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100B
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stringlengths 6
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stringlengths 7
6.48k
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stringlengths 8
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math_qa__ZvSmw1QvoVEE3AL7 | The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? Choose the correct choice from the following options: A) 39 % B) 40 % C) 41 % D) 42 % E) 43 % | <gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>B</result> | B | 40 | The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? | {
"A": "39 %",
"B": "40 %",
"C": "41 %",
"D": "42 %",
"E": "43 %"
} | multiply(divide(add(1, 3), add(add(4, 2), add(1, 3))), const_100) | add(n1,n3)|add(n0,n2)|add(#1,#0)|divide(#0,#2)|multiply(#3,const_100) | let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 10 + 3 v / 10 = 4 v / 10 = 2 v / 5 . the concentration of alcohol is 2 / 5 = 40 % the answer is b . | general |
math_qa__Ko365oBbZcTyJoRF | At what rate percent on simple interest will Rs.750 amount to Rs.900 in 4 years?
Pick one:
A) 6 % B) 2 % C) 4 % D) 5 % E) 3 % | <gadget id="calculator">900 - 750</gadget>
<output>150</output>
<gadget id="calculator">150 / 750</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) / 4</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>D</result> | D | 5 | At what rate percent on simple interest will Rs.750 amount to Rs.900 in 4 years? | {
"A": "6 %",
"B": "2 %",
"C": "4 %",
"D": "5 %",
"E": "3 %"
} | multiply(divide(divide(subtract(900, 750), 750), 4), const_100) | subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)| | "150 = ( 750 * 4 * r ) / 100 r = 5 % answer : d" | gain |
math_qa__9NodZIoZz64lFnT5 | If m is not equal to zero, and m+1/m = 1, then what is the value of m^4 + (1/m)^4? Choose the correct choice
A) - 5 B) - 4 C) - 3 D) - 2 E) - 1 | <gadget id="calculator">1 - 2</gadget>
<output>-1</output>
<result>E</result> | E | -1 | If m is not equal to zero, and m+1/m = 1, then what is the value of m^4 + (1/m)^4? | {
"A": "- 5",
"B": "- 4",
"C": "- 3",
"D": "- 2",
"E": "- 1"
} | subtract(1, const_2) | subtract(n0,const_2) | m + 1 / m = 1 we square both sides so we have m ^ 2 + 1 / m ^ 2 + 2 = 1 or m ^ 2 + 1 / m ^ 2 = - 1 squaring again we have m ^ 4 + 1 / m ^ 4 + 2 = 1 or m ^ 4 + 1 / m ^ 4 = - 1 answer = - 1 ( e ) | general |
math_qa__SsZlNQr1cfDpxGhX | The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 539, Krishan has ?
Choose one:
A) s . 2890 B) s . 2330 C) s . 1190 D) s . 1620 E) s . 3179 | <gadget id="calculator">539 / 7</gadget>
<output>77</output>
<gadget id="calculator">77 * 17</gadget>
<output>1_309</output>
<gadget id="calculator">1_309 / 7</gadget>
<output>187</output>
<gadget id="calculator">187 * 17</gadget>
<output>3_179</output>
<result>E</result> | E | 3,179 | The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 539, Krishan has ? | {
"A": "s . 2890",
"B": "s . 2330",
"C": "s . 1190",
"D": "s . 1620",
"E": "s . 3179"
} | multiply(divide(multiply(divide(539, 7), 17), 7), 17) | divide(n4,n0)|multiply(n1,#0)|divide(#1,n0)|multiply(n1,#2)| | "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 539 : n & there n = 289 x 539 / 49 = rs . 3179 answer : e" | other |
math_qa__y51gOvOUBevBAdHK | The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of Choices.
