,#3)| | "40 * t = 120 therefore t = 120 / 40 = 3 on return speed * ( 5.4 - 3 ) = 120 therefore t = 120 / 2.4 = 50 e" | physics |
math_qa__cPbYF30oudYdWc9Y | The ratio between the present ages of A and B is 4:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
Pick:
A) 3 : 4
B) 3 : 0
C) 3 : 1
D) 3 : 2
E) 9 : 5 | <gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">8 / 1</gadget>
<output>8</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">32 + 4</gadget>
<output>36</output>
<gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">24 - 4</gadget>
<output>20</output>
<gadget id="calculator">36 / 20</gadget>
<output>9/5 = around 1.8</output>
<result>E</result> | E | 1.8 | The ratio between the present ages of A and B is 4:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? | {
"A": "3 : 4",
"B": "3 : 0",
"C": "3 : 1",
"D": "3 : 2",
"E": "9 : 5"
} | divide(add(multiply(4, divide(add(4, 4), subtract(4, 3))), 4), subtract(multiply(3, divide(add(4, 4), subtract(4, 3))), 4)) | add(n0,n0)|subtract(n0,n1)|divide(#0,#1)|multiply(n0,#2)|multiply(n1,#2)|add(n0,#3)|subtract(#4,n0)|divide(#5,#6)| | let the present ages of a and b be 4 x and 3 x years respectively . then , ( 4 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1 x = 8 = > x = 8 required ratio = ( 4 x + 4 ) : ( 3 x - 4 ) = 36 : 20 = 9 : 5 . answer : e | other |
math_qa__Lj4PqpMdh3CBglpa | Find value of x
(11^2 + 12^2 + 13^2 + ... + 20^2) = x Choose the correct option
A) 1200 B) 1340 C) 1234 D) 1203 E) 2485 | <gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">20 * 21</gadget>
<output>420</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">40 + 1</gadget>
<output>41</output>
<gadget id="calculator">420 * 41</gadget>
<output>17_220</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">17_220 / 6</gadget>
<output>2_870</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">10 * 11</gadget>
<output>110</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">110 * 21</gadget>
<output>2_310</output>
<gadget id="calculator">2_310 / 6</gadget>
<output>385</output>
<gadget id="calculator">2_870 - 385</gadget>
<output>2_485</output>
<result>E</result> | E | 2,485 | Find value of x
(11^2 + 12^2 + 13^2 + ... + 20^2) = x | {
"A": "1200",
"B": "1340",
"C": "1234",
"D": "1203",
"E": "2485"
} | subtract(divide(multiply(multiply(20, add(20, const_1)), add(multiply(2, 20), const_1)), multiply(const_2, const_3)), divide(multiply(multiply(const_10, add(const_10, const_1)), add(multiply(2, const_10), const_1)), multiply(const_2, const_3))) | add(n6,const_1)|add(const_1,const_10)|multiply(n1,n6)|multiply(const_2,const_3)|multiply(n1,const_10)|add(#2,const_1)|add(#4,const_1)|multiply(n6,#0)|multiply(#1,const_10)|multiply(#5,#7)|multiply(#6,#8)|divide(#9,#3)|divide(#10,#3)|subtract(#11,#12) | ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 20 ^ 2 ) - ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 10 ^ 2 ) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = ( 2870 - 385 ) = 2485 e | general |
math_qa__r1yLxOeBpebkKcD1 | In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is
Choose the correct choice from the following
A) 20 liters B) 30 liters C) 50 liters D) 60 liters E) none of these | <gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">80 - 20</gadget>
<output>60</output>
<result>D</result> | D | 60 | In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is | {
"A": "20 liters",
"B": "30 liters",
"C": "50 liters",
"D": "60 liters",
"E": "none of these"
} | subtract(multiply(subtract(60, divide(60, add(2, 1))), 2), divide(60, add(2, 1))) | add(n1,n2)|divide(n0,#0)|subtract(n0,#1)|multiply(n1,#2)|subtract(#3,#1)| | "explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters as per question we need to add water to get quantity 2 : 1 = > 40 / ( 20 + x ) = 1 / 2 = > 20 + x = 80 = > x = 60 liters option d" | general |
math_qa__LiLWeuiFqxt8cRxu | A circular ground whose radius is 15 metres, has a 1.2 metre-broad garden around it. What is the area of the garden in square metres? Choose the correct answer:
A) 118.67 B) 116.67 C) 117.67 D) 120.56 E) 120.57 | <gadget id="calculator">15 + 1.2</gadget>
<output>16.2</output>
<gadget id="calculator">pi * (16.2 ** 2)</gadget>
<output>262.44*pi = around 824.479576</output>
<gadget id="calculator">pi * (15 ** 2)</gadget>
<output>225*pi = around 706.858347</output>
<gadget id="calculator">(262.44*pi) - (225*pi)</gadget>
<output>37.44*pi = around 117.621229</output>
<result>C</result> | C | 117.67 | A circular ground whose radius is 15 metres, has a 1.2 metre-broad garden around it. What is the area of the garden in square metres? | {
"A": "118.67",
"B": "116.67",
"C": "117.67",
"D": "120.56",
"E": "120.57"
} | subtract(circle_area(add(15, 1.2)), circle_area(15)) | add(n0,n1)|circle_area(n0)|circle_area(#0)|subtract(#2,#1) | req . area = ï € [ ( 16.2 ) 2 â € “ ( 15 ) 2 ] = 22 â „ 7 ã — ( 31.2 ã — 1.2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 31.2 ã — 1.2 ) / 7 = 117.67 sq m answer c | geometry |
math_qa__nVKegER7DqmmG9sv | Rahim bought 65 books for Rs.1160 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ? Choose the correct choice from the following choices: A) rs . 18.28 B) rs . 20 C) rs . 18.08 D) rs . 28.08 E) rs . 38.08 | <gadget id="calculator">1_160 + 920</gadget>
<output>2_080</output>
<gadget id="calculator">65 + 50</gadget>
<output>115</output>
<gadget id="calculator">2_080 / 115</gadget>
<output>416/23 = around 18.086957</output>
<result>C</result> | C | 18.08 | Rahim bought 65 books for Rs.1160 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ? | {
"A": "rs . 18.28",
"B": "rs . 20",
"C": "rs . 18.08",
"D": "rs . 28.08",
"E": "rs . 38.08"
} | divide(add(1160, 920), add(65, 50)) | add(n1,n3)|add(n0,n2)|divide(#0,#1) | average price per book = ( 1160 + 920 ) / ( 65 + 50 ) = 2080 / 115 = rs . 18.08 answer : c | general |
math_qa__5HEHXDh3LlGPygrH | The ratio of the volumes of two cubes is 512 : 729. What is the ratio of their total surface areas?
Answers.
A) 1 : 22
B) 81 : 12
C) 41 : 46
D) 41 : 19
E) 84 : 12 | <gadget id="calculator">512 / 729</gadget>
<output>512/729 = around 0.702332</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(512/729) ** (1/3)</gadget>
<output>8/9 = around 0.888889</output>
<result>C</result> | C | 0.891304 | The ratio of the volumes of two cubes is 512 : 729. What is the ratio of their total surface areas? | {
"A": "1 : 22",
"B": "81 : 12",
"C": "41 : 46",
"D": "41 : 19",
"E": "84 : 12"
} | power(divide(512, 729), divide(const_1, const_3)) | divide(n0,n1)|divide(const_1,const_3)|power(#0,#1)| | "ratio of the sides = ³ √ 512 : ³ √ 729 = 8 : 9 ratio of surface areas = 82 : 92 = 41 : 46 answer : c" | geometry |
math_qa__ZbNHAHyfdymOyCUN | if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ?