A) 33
B) 40
C) 99
D) 28
E) 72 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">(4/5) * 75</gadget>
<output>60</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<result>B</result> | B | 40 | The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of | {
"A": "33",
"B": "40",
"C": "99",
"D": "28",
"E": "72"
} | subtract(const_100, multiply(divide(subtract(const_100, 20), const_100), subtract(const_100, 25))) | subtract(const_100,n1)|subtract(const_100,n0)|divide(#0,const_100)|multiply(#2,#1)|subtract(const_100,#3)| | "explanation : let the original price of the cycle be 100 . after the first reduction the price will be 75 . this new price is then reduced by 20 % = 0.8 x 75 = 60 60 represents a reduction of 40 percent on the original . answer : b ) 40 %" | general |
math_qa__Yc9yFKi2HP8rD4AV | Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3960. What is the difference between Rohan’s and Sudhir’s share in the profit? Choose the correct answer:
A) s . 345 B) s . 350 C) s . 352 D) s . 360 E) s . 368 | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">12_000 * (3/4)</gadget>
<output>9_000</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">9_000 * (2/3)</gadget>
<output>6_000</output>
<gadget id="calculator">9_000 - 6_000</gadget>
<output>3_000</output>
<gadget id="calculator">18_000 + 9_000</gadget>
<output>27_000</output>
<gadget id="calculator">27_000 + 6_000</gadget>
<output>33_000</output>
<gadget id="calculator">3_960 / 33_000</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">3_000 * (3/25)</gadget>
<output>360</output>
<result>D</result> | D | 360 | Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3960. What is the difference between Rohan’s and Sudhir’s share in the profit? | {
"A": "s . 345",
"B": "s . 350",
"C": "s . 352",
"D": "s . 360",
"E": "s . 368"
} | multiply(subtract(multiply(12000, divide(subtract(multiply(3, 4), 3), multiply(3, 4))), multiply(9000, divide(subtract(multiply(3, 4), 4), multiply(3, 4)))), divide(3960, add(add(18000, multiply(12000, divide(subtract(multiply(3, 4), 3), multiply(3, 4)))), multiply(9000, divide(subtract(multiply(3, 4), 4), multiply(3, 4)))))) | multiply(n1,n2)|subtract(#0,n1)|subtract(#0,n2)|divide(#1,#0)|divide(#2,#0)|multiply(n3,#3)|multiply(n4,#4)|add(n0,#5)|subtract(#5,#6)|add(#7,#6)|divide(n5,#9)|multiply(#10,#8)| | "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3960 × 1 / 11 = rs . 360 . d" | gain |
math_qa__tT7bdnSAFz4LgeBO | If 20% of a certain number is 60, then what is 80% of that number? Options:
A) 220
B) 210
C) 240
D) 250
E) 260 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">60 / (1/5)</gadget>
<output>300</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">300 * (4/5)</gadget>
<output>240</output>
<result>C</result> | C | 240 | If 20% of a certain number is 60, then what is 80% of that number? | {
"A": "220",
"B": "210",
"C": "240",
"D": "250",
"E": "260"
} | multiply(divide(60, divide(20, const_100)), divide(80, const_100)) | divide(n0,const_100)|divide(n2,const_100)|divide(n1,#0)|multiply(#2,#1)| | "explanation : 20 % = 20 * 3 = 60 80 % = 80 * 3 = 240 answer : option c" | gain |
math_qa__9DtDczXsgpetaVmQ | A customer went to a shop and paid a total of $30, out of which $1.28 was for sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items? Choices:
A) $ 9.84
B) $ 10.68
C) $ 11.26
D) $ 12.72
E) $ 13.54 | <gadget id="calculator">30 - 1.28</gadget>
<output>28.72</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">28.72 - 16</gadget>
<output>12.72</output>