Select the correct option
A) 426 B) 526 C) 247 D) 204 E) 297 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) + (1/3)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(5/6) + (3/4)</gadget>
<output>19/12 = around 1.583333</output>
<gadget id="calculator">(1/2) / (19/12)</gadget>
<output>6/19 = around 0.315789</output>
<gadget id="calculator">(6/19) * 782</gadget>
<output>4_692/19 = around 246.947368</output>
<result>C</result> | C | 247 | if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ? | {
"A": "426",
"B": "526",
"C": "247",
"D": "204",
"E": "297"
} | multiply(divide(divide(1, 2), add(add(divide(1, 2), divide(1, 3)), divide(3, 4))), 782) | divide(n2,n3)|divide(n2,n1)|divide(n1,n7)|add(#0,#1)|add(#3,#2)|divide(#0,#4)|multiply(n0,#5) | given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 6 / 19 = rs . 247 answer : c | general |
math_qa__bkHOIKJ7jIpVRWRr | A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 6t seconds, then what is the length of the platform? Choices.
A) l
B) 3 l
C) 5 l
D) 7 l
E) 9 l | <gadget id="calculator">6 - 1</gadget>
<output>5</output>
<result>C</result> | C | 5 | A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 6t seconds, then what is the length of the platform? | {
"A": "l",
"B": "3 l",
"C": "5 l",
"D": "7 l",
"E": "9 l"
} | subtract(6, const_1) | subtract(n0,const_1)| | "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 6 t ( l + p ) / ( l / t ) = 6 t p = 5 l the answer is c ." | physics |
math_qa__9VaMpsFrYoVOJ4gU | A bus 15 m long is running with a speed of 40 km/hr. In what time will it pass a man who is skateboarding at 8 km/hr in the direction opposite to that in which the car is going? Options
A) 1.125
B) 1.5
C) 1.75
D) 1.25
E) 1 | <gadget id="calculator">15 * 3_600</gadget>
<output>54_000</output>
<gadget id="calculator">40 + 8</gadget>
<output>48</output>
<gadget id="calculator">54_000 / 48</gadget>
<output>1_125</output>
<gadget id="calculator">1_125 / 1_000</gadget>
<output>9/8 = around 1.125</output>
<result>A</result> | A | 1.125 | A bus 15 m long is running with a speed of 40 km/hr. In what time will it pass a man who is skateboarding at 8 km/hr in the direction opposite to that in which the car is going? | {
"A": "1.125",
"B": "1.5",
"C": "1.75",
"D": "1.25",
"E": "1"
} | divide(divide(multiply(15, const_3600), add(40, 8)), const_1000) | add(n1,n2)|multiply(n0,const_3600)|divide(#1,#0)|divide(#2,const_1000) | speed of bus relative to man = 40 + 8 = 48 km / hr . = 48 * 5 / 18 = 40 / 3 m / sec . time taken to pass the man = 5 * 3 / 40 = 1.125 sec . answer : a | physics |
math_qa__Cx7c0Jz5ZYEKR4Gr | Victor gets 92 % marks in examinations. If these are 368 marks, find the maximum marks. Choose the correct choice from the following answers
A) 334 B) 500 C) 400 D) 288 E) 271 | <gadget id="calculator">92 / 100</gadget>
<output>23/25 = around 0.92</output>
<gadget id="calculator">368 / (23/25)</gadget>
<output>400</output>
<result>C</result> | C | 400 | Victor gets 92 % marks in examinations. If these are 368 marks, find the maximum marks. | {
"A": "334",
"B": "500",
"C": "400",
"D": "288",
"E": "271"
} | divide(368, divide(92, const_100)) | divide(n0,const_100)|divide(n1,#0)| | "let the maximum marks be m then 92 % of m = 368 ⇒ 92 / 100 × m = 368 ⇒ m = ( 368 × 100 ) / 92 ⇒ m = 36800 / 92 ⇒ m = 400 therefore , maximum marks in the examinations are 400 . answer : c" | gain |
math_qa__ta33TCN6cGfqJCoK | A train running at the speed of 300 km/hr crosses a pole in 15 seconds. What is the length of the train?
Select the correct option: A) 1200 m B) 1250 m C) 1300 m D) 1350 m E) 1450 m | <gadget id="calculator">300 * 1_000</gadget>
<output>300_000</output>
<gadget id="calculator">300_000 / 3_600</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">(250/3) * 15</gadget>
<output>1_250</output>
<result>B</result> | B | 1,250 | A train running at the speed of 300 km/hr crosses a pole in 15 seconds. What is the length of the train? | {
"A": "1200 m",
"B": "1250 m",
"C": "1300 m",
"D": "1350 m",
"E": "1450 m"
} | multiply(divide(multiply(300, const_1000), const_3600), 15) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = ( 300 * 5 / 18 ) m / sec = ( 250 / 3 ) m / sec length of the train = ( speed x time ) = ( 250 / 3 * 15 ) m = 1250 m . answer : b" | physics |
math_qa__NrWJYhJfeipLOnkz | A starts business with Rs.3500 and after 6 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ? Choose the correct choice from the following:
A) 24887
B) 20778
C) 23788
D) 10500
E) 2811 | <gadget id="calculator">3_500 * 12</gadget>
<output>42_000</output>
<gadget id="calculator">42_000 * 3</gadget>
<output>126_000</output>
<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">126_000 / 12</gadget>
<output>10_500</output>
<result>D</result> | D | 10,500 | A starts business with Rs.3500 and after 6 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ? | {
"A": "24887",
"B": "20778",
"C": "23788",
"D": "10500",
"E": "2811"
} | divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 6), 2)) | multiply(n0,const_12)|subtract(const_12,n1)|multiply(n3,#0)|multiply(n2,#1)|divide(#2,#3)| | "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 6 = 6 months . so there profit ratio = ( 3500 ã — 12 ) : ( 6 x ) = 2 : 3 â ‡ ’ x = 10500 answer : d" | other |
math_qa__MXIrVrfzVToDfe3j | The population of a village is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years? Choose the most appropriate option.
A) 10000 B) 12000 C) 13000 D) 14000 E) 14400 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">10_000 * (36/25)</gadget>
<output>14_400</output>
<result>E</result> | E | 14,400 | The population of a village is 10000. It increases annually at the rate of 20% p.a. What will be its population after 2 years? | {
"A": "10000",
"B": "12000",
"C": "13000",
"D": "14000",
"E": "14400"
} | multiply(10000, power(add(const_1, divide(20, const_100)), 2)) | divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 e" | gain |
math_qa__mudycOMajruHfgmk | In a class of 30 students, 5 students did not borrow any books from the library, 12 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ? Choose the correct choice from the following options.
A) 5 B) 8 C) 15 D) 18 E) 20 | <gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">12 + 16</gadget>
<output>28</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">28 + 15</gadget>
<output>43</output>
<gadget id="calculator">60 - 43</gadget>
<output>17</output>
<gadget id="calculator">17 + 3</gadget>
<output>20</output>
<result>E</result> | E | 20 | In a class of 30 students, 5 students did not borrow any books from the library, 12 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ? | {
"A": "5",
"B": "8",
"C": "15",
"D": "18",
"E": "20"
} | add(subtract(multiply(30, 2), add(add(12, multiply(8, 2)), multiply(5, 3))), 3) | multiply(n0,n5)|multiply(n4,n5)|multiply(n1,n6)|add(n2,#1)|add(#3,#2)|subtract(#0,#4)|add(n6,#5) | the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e . | general |
math_qa__uys62xOsXf6WVt8o | Mr. Kutty has only hens and sheep. If the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep? Choose the most appropriate option.