<result>D</result> | D | 12.72 | A customer went to a shop and paid a total of $30, out of which $1.28 was for sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items? | {
"A": "$ 9.84",
"B": "$ 10.68",
"C": "$ 11.26",
"D": "$ 12.72",
"E": "$ 13.54"
} | subtract(subtract(30, 1.28), multiply(8, const_2)) | multiply(n2,const_2)|subtract(n0,n1)|subtract(#1,#0) | the total cost was $ 30 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 30 - $ 16 - $ 1.28 = $ 12.72 the answer is d . | gain |
math_qa__FhP46vamjeEqa9YJ | If a number p is prime, and 2p+5= q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? Options
A) 1
B) 3
C) 5
D) 7
E) 9 | <gadget id="calculator">166 + 1</gadget>
<output>167</output>
<gadget id="calculator">167 - 5</gadget>
<output>162</output>
<gadget id="calculator">162 / 2</gadget>
<output>81</output>
<gadget id="calculator">81 - 1</gadget>
<output>80</output>
<gadget id="calculator">81 - 80</gadget>
<output>1</output>
<result>A</result> | A | 1 | If a number p is prime, and 2p+5= q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q? | {
"A": "1",
"B": "3",
"C": "5",
"D": "7",
"E": "9"
} | subtract(divide(subtract(add(166, 1), 5), 2), subtract(divide(subtract(add(166, 1), 5), 2), 1)) | add(n2,n4)|subtract(#0,n1)|divide(#1,n0)|subtract(#2,n2)|subtract(#2,#3) | 1 / 7 = 014285 . . . ( a repeating pattern one digit long ) a | general |
math_qa__tSdSxvwEQokoCdK6 | Walking at 25% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
Choose the correct choice from the following answers:
A) 8
B) 16
C) 42
D) 48
E) 54 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / (1/4)</gadget>
<output>4</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>A</result> | A | 8 | Walking at 25% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance? | {
"A": "8",
"B": "16",
"C": "42",
"D": "48",
"E": "54"
} | divide(24, subtract(divide(const_1, divide(25, const_100)), const_1)) | divide(n0,const_100)|divide(const_1,#0)|subtract(#1,const_1)|divide(n1,#2)| | "speed is inversly proprtional to time walking at 25 % of speed meand 1 / 4 s takes 4 t . it takes 24 minutes extra to cover the distance . then 4 t = t + 24 3 t = 24 t = 8 . option a is correct" | physics |
math_qa__wfwyyNuGeHJcUyD9 | father is aged 3 times more than his son ronit . after 8 years , he would be two and half times if ronit ' s age . after further 8 years , how many times would he be of ronit ' s age ? Choose the correct choice.
A) 2 times B) 2.5 times C) 3 times D) 3.8 times E) 4 times | <gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">8 + 8</gadget>
<output>16</output>
<gadget id="calculator">32 + 16</gadget>
<output>48</output>
<gadget id="calculator">8 + 16</gadget>
<output>24</output>
<gadget id="calculator">48 / 24</gadget>
<output>2</output>
<result>A</result> | A | 2 | father is aged 3 times more than his son ronit . after 8 years , he would be two and half times if ronit ' s age . after further 8 years , how many times would he be of ronit ' s age ? | {
"A": "2 times",
"B": "2.5 times",
"C": "3 times",
"D": "3.8 times",
"E": "4 times"
} | divide(add(multiply(const_4, 8), add(8, 8)), add(8, add(8, 8))) | add(n1,n1)|multiply(n1,const_4)|add(#0,#1)|add(n1,#0)|divide(#2,#3) | ronit ' s present age be x years . then , father ' s present age = ( x + 3 x ) years = 4 x years therefore ( 4 x + 8 ) = 5 / 2 ( x + 8 ) 8 x + 16 = 5 x + 40 3 x = 24 , x = 8 , ratio = ( 4 x + 16 ) / ( x + 16 ) = 48 / 24 = 2 , correct answer ( a ) | general |
math_qa__utVWfkm0plX3Gtpg | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 54° is? Choose the correct choice from the following answers.