A) 2 : 1
B) 1 : 2
C) 6 : 13
D) 13 : 6
E) none of these | <gadget id="calculator">38 * 2</gadget>
<output>76</output>
<gadget id="calculator">100 - 76</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">38 - 12</gadget>
<output>26</output>
<gadget id="calculator">26 / 12</gadget>
<output>13/6 = around 2.166667</output>
<result>D</result> | D | 2.166667 | Mr. Kutty has only hens and sheep. If the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep? | {
"A": "2 : 1",
"B": "1 : 2",
"C": "6 : 13",
"D": "13 : 6",
"E": "none of these"
} | divide(subtract(38, divide(subtract(100, multiply(38, const_2)), const_2)), divide(subtract(100, multiply(38, const_2)), const_2)) | multiply(n0,const_2)|subtract(n1,#0)|divide(#1,const_2)|subtract(n0,#2)|divide(#3,#2) | let the total number of hens and sheep be x and y respectively . i . e . , x + y = 38 and 2 x + 4 y = 100 ∴ ratio = 13 : 6 answer d | other |
math_qa__uEO26yNpOrFqH9mm | A boat covers a certain distance downstream in 1 hour, while it comes back in 1.30 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water? Select the correct option: A) 10 B) 13 C) 11 D) 08 E) 15 | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 3</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) + 3</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(15/2) / (1/2)</gadget>
<output>15</output>
<result>E</result> | E | 15 | A boat covers a certain distance downstream in 1 hour, while it comes back in 1.30 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water? | {
"A": "10",
"B": "13",
"C": "11",
"D": "08",
"E": "15"
} | divide(add(multiply(divide(3, const_2), 3), 3), subtract(divide(3, const_2), 1)) | divide(n2,const_2)|multiply(n2,#0)|subtract(#0,n0)|add(n2,#1)|divide(#3,#2)| | "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x − 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 1 1 ⁄ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 1 1 ⁄ 2 hour since distance = speed × time , we have ( x + 3 ) × 1 = ( x − 3 ) 3 / 2 ⇒ 2 ( x + 3 ) = 3 ( x − 3 ) ⇒ 2 x + 6 = 3 x − 9 ⇒ x = 6 + 9 = 15 kmph answer is e ." | physics |
math_qa__4vv35NrT4Zr8VRuD | In how many ways can 11 books on English and 9 books on French be placed in a row on a shelf so that two books on French may not be together? Pick one: A) 220 . B) 240 C) 260 D) 280 E) 300 | <gadget id="calculator">11 - 1</gadget>
<output>10</output>
<gadget id="calculator">binomial(10, 3)</gadget>
<output>120</output>
<gadget id="calculator">factorial(10) / factorial(10 - 2)</gadget>
<output>90</output>
<gadget id="calculator">120 + 90</gadget>
<output>210</output>
<gadget id="calculator">binomial(10, 1)</gadget>
<output>10</output>
<gadget id="calculator">210 + 10</gadget>
<output>220</output>
<result>A</result> | A | 220 | In how many ways can 11 books on English and 9 books on French be placed in a row on a shelf so that two books on French may not be together? | {
"A": "220 .",
"B": "240",
"C": "260",
"D": "280",
"E": "300"
} | add(add(choose(subtract(11, const_1), const_3), permutation(subtract(11, const_1), const_2)), choose(subtract(11, const_1), const_1)) | subtract(n0,const_1)|choose(#0,const_3)|choose(#0,const_1)|permutation(#0,const_2)|add(#1,#3)|add(#4,#2) | we have 11 english and 9 french books , no french books should be adjacent . imagine 11 english books in a row and empty slots like below : * e * e * e * e * e * e * e * e * e * e * e * now if 9 french books would be placed in 12 empty slots , all french books will be separated by english books . so we can ` ` choose ' ' 9 empty slots from 12 available for french books , which is 12 c 9 = 220 . ans : a _________________ | probability |
math_qa__S89UPIql4mrn77Kr | If 35 percent of 400 is 20 percent of x, then x =
Choose the correct choice from the following.
A) 200
B) 350
C) 700
D) 900
E) 1,400 | <gadget id="calculator">35 * 400</gadget>
<output>14_000</output>
<gadget id="calculator">14_000 / 20</gadget>
<output>700</output>
<result>C</result> | C | 700 | If 35 percent of 400 is 20 percent of x, then x = | {
"A": "200",
"B": "350",
"C": "700",
"D": "900",
"E": "1,400"
} | divide(multiply(35, 400), 20) | multiply(n0,n1)|divide(#0,n2)| | "5 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . answer : c" | general |
math_qa__wfdGBNPYuEQz8kP4 | The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Choose the correct choice from the following answers
A) 488 B) 429 C) 418 D) 480 E) 410 | <gadget id="calculator">2 * 26</gadget>
<output>52</output>
<gadget id="calculator">52 ** 2</gadget>
<output>2_704</output>
<gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">2_704 - 400</gadget>
<output>2_304</output>
<gadget id="calculator">2_304 ** (1/2)</gadget>
<output>48</output>
<gadget id="calculator">20 * 48</gadget>
<output>960</output>
<gadget id="calculator">960 / 2</gadget>
<output>480</output>
<result>D</result> | D | 480 | The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is? | {
"A": "488",
"B": "429",
"C": "418",
"D": "480",
"E": "410"
} | divide(multiply(20, sqrt(subtract(power(multiply(const_2, 26), const_2), power(20, const_2)))), const_2) | multiply(n0,const_2)|power(n1,const_2)|power(#0,const_2)|subtract(#2,#1)|sqrt(#3)|multiply(n1,#4)|divide(#5,const_2) | 262 – 102 = 242 d 1 = 20 d 2 = 48 1 / 2 * 20 * 48 = 480 answer : d | geometry |
math_qa__vxFlpf5apQoqnQTq | 10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? Options:
A) 90 B) 98 C) 35 D) 99 E) 80 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">10 * 9</gadget>
<output>90</output>
<result>A</result> | A | 90 | 10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? | {
"A": "90",
"B": "98",
"C": "35",
"D": "99",
"E": "80"
} | multiply(10, subtract(10, const_1)) | subtract(n0,const_1)|multiply(n0,#0)| | "though 2 * ( 10 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 9 , so he ' ll play 18 matches . similarly , second guy has to play with the rest of 8 as his 2 games with the first guy are already played . so he plays 16 matches . this continues like this and the total matches are 18 + 16 + 14 . . . + 2 18 + 16 + . . . + 2 = 2 ( 9 + 8 + . . . + 1 ) = 2 ( ( 9 * 10 ) / 2 ) = 9 * 10 = 90 . answer : a" | general |
math_qa__pBjsdSxUuXdqRvvn | John is building a rectangular fence around a garden. The length will be 5 feet shorter than its width. If the total area of the garden is 176 square feet, what is the length of the diagonal (in feet)? Answers:
A) between 18 and 19
B) between 19 and 20
C) between 20 and 21
D) between 21 and 22
E) between 22 and 23 | <gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 ** 2</gadget>
<output>121</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<gadget id="calculator">121 + 256</gadget>
<output>377</output>
<gadget id="calculator">377 ** (1/2)</gadget>
<output>sqrt(377) = around 19.416488</output>
<result>B</result> | B | 19 | John is building a rectangular fence around a garden. The length will be 5 feet shorter than its width. If the total area of the garden is 176 square feet, what is the length of the diagonal (in feet)? | {
"A": "between 18 and 19",
"B": "between 19 and 20",
"C": "between 20 and 21",
"D": "between 21 and 22",
"E": "between 22 and 23"
} | sqrt(add(power(add(const_10, const_1), const_2), power(add(const_10, add(5, const_1)), const_2))) | add(const_1,const_10)|add(n0,const_1)|add(#1,const_10)|power(#0,const_2)|power(#2,const_2)|add(#3,#4)|sqrt(#5) | to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the length , so by using the roots , we get 16 as the width ( x ) , and 11 as the length ( x - 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 16 ^ 2 + 11 ^ 2 = 256 + 121 = 377 the square root of 377 is less than 20 , since 20 ^ 2 = 400 . going down a number , we can compute 19 ^ 2 = 361 < 377 . therefore , the length of the diagonal must be between 19 and 20 . the correct answer is b . | geometry |
math_qa__YvXUxCaWp7wiTp8S | A train passes a platform in 22 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Choose the correct choice from the following answers: A) 40 B) 50 C) 60 D) 30 E) 20 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<gadget id="calculator">22 - 20</gadget>
<output>2</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<result>D</result> | D | 30 | A train passes a platform in 22 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is | {
"A": "40",
"B": "50",
"C": "60",
"D": "30",
"E": "20"
} | multiply(multiply(const_0_2778, 54), subtract(22, 20)) | multiply(n2,const_0_2778)|subtract(n0,n1)|multiply(#0,#1)| | "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 12 = > 300 + l = 15 × 22 = 330 = > l = 330 - 300 = 30 meter answer is d ." | physics |
math_qa__MJeSviAB5yxahIJl | In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 184 votes. Find the total number of valid votes?
Answers
A) 430 B) 438 C) 436 D) 434 E) 460 | <gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">70 - 30</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">184 / (2/5)</gadget>
<output>460</output>
<result>E</result> | E | 460 | In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 184 votes. Find the total number of valid votes? | {
"A": "430",
"B": "438",
"C": "436",
"D": "434",
"E": "460"
} | divide(184, divide(subtract(70, subtract(const_100, 70)), const_100)) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)| | "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 184 = > 4 x / 10 = 184 = > 4 x = 1840 = > x = 460 . answer : e" | gain |
math_qa__vmlggFUqwFBeaJ0Y | A rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed? Choose the correct choice from the following answers.
A) 46 m
B) 26 m
C) 26 m
D) 56 m
E) 25 m | <gadget id="calculator">15 + 50</gadget>
<output>65</output>
<gadget id="calculator">65 * 2</gadget>
<output>130</output>
<gadget id="calculator">130 / 5</gadget>
<output>26</output>
<result>B</result> | B | 26 | A rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed? | {
"A": "46 m",
"B": "26 m",
"C": "26 m",
"D": "56 m",
"E": "25 m"
} | divide(multiply(add(15, 50), const_2), 5) | add(n0,n1)|multiply(#0,const_2)|divide(#1,n2)| | "perimeter of the plot = 2 ( 15 + 50 ) = 130 m no of poles = 130 / 5 = 26 m answer : b" | physics |
math_qa__pTYNmL7j15oOUCj4 | If a train, travelling at a speed of 270 kmph, crosses a pole in 5 sec, then the length of train is? Answers: A) 281 m B) 325 m C) 117 m D) 375 m E) 350 m | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">270 * (5/18)</gadget>
<output>75</output>
<gadget id="calculator">75 * 5</gadget>
<output>375</output>
<result>D</result> | D | 375 | If a train, travelling at a speed of 270 kmph, crosses a pole in 5 sec, then the length of train is? | {
"A": "281 m",
"B": "325 m",
"C": "117 m",
"D": "375 m",
"E": "350 m"
} | multiply(multiply(270, const_0_2778), 5) | multiply(n0,const_0_2778)|multiply(n1,#0)| | "d d = 270 * 5 / 18 * 5 = 375 m" | physics |
math_qa__fPGJWsEPYMPL51ro | A certain car uses one gallon of gasoline every 36 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway? Choose the correct choice from the following options:
A) 15 % B) 20 % C) 22.5 % D) 25 % E) 40 % | <gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 4</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">4 * (1/36)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/5) + (1/9)</gadget>
<output>14/45 = around 0.311111</output>
<gadget id="calculator">8 * (1/36)</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(14/45) - (2/9)</gadget>
<output>4/45 = around 0.088889</output>
<gadget id="calculator">(4/45) / (2/9)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>E</result> | E | 40 | A certain car uses one gallon of gasoline every 36 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway? | {
"A": "15 %",
"B": "20 %",
"C": "22.5 %",
"D": "25 %",
"E": "40 %"
} | multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 36))), multiply(8, divide(const_1, 36))), multiply(8, divide(const_1, 36))), const_100) | divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|multiply(n2,#1)|multiply(n4,#1)|add(#2,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)| | "4 miles on the highway = 4 / 36 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 36 + 4 / 20 = 14 / 45 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 14 / 45 - 8 / 36 ) / ( 8 / 36 ) = 0.40 . answer : e ." | general |
math_qa__nYvHIGCIv2GXTxJF | The calendar of the year 2060 can be used again in the year? Answers:
A) 2081 B) 2083 C) 2088 D) 1971 E) 1973 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<gadget id="calculator">14 * 2</gadget>
<output>28</output>
<gadget id="calculator">28 + 2_060</gadget>
<output>2_088</output>
<result>C</result> | C | 2,088 | The calendar of the year 2060 can be used again in the year? | {
"A": "2081",
"B": "2083",
"C": "2088",
"D": "1971",
"E": "1973"
} | add(multiply(subtract(multiply(const_4, const_4), const_2), const_2), 2060) | multiply(const_4,const_4)|subtract(#0,const_2)|multiply(#1,const_2)|add(n0,#2)| | "explanation : given year 2060 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2060 + 28 = 2088 answer : c" | gain |
math_qa__y9jk0uUFGdmLB5cj | The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 75 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B? Choices: A) 75 % B) 80 % C) 145 % D) 150 % E) 180 % | <gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 75</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">2 + (3/2)</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) ** 2</gadget>
<output>49/4 = around 12.25</output>
<gadget id="calculator">(49/4) - 1</gadget>
<output>45/4 = around 11.25</output>
<gadget id="calculator">(45/4) - 4</gadget>
<output>29/4 = around 7.25</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">(29/4) / 5</gadget>
<output>29/20 = around 1.45</output>
<gadget id="calculator">(29/20) * 100</gadget>
<output>145</output>
<result>C</result> | C | 145 | The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 75 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B? | {
"A": "75 %",
"B": "80 %",
"C": "145 %",
"D": "150 %",
"E": "180 %"
} | multiply(divide(subtract(subtract(square_area(add(add(const_1, divide(100, 100)), divide(multiply(add(const_1, divide(100, 100)), 75), 100))), const_1), const_4), add(const_1, square_area(add(const_1, divide(100, 100))))), 100) | divide(n0,n0)|add(#0,const_1)|multiply(n1,#1)|square_area(#1)|add(#3,const_1)|divide(#2,n0)|add(#1,#5)|square_area(#6)|subtract(#7,const_1)|subtract(#8,const_4)|divide(#9,#4)|multiply(n0,#10)| | "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 75 percent to make square c length of each side of square c = 1.75 * 20 = 35 area of c = 35 ^ 2 = 1225 difference in areas of c and cummulative areas of a and b = 1225 - ( 400 + 100 ) = 725 percent is the area of square c greater than the sum of the areas of squares a and b = ( 725 / 500 ) * 100 % = 145 % answer c" | geometry |
math_qa__UnjDQx611S5YmjHd | P and Q are the only two applicants qualified for a short-term research project that pays 480 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? Choices
A) $ 5
B) $ 8
C) $ 11
D) $ 14
E) $ 17 | <gadget id="calculator">3 / 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">10 / (1/2)</gadget>
<output>20</output>
<gadget id="calculator">480 / 20</gadget>
<output>24</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">480 / 30</gadget>
<output>16</output>
<gadget id="calculator">24 - 16</gadget>
<output>8</output>
<result>B</result> | B | 8 | P and Q are the only two applicants qualified for a short-term research project that pays 480 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage? | {
"A": "$ 5",
"B": "$ 8",
"C": "$ 11",
"D": "$ 14",
"E": "$ 17"
} | subtract(divide(480, divide(10, subtract(divide(const_3, const_2), const_1))), divide(480, add(divide(10, subtract(divide(const_3, const_2), const_1)), 10))) | divide(const_3,const_2)|subtract(#0,const_1)|divide(n2,#1)|add(n2,#2)|divide(n0,#2)|divide(n0,#3)|subtract(#4,#5)| | "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 480 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 480 / 30 = $ 16 p ' s hourly wage is 480 / ( t - 10 ) = $ 24 which is $ 8 per hour more . the answer is b ." | general |
math_qa__ugVrhBCTPcf8isVL | The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is Choose the correct choice from the following answers.