A) 52.6 B) 52.9 C) 67.9 D) 52.1 E) 52.2 | <gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">144 * (22/7)</gadget>
<output>3_168/7 = around 452.571429</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">54 / 360</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3_168/7) * (3/20)</gadget>
<output>2_376/35 = around 67.885714</output>
<result>C</result> | C | 67.9 | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 54° is? | {
"A": "52.6",
"B": "52.9",
"C": "67.9",
"D": "52.1",
"E": "52.2"
} | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(54, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7)| | "54 / 360 * 22 / 7 * 12 * 12 = 67.9 m 2 answer : c" | geometry |
math_qa__Mswjd2maXYDQQSUd | what is the greatest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ? Select the correct option:
A) 9800 B) 9600 C) 9400 D) 9500 E) 9200 | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">lcm(15, 25)</gadget>
<output>75</output>
<gadget id="calculator">lcm(75, 40)</gadget>
<output>600</output>
<gadget id="calculator">lcm(600, 75)</gadget>
<output>600</output>
<gadget id="calculator">10_000 / 600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">floor(50/3)</gadget>
<output>16</output>
<gadget id="calculator">16 * 600</gadget>
<output>9_600</output>
<result>B</result> | B | 9,600 | what is the greatest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ? | {
"A": "9800",
"B": "9600",
"C": "9400",
"D": "9500",
"E": "9200"
} | multiply(floor(divide(multiply(const_100, const_100), lcm(lcm(lcm(15, 25), 40), 75))), lcm(lcm(lcm(15, 25), 40), 75)) | lcm(n1,n2)|multiply(const_100,const_100)|lcm(n3,#0)|lcm(n4,#2)|divide(#1,#3)|floor(#4)|multiply(#5,#3) | greatest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , greatest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : b | general |
math_qa__uphdptgLjMS42XRq | A one-foot stick is marked in 1/3 and 1/4 portion. How many total markings will there be, including the end points? Choose the most appropriate option: A) 8 B) 9 C) 7 D) 6 E) 5 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<result>C</result> | C | 7 | A one-foot stick is marked in 1/3 and 1/4 portion. How many total markings will there be, including the end points? | {
"A": "8",
"B": "9",
"C": "7",
"D": "6",
"E": "5"
} | add(3, 4) | add(n1,n3)| | "lcm of 12 = 12 1 / 3 marking are ( table of 4 ) 0 . . . . . . 4 . . . . . . 8 . . . . . 12 ( total = 4 ) 1 / 4 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 ( total = 5 ) overlapping markings are 0 . . . . . . . . 12 ( total = 2 ) total markings = 4 + 5 - 2 = 7 answer = c" | general |
math_qa__hNOnYdzH8sIQAlOf | A company has a hierarchical system where for every 10 workers, there is one team lead, and for every 3 teams leads, there is one supervisor. If the company has 13 supervisors, how many workers does it have? Choose one:
A) 140 B) 321 C) 390 D) 500 E) 130 | <gadget id="calculator">13 * 3</gadget>
<output>39</output>
<gadget id="calculator">39 * 10</gadget>
<output>390</output>
<result>C</result> | C | 390 | A company has a hierarchical system where for every 10 workers, there is one team lead, and for every 3 teams leads, there is one supervisor. If the company has 13 supervisors, how many workers does it have? | {
"A": "140",
"B": "321",
"C": "390",
"D": "500",
"E": "130"
} | multiply(multiply(13, 3), 10) | multiply(n1,n2)|multiply(n0,#0) | some students may initially answer 130 to this question , especially if answering similar problems . however , that would be incorrect , as this is not a straight - forward ratio of 1 : 3 : 10 . the ratio of supervisors to team leads is 1 : 3 , and the ratio of team leads to workers is 1 : 10 . therefore , the ratio of supervisors to workers is 1 : 30 . therefore , 13 * 30 = 390 answer : c ) | physics |
math_qa__hlSL3qRZeVftMJnX | If a*b denotes the greatest common divisor of a and b, then ((20*16)*(18*24)) = ? Answers.