A) 237
B) 154
C) 2376
D) 198
E) 171 | <gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">pi * (7 ** 2)</gadget>
<output>49*pi = around 153.93804</output>
<result>B</result> | B | 154 | The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is | {
"A": "237",
"B": "154",
"C": "2376",
"D": "198",
"E": "171"
} | circle_area(divide(14, const_2)) | divide(n1,const_2)|circle_area(#0) | explanation : the diameter is equal to the shortest side of the rectangle . so radius = 14 / 2 = 7 cm . answer : b ) 154 | geometry |
math_qa__XjJPNQoxQBVCkjaf | What profit percent is made by selling an article at a certain price, if by selling at 1/3rd of that price, there would be a loss of 20%? Choose the correct option
A) 140 % B) 29 % C) 70 % D) 27 % E) 28 % | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">80 / (1/3)</gadget>
<output>240</output>
<gadget id="calculator">240 - 100</gadget>
<output>140</output>
<result>A</result> | A | 140 | What profit percent is made by selling an article at a certain price, if by selling at 1/3rd of that price, there would be a loss of 20%? | {
"A": "140 %",
"B": "29 %",
"C": "70 %",
"D": "27 %",
"E": "28 %"
} | subtract(divide(subtract(const_100, 20), divide(1, 3)), const_100) | divide(n0,n1)|subtract(const_100,n2)|divide(#1,#0)|subtract(#2,const_100)| | "sp 2 = 1 / 3 sp 1 cp = 100 sp 2 = 80 1 / 3 sp 1 = 80 sp 1 = 240 100 - - - 240 = > 140 % answer : a" | gain |
math_qa__dqiPYPIB3xEVUMkU | A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 4 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
Answers:
A) 2
B) 9
C) 15
D) 18
E) 30 | <gadget id="calculator">0.06 * 4</gadget>
<output>0.24</output>
<gadget id="calculator">0.6 - 0.24</gadget>
<output>0.36</output>
<gadget id="calculator">0.08 - 0.06</gadget>
<output>0.02</output>
<gadget id="calculator">0.36 / 0.02</gadget>
<output>18</output>
<result>D</result> | D | 18 | A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 4 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B? | {
"A": "2",
"B": "9",
"C": "15",
"D": "18",
"E": "30"
} | divide(subtract(0.60, multiply(0.06, 4)), subtract(0.08, 0.06)) | multiply(n1,n2)|subtract(n3,n2)|subtract(n0,#0)|divide(#2,#1)| | "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 4 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 4 ) = 0.08 t - - > 60 + 6 ( t - 4 ) = 8 t - - > t = 18 . answer : d ." | other |
math_qa__bTiuBYjYtxkU6nlC | Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed
Choices: A) 486 B) 366 C) 299 D) 278 E) 1888 | <gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">6 ** 3</gadget>
<output>216</output>
<gadget id="calculator">1 + 216</gadget>
<output>217</output>
<gadget id="calculator">8 ** 3</gadget>
<output>512</output>
<gadget id="calculator">217 + 512</gadget>
<output>729</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">729 ** (1/3)</gadget>
<output>9</output>
<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">3 * 81</gadget>
<output>243</output>
<gadget id="calculator">243 * 2</gadget>
<output>486</output>
<result>A</result> | A | 486 | Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed | {
"A": "486",
"B": "366",
"C": "299",
"D": "278",
"E": "1888"
} | multiply(multiply(const_3, power(power(add(add(power(1, const_3), power(6, const_3)), power(8, const_3)), const_0_33), const_2)), const_2) | power(n0,const_3)|power(n1,const_3)|power(n2,const_3)|add(#0,#1)|add(#3,#2)|power(#4,const_0_33)|power(#5,const_2)|multiply(#6,const_3)|multiply(#7,const_2) | explanation : volume of new cube = = edge of new cube = = 9 cm surface area of the new cube = ( 6 x 9 x 9 ) = 486 answer : a ) 486 | geometry |
math_qa__irLXlC7VVZ74pWeO | A man swims downstream 45 km and upstream 25 km taking 5 hours each time, what is the speed of the man in still water? Pick one
A) 17 B) 24 C) 7 D) 24 E) 20 | <gadget id="calculator">25 / 5</gadget>
<output>5</output>
<gadget id="calculator">45 / 5</gadget>
<output>9</output>
<gadget id="calculator">5 + 9</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>C</result> | C | 7 | A man swims downstream 45 km and upstream 25 km taking 5 hours each time, what is the speed of the man in still water? | {
"A": "17",
"B": "24",
"C": "7",
"D": "24",
"E": "20"
} | divide(add(divide(25, 5), divide(45, 5)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | "45 - - - 5 ds = 9 ? - - - - 1 25 - - - 5 us = 5 ? - - - - 1 m = ? m = ( 9 + 5 ) / 2 = 14 / 2 = 7 answer : c" | physics |
math_qa__3j8tjoghhD0ZpQiT | The length of a bridge in meters, which a train 90-meters long and traveling at 45 km/hr can cross in 30 seconds is? Choices
A) 145
B) 215
C) 265
D) 285
E) 375 | <gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 90</gadget>
<output>285</output>
<result>D</result> | D | 285 | The length of a bridge in meters, which a train 90-meters long and traveling at 45 km/hr can cross in 30 seconds is? | {
"A": "145",
"B": "215",
"C": "265",
"D": "285",
"E": "375"
} | subtract(multiply(divide(multiply(45, const_1000), const_3600), 30), 90) | multiply(n1,const_1000)|divide(#0,const_3600)|multiply(n2,#1)|subtract(#2,n0) | 45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 90 = 375 meters x = 285 meters the answer is d . | physics |
math_qa__Ec6NOUHfi3FPt1ue | If 3<x<6<y<8, then what is the greatest possible positive integer difference of x and y? Choose the most appropriate option:
A) 3
B) 4
C) 5
D) 6
E) 7 | <gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<result>B</result> | B | 4 | If 3<x<6<y<8, then what is the greatest possible positive integer difference of x and y? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | subtract(subtract(8, 3), const_1) | subtract(n2,n0)|subtract(#0,const_1) | 3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b . | general |
math_qa__Cd28uBzJHh46FMou | In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground? Answers.
A) 70
B) 52
C) 62
D) 59
E) 50 | <gadget id="calculator">16 + 12</gadget>
<output>28</output>
<gadget id="calculator">18 + 13</gadget>
<output>31</output>
<gadget id="calculator">28 + 31</gadget>
<output>59</output>
<result>D</result> | D | 59 | In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground? | {
"A": "70",
"B": "52",
"C": "62",
"D": "59",
"E": "50"
} | add(add(16, 12), add(18, 13)) | add(n1,n2)|add(n3,n4)|add(#0,#1)| | "total number of players = 16 + 12 + 18 + 13 = 59 answer is d" | physics |
math_qa__BLbtCTY778Q1hf47 | In a class of 69 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course? Choose the correct answer:
A) 6
B) 15
C) 24
D) 33
E) 54 | <gadget id="calculator">41 + 22</gadget>
<output>63</output>
<gadget id="calculator">63 - 9</gadget>
<output>54</output>
<gadget id="calculator">69 - 54</gadget>
<output>15</output>
<result>B</result> | B | 15 | In a class of 69 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course? | {
"A": "6",
"B": "15",
"C": "24",
"D": "33",
"E": "54"
} | subtract(69, subtract(add(41, 22), 9)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)| | "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 69 54 + not = 69 not = 69 - 54 = 15 so answer is b" | other |
math_qa__qraIlG2BTg5vu9yi | The charge for a single room at Hotel P is 50 percent less than the charge for a single room at Hotel R and 20 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G? Select:
A) 50 %
B) 60 %
C) 75 %
D) 80 %
E) 90 % | <gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">50 / 80</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(5/8) * 100</gadget>
<output>125/2 = around 62.5</output>
<gadget id="calculator">100 - (125/2)</gadget>
<output>75/2 = around 37.5</output>
<gadget id="calculator">(75/2) / (125/2)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>B</result> | B | 60 | The charge for a single room at Hotel P is 50 percent less than the charge for a single room at Hotel R and 20 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G? | {
"A": "50 %",
"B": "60 %",
"C": "75 %",
"D": "80 %",
"E": "90 %"
} | multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 50), subtract(const_100, 20)), const_100)), multiply(divide(subtract(const_100, 50), subtract(const_100, 20)), const_100)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)| | "p = 0.5 r = 0.8 g r = 0.8 g / 0.5 = 1.6 * g thus r is 60 % greater than g . the answer is b ." | gain |
math_qa__J8q7mw9gkKvJ3Vfe | Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 18 kmph and Prasanna moves southward at a speed of 27 kmph. How far will be Prasanna from Laxmi after 60 minutes ? Choose the correct choice from the following answers: A) 11 B) 50 C) 28 D) 45 E) 18 | <gadget id="calculator">18 + 27</gadget>
<output>45</output>
<result>D</result> | D | 45 | Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 18 kmph and Prasanna moves southward at a speed of 27 kmph. How far will be Prasanna from Laxmi after 60 minutes ? | {
"A": "11",
"B": "50",
"C": "28",
"D": "45",
"E": "18"
} | add(18, 27) | add(n0,n1)| | "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 18 kmph x 1 hr = 18 km total southward prasanna ' s distance = 27 kmph x 1 hr = 27 km total distance between prasanna and laxmi is = 18 + 27 = 45 km . answer : d" | physics |
math_qa__9aH3b7Q0T5huLwZa | TOM traveled the entire 80 miles trip. If he did the first 30 miles of at a constant rate 30 miles per hour and the remaining trip of at a constant rate 50 miles per hour, what is the his average speed, in miles per hour? Answers.
A) 55 mph B) 50 mph C) 40 mph D) 60 mph E) 70 mph | <gadget id="calculator">80 - 30</gadget>
<output>50</output>
<gadget id="calculator">50 / 50</gadget>
<output>1</output>
<gadget id="calculator">30 / 30</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>C</result> | C | 40 | TOM traveled the entire 80 miles trip. If he did the first 30 miles of at a constant rate 30 miles per hour and the remaining trip of at a constant rate 50 miles per hour, what is the his average speed, in miles per hour? | {
"A": "55 mph",
"B": "50 mph",
"C": "40 mph",
"D": "60 mph",
"E": "70 mph"
} | divide(80, add(divide(50, subtract(80, 30)), divide(30, 30))) | divide(n1,n2)|subtract(n0,n1)|divide(n3,#1)|add(#2,#0)|divide(n0,#3)| | "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 30 + 50 ) / ( ( 30 / 30 ) + ( 50 / 50 ) ) = 80 / 2 = 40 mph c" | physics |
math_qa__iHYOb87bSbCV46nM | There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted?
Answers:
A) 6 B) 7 C) 8 D) 2 E) 9 | <gadget id="calculator">3 * 24</gadget>
<output>72</output>
<gadget id="calculator">72 - 24</gadget>
<output>48</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<result>A</result> | A | 6 | There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted? | {
"A": "6",
"B": "7",
"C": "8",
"D": "2",
"E": "9"
} | divide(subtract(multiply(3, 24), 24), subtract(multiply(3, 3), 1)) | multiply(n0,n1)|multiply(n1,n1)|subtract(#0,n0)|subtract(#1,n2)|divide(#2,#3) | let xx be the number of roses . then the number of birches is 24 − x 24 − x , and the number of boys is 3 × ( 24 − x ) 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 x + 216 − 9 x = 72 216 − 72 = 8 x 216 − 72 = 8 x 1448 = x 1448 = x x = 18 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . answer : a | physics |
math_qa__8bbCkIbNX7pF4FAK | Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is this student’s weekly allowance? Pick: A) $ 1.20 B) $ 1.50 C) $ 1.80 D) $ 2.00 E) $ 2.50 | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 * 0.4</gadget>
<output>6</output>
<gadget id="calculator">6 / 4</gadget>
<output>3/2 = around 1.5</output>
<result>B</result> | B | 1.5 | Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is this student’s weekly allowance? | {
"A": "$ 1.20",
"B": "$ 1.50",
"C": "$ 1.80",
"D": "$ 2.00",
"E": "$ 2.50"
} | divide(multiply(multiply(3, 5), 0.40), const_4) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_4)| | "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 40 cents ( 4 / 15 ) x = 40 x = $ 1.50 the answer is b ." | general |
math_qa__UWySHXY0m8C5L2PO | Robert left from a Pvt Company. Management hold his salary Rs. 15000/- for one month. Earlier Robert earned a performance incentive Rs. 7280/- from company. But Robert forgot that. After one month Robert asked his salary and accountant gives Rs.18500/- to him. What is the bonus amount given to Robert?
Choose the correct choice from the following options.
A) 9500 B) 12500 C) 10780 D) 10500 E) 8600 | <gadget id="calculator">18_500 - 7_280</gadget>
<output>11_220</output>
<result>C</result> | C | 10,780 | Robert left from a Pvt Company. Management hold his salary Rs. 15000/- for one month. Earlier Robert earned a performance incentive Rs. 7280/- from company. But Robert forgot that. After one month Robert asked his salary and accountant gives Rs.18500/- to him. What is the bonus amount given to Robert? | {
"A": "9500",
"B": "12500",
"C": "10780",
"D": "10500",
"E": "8600"
} | subtract(18500, 7280) | subtract(n2,n1) | total salary = rs . 15000 / - incentive earned earlier = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - bonus = 18500 - 7720 = 10780 / - answer is c | general |
math_qa__PUQ0xFJzKtmP3zFR | if A and B run on a circular path in opposite directions of constant speeds with different velocities from P and Q. First time they meet 800 mts away from P and second time they meet 700 mts away from P, what is the lenght of the circular path.
Select the correct option
A) 2300 mtrs
B) 2400 mtrs
C) 2500 mtrs
D) 2600 mtrs
E) 2700 mtrs | <gadget id="calculator">800 * 2</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 + 700</gadget>
<output>2_300</output>
<result>A</result> | A | 2,300 | if A and B run on a circular path in opposite directions of constant speeds with different velocities from P and Q. First time they meet 800 mts away from P and second time they meet 700 mts away from P, what is the lenght of the circular path. | {
"A": "2300 mtrs",
"B": "2400 mtrs",
"C": "2500 mtrs",
"D": "2600 mtrs",
"E": "2700 mtrs"
} | add(multiply(800, const_2), 700) | multiply(n0,const_2)|add(n1,#0) | 800 + 800 + 700 = 2300 mtrs answer : a | physics |
math_qa__WJSPeLP9Pyuw9sXS | The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year?
Options: A) 1 % B) 1.1 % C) 9.1 % D) 10 % E) 10.8 % | <gadget id="calculator">11 * 100</gadget>
<output>1_100</output>
<gadget id="calculator">11 + 100</gadget>
<output>111</output>
<gadget id="calculator">1_100 / 111</gadget>
<output>1_100/111 = around 9.90991</output>
<result>D</result> | D | 10 | The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year? | {
"A": "1 %",
"B": "1.1 %",
"C": "9.1 %",
"D": "10 %",
"E": "10.8 %"
} | divide(multiply(11, const_100), add(11, const_100)) | add(n1,const_100)|multiply(n1,const_100)|divide(#1,#0)| | "let us suppose the interest rate last year is x , this year the interest rate is increased by 10 % . hence this year interest rate would be 1.1 * x . setting up the equation - - - - - > 11 = 1.1 * x x = 10 % answer : d" | gain |
math_qa__fRkbjwF9f5u01g6R | The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 squares feet, how much will it cost to paint outside of a cube having 8 feet each side? Select: A) rs . 692 B) rs . 768 C) rs . 876 D) rs . 972 E) none | <gadget id="calculator">6 * (8 ** 2)</gadget>
<output>384</output>
<gadget id="calculator">384 / 16</gadget>
<output>24</output>
<gadget id="calculator">24 * 36.5</gadget>
<output>876</output>
<result>C</result> | C | 876 | The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 squares feet, how much will it cost to paint outside of a cube having 8 feet each side? | {
"A": "rs . 692",
"B": "rs . 768",
"C": "rs . 876",
"D": "rs . 972",
"E": "none"
} | multiply(divide(surface_cube(8), 16), 36.50) | surface_cube(n3)|divide(#0,n2)|multiply(n0,#1)| | "solution surface area of the cube = ( 6 × 82 ) sq . ft = 384 sq . ft . quantity of paint required = ( 384 / 16 ) kg ‹ = › 24 kg . cost of painting = rs . ( 36.50 × 24 ) = rs . 876 . answer c" | geometry |
math_qa__Qy916BRB3c4TcK0O | Express a speed of 84 kmph in meters per second? Choose the correct choice:
A) 13.33 mps B) 23.33 mps C) 33.33 mps D) 25.33 mps E) 43.33 mps | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 84</gadget>
<output>70/3 = around 23.333333</output>
<result>B</result> | B | 23.33 | Express a speed of 84 kmph in meters per second? | {
"A": "13.33 mps",
"B": "23.33 mps",
"C": "33.33 mps",
"D": "25.33 mps",
"E": "43.33 mps"
} | multiply(const_0_2778, 84) | multiply(n0,const_0_2778)| | "84 * 5 / 18 = 23.33 mps answer : b" | physics |
math_qa__7WjIwPmU6I6gX8Ww | A shopkeeper sells 300 metres of cloth for Rs. 9000 at a loss of Rs.6 per metre. Find his cost price for one metre of cloth? Choose the correct choice from the following: A) s . 59 B) s . 58 C) s . 36 D) s . 46 E) s . 13 | <gadget id="calculator">9_000 / 300</gadget>
<output>30</output>
<gadget id="calculator">30 + 6</gadget>
<output>36</output>
<result>C</result> | C | 36 | A shopkeeper sells 300 metres of cloth for Rs. 9000 at a loss of Rs.6 per metre. Find his cost price for one metre of cloth? | {
"A": "s . 59",
"B": "s . 58",
"C": "s . 36",
"D": "s . 46",
"E": "s . 13"
} | add(divide(9000, 300), 6) | divide(n1,n0)|add(n2,#0)| | "sp per metre = 9000 / 300 = rs . 30 loss per metre = rs . 6 cp per metre = 30 + 6 = rs . 36 answer : c" | gain |
math_qa__dnw5OlbURPOHhs2J | The H.C.F. of two numbers is 42 and the other two factors of their L.C.M. are 12 and 14. The larger of the two numbers is:
Select the correct option.
A) 588 B) 642 C) 567 D) 344 E) 789 | <gadget id="calculator">42 * 14</gadget>
<output>588</output>
<result>A</result> | A | 588 | The H.C.F. of two numbers is 42 and the other two factors of their L.C.M. are 12 and 14. The larger of the two numbers is: | {
"A": "588",
"B": "642",
"C": "567",
"D": "344",
"E": "789"
} | multiply(42, 14) | multiply(n0,n2)| | "explanation : clearly , the numbers are ( 42 x 12 ) and ( 42 x 14 ) . { \ color { blue } \ therefore } larger number = ( 42 x 14 ) = 588 . answer : a ) 588" | other |
math_qa__qchUX8pN3K5XO839 | How much is 75% of 40 is greater than 4/5 of 25? Choose the correct choice from the following answers:
A) 22
B) 67
C) 10
D) 12
E) 66 | <gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">40 * (3/4)</gadget>
<output>30</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 25</gadget>
<output>20</output>
<gadget id="calculator">30 - 20</gadget>
<output>10</output>
<result>C</result> | C | 10 | How much is 75% of 40 is greater than 4/5 of 25? | {
"A": "22",
"B": "67",
"C": "10",
"D": "12",
"E": "66"
} | subtract(multiply(40, divide(75, const_100)), multiply(divide(4, 5), 25)) | divide(n0,const_100)|divide(n2,n3)|multiply(n1,#0)|multiply(n4,#1)|subtract(#2,#3)| | "( 75 / 100 ) * 40 – ( 4 / 5 ) * 25 = 10 answer : c" | general |
math_qa__HOJjgCNNBBVcOfw8 | A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number? Choose the correct answer.
A) 12
B) 29
C) 27
D) 15
E) 99 | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">105 - 15</gadget>
<output>90</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">90 / 6</gadget>
<output>15</output>
<result>D</result> | D | 15 | A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number? | {
"A": "12",
"B": "29",
"C": "27",
"D": "15",
"E": "99"
} | divide(subtract(105, multiply(const_3, 5)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 105 6 x + 15 = 105 6 x = 90 x = 15 answer : d" | general |
math_qa__K9JkRCKctqSpoXuD | 10 play kabadi, 35 play kho kho only, 5 play both gmaes. Then how many in total?
Choices: A) 30 B) 35 C) 38 D) 40 E) 45 | <gadget id="calculator">35 + 5</gadget>
<output>40</output>
<gadget id="calculator">10 + 40</gadget>
<output>50</output>
<gadget id="calculator">50 - 5</gadget>
<output>45</output>
<result>E</result> | E | 45 | 10 play kabadi, 35 play kho kho only, 5 play both gmaes. Then how many in total? | {
"A": "30",
"B": "35",
"C": "38",
"D": "40",
"E": "45"
} | subtract(add(10, add(35, 5)), 5) | add(n1,n2)|add(n0,#0)|subtract(#1,n2)| | "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 35 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 35 + 5 = 40 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 40 - 5 = 45 answer : e" | general |
math_qa__FonsOL6oHBXzFYdH | If the average of 12x and 8y is greater than 200, and x is twice y, what is the least integer value of x ?
Choose the correct option
A) 20
B) 30
C) 40
D) 25
E) 35 | <gadget id="calculator">12 * 2</gadget>
<output>24</output>
<result>D</result> | D | 25 | If the average of 12x and 8y is greater than 200, and x is twice y, what is the least integer value of x ? | {
"A": "20",
"B": "30",
"C": "40",
"D": "25",
"E": "35"
} | multiply(12, const_2) | multiply(n0,const_2) | substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 12 x and 4 x is greater than 200 . average of 12 x and 4 x is 8 x . so , 8 x > 200 x > 25 answer : d | general |
math_qa__iKcJa6Iz4gqzcJbk | I sold a book at a profit of 10%. Had I sold it for $150 more, 15% would have been gained. Find the cost price? Choose one:
A) $ 2000
B) $ 2500
C) $ 3000
D) $ 3120
E) $ 1540 | <gadget id="calculator">150 * 10</gadget>
<output>1_500</output>
<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">1_500 / 5</gadget>
<output>300</output>
<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 10</gadget>
<output>3_000</output>
<result>C</result> | C | 3,000 | I sold a book at a profit of 10%. Had I sold it for $150 more, 15% would have been gained. Find the cost price? | {
"A": "$ 2000",
"B": "$ 2500",
"C": "$ 3000",
"D": "$ 3120",
"E": "$ 1540"
} | divide(multiply(divide(multiply(150, 10), subtract(15, 10)), const_100), 10) | multiply(n0,n1)|subtract(n2,n0)|divide(#0,#1)|multiply(#2,const_100)|divide(#3,n0)| | "115 % of cost - 110 % of cost = $ 150 5 % of cost = $ 150 cost = 150 * 100 / 5 = $ 3000 answer is c" | gain |
math_qa__3FD0RhbsFNTZnlIM | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers? Choose the correct choice:
A) 26
B) 27
C) 28
D) 29
E) 30 | <gadget id="calculator">24 * 8</gadget>
<output>192</output>
<gadget id="calculator">192 / 7</gadget>
<output>192/7 = around 27.428571</output>
<gadget id="calculator">floor(192/7)</gadget>
<output>27</output>
<result>B</result> | B | 27 | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers? | {
"A": "26",
"B": "27",
"C": "28",
"D": "29",
"E": "30"
} | floor(divide(multiply(24, 8), 7)) | multiply(n1,n2)|divide(#0,n0)|floor(#1) | 8 / 7 * 24 = 27.4 the answer is b . | general |
math_qa__fnNAWY2tosU7felQ | add 8% of 24 and 10% of 40. Answers
A) 9.5 B) 10.5 C) 5.5 D) 5.9 E) 8.5 | <gadget id="calculator">8 * 24</gadget>
<output>192</output>
<gadget id="calculator">192 / 100</gadget>
<output>48/25 = around 1.92</output>
<gadget id="calculator">10 * 40</gadget>
<output>400</output>
<gadget id="calculator">400 / 100</gadget>
<output>4</output>
<gadget id="calculator">(48/25) + 4</gadget>
<output>148/25 = around 5.92</output>
<result>D</result> | D | 5.9 | add 8% of 24 and 10% of 40. | {
"A": "9.5",
"B": "10.5",
"C": "5.5",
"D": "5.9",
"E": "8.5"
} | add(divide(multiply(8, 24), const_100), divide(multiply(10, 40), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)| | "8 % of 24 + 10 % of 40 24 * 8 / 100 + 40 * 10 / 100 1.9 + 4 = 5.9 answer d" | gain |
math_qa__rTzzNEgm8SMcA4cj | In a certificate by mistake a candidate gave his height as 20% more than actual height. In the interview panel, he clarified that his height was 5 feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height? Choose one:
A) 13 B) 20 C) 30 D) 43 E) 50 | <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">20 + (1/2)</gadget>
<output>41/2 = around 20.5</output>
<gadget id="calculator">(41/2) - 5</gadget>
<output>31/2 = around 15.5</output>
<gadget id="calculator">100 + (31/2)</gadget>
<output>231/2 = around 115.5</output>
<gadget id="calculator">(31/2) / (231/2)</gadget>
<output>31/231 = around 0.134199</output>
<gadget id="calculator">(31/231) * 100</gadget>
<output>3_100/231 = around 13.419913</output>
<result>A</result> | A | 13 | In a certificate by mistake a candidate gave his height as 20% more than actual height. In the interview panel, he clarified that his height was 5 feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height? | {
"A": "13",
"B": "20",
"C": "30",
"D": "43",
"E": "50"
} | multiply(divide(subtract(add(20, add(const_0_25, const_0_25)), 5), add(const_100, subtract(add(20, add(const_0_25, const_0_25)), 5))), const_100) | add(const_0_25,const_0_25)|add(n0,#0)|subtract(#1,n1)|add(#2,const_100)|divide(#2,#3)|multiply(#4,const_100)| | "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.20 - 1 ) = 13 a" | gain |
math_qa__e3DfwnT9LdA56z5g | One pack of cake mix is being stirred before being poured into two separate baking trays. The first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first. If the total number of cups poured is 500, how many cups of batter does the second tray hold? Choose the correct choice:
A) 250
B) 260
C) 500
D) 280
E) 240 | <gadget id="calculator">500 - 20</gadget>
<output>480</output>
<gadget id="calculator">480 / 2</gadget>
<output>240</output>
<result>E</result> | E | 240 | One pack of cake mix is being stirred before being poured into two separate baking trays. The first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first. If the total number of cups poured is 500, how many cups of batter does the second tray hold? | {
"A": "250",
"B": "260",
"C": "500",
"D": "280",
"E": "240"
} | divide(subtract(500, 20), const_2) | subtract(n1,n0)|divide(#0,const_2) | tray one as t 1 and tray two as t 2 . t 2 = t 1 - 20 cups as equation a . t 1 + t 2 = 500 cups in total as equation b . substitute equation a into equation b , resulting in t 1 + ( t 1 - 20 ) = 500 transpose like terms , 2 * t 1 = 500 + 20 ( 2 * t 1 ) / 2 = 520 / 2 t 1 = 260 , thus t 2 is t 1 less 20 cups , which is 240 cups . answer is e . | general |
math_qa__PYHMiioiZnzeo7vo | A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 14 multiples of 14, how many multiples of 7 are there in Q? Choose one.
A) 26
B) 27
C) 28
D) 29
E) 30 | <gadget id="calculator">14 * 2</gadget>
<output>28</output>
<gadget id="calculator">28 - 1</gadget>
<output>27</output>
<result>B</result> | B | 27 | A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 14 multiples of 14, how many multiples of 7 are there in Q? | {
"A": "26",
"B": "27",
"C": "28",
"D": "29",
"E": "30"
} | subtract(multiply(14, const_2), const_1) | multiply(n1,const_2)|subtract(#0,const_1)| | "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 14 + 13 = 27 . the answer is b ." | physics |
math_qa__TZ5m4z0sllC1TBs7 | The length of a train and that of a platform are equal. If with a speed of 180 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Choose the correct choice from the following answers:
A) 1500 B) 266 C) 299 D) 750 E) 261 | <gadget id="calculator">180 * 1_000</gadget>
<output>180_000</output>
<gadget id="calculator">60 / 1</gadget>
<output>60</output>
<gadget id="calculator">180_000 / 60</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 2</gadget>
<output>1_500</output>
<result>A</result> | A | 1,500 | The length of a train and that of a platform are equal. If with a speed of 180 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? | {
"A": "1500",
"B": "266",
"C": "299",
"D": "750",
"E": "261"
} | divide(divide(multiply(180, const_1000), divide(const_60, const_1)), const_2) | divide(const_60,const_1)|multiply(n0,const_1000)|divide(#1,#0)|divide(#2,const_2)| | "speed = [ 180 * 5 / 18 ] m / sec = 50 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 50 = > x = 50 * 60 / 2 = 1500 answer : a" | physics |
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