A) 24
B) 12
C) 6
D) 4
E) 2 | <gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">6 / 3</gadget>
<output>2</output>
<result>E</result> | E | 2 | If a*b denotes the greatest common divisor of a and b, then ((20*16)*(18*24)) = ? | {
"A": "24",
"B": "12",
"C": "6",
"D": "4",
"E": "2"
} | divide(divide(18, const_3), const_3) | divide(n2,const_3)|divide(#0,const_3)| | "the greatest common divisor of 20 and 16 is 4 . hence 20 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 20 * 16 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ." | general |
math_qa__mpbfdgoJHyeoYgAs | How many quarters are equal to 2 dollars? Options: A) 1 B) 8 C) 12 D) 9 E) 7 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<result>B</result> | B | 8 | How many quarters are equal to 2 dollars? | {
"A": "1",
"B": "8",
"C": "12",
"D": "9",
"E": "7"
} | multiply(2, const_4) | multiply(n0,const_4)| | b . 8 quarters | general |
math_qa__OVb3IPu5FJ0yEuQL | David obtained 86, 85, 82, 87 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? Pick: A) 75 B) 276 C) 87 D) 85 E) 11 | <gadget id="calculator">86 + 85</gadget>
<output>171</output>
<gadget id="calculator">171 + 82</gadget>
<output>253</output>
<gadget id="calculator">253 + 87</gadget>
<output>340</output>
<gadget id="calculator">340 + 85</gadget>
<output>425</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">425 / 5</gadget>
<output>85</output>
<result>D</result> | D | 85 | David obtained 86, 85, 82, 87 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? | {
"A": "75",
"B": "276",
"C": "87",
"D": "85",
"E": "11"
} | divide(add(add(add(add(86, 85), 82), 87), 85), add(const_2, const_3)) | add(n0,n1)|add(const_2,const_3)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "explanation : average = ( 86 + 85 + 82 + 87 + 85 ) / 5 = 425 / 5 = 85 . answer : d" | general |
math_qa__iDOBBylna6j9xqgg | A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 50$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost? Choose the most appropriate option.
A) 39.55 $ B) 40.63 $ C) 41.63 $ D) 42.15 $ E) 43.15 $ | <gadget id="calculator">7 + 15</gadget>
<output>22</output>
<gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">(11/50) + 1</gadget>
<output>61/50 = around 1.22</output>
<gadget id="calculator">50 / (61/50)</gadget>
<output>2_500/61 = around 40.983607</output>
<result>B</result> | B | 40.63 | A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 50$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost? | {
"A": "39.55 $",
"B": "40.63 $",
"C": "41.63 $",
"D": "42.15 $",
"E": "43.15 $"
} | divide(50, add(divide(add(7, 15), const_100), const_1)) | add(n1,n2)|divide(#0,const_100)|add(#1,const_1)|divide(n0,#2)| | "let x be the amount the most their food can cost . x + 0.07 x + 0 . 15 x = 50 solving for x , x = 40.98 $ , this is the maximum amount that can be used for food . hence 40.63 $ is the maximum value less than 40.98 $ hence option b" | general |
math_qa__AjH6bsqtYvXcQAk8 | The sum of present age of Abe and the age before 7 years is 37. Find the present age of Abe. What will be his age after 7 years? Select:
A) 25 B) 26 C) 27 D) 28 E) 29 | <gadget id="calculator">37 + 7</gadget>
<output>44</output>
<gadget id="calculator">44 / 2</gadget>
<output>22</output>
<gadget id="calculator">22 + 7</gadget>
<output>29</output>
<result>E</result> | E | 29 | The sum of present age of Abe and the age before 7 years is 37. Find the present age of Abe. What will be his age after 7 years? | {
"A": "25",
"B": "26",
"C": "27",
"D": "28",
"E": "29"
} | add(divide(add(37, 7), const_2), 7) | add(n0,n1)|divide(#0,const_2)|add(n0,#1)| | "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 37 2 x - 7 = 37 2 x = 37 + 7 x = 44 / 2 x = 22 z = x + 7 = 22 + 7 = 29 answer : e" | general |
math_qa__Ln6W66QEuhe4d9l9 | A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price w of the machine? Choose one
A) 81 B) 100 C) 120 D) 135 E) 160 | <gadget id="calculator">90 * 20</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 100</gadget>
<output>18</output>
<gadget id="calculator">90 + 18</gadget>
<output>108</output>
<gadget id="calculator">108 * 100</gadget>
<output>10_800</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">10_800 / 90</gadget>
<output>120</output>
<result>C</result> | C | 120 | A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price w of the machine? | {
"A": "81",
"B": "100",
"C": "120",
"D": "135",
"E": "160"
} | divide(multiply(add(90, divide(multiply(90, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10)) | multiply(n0,n2)|multiply(const_3,const_3)|divide(#0,const_100)|multiply(n1,#1)|add(n0,#2)|multiply(#4,const_100)|divide(#5,#3)| | "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price w = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c" | gain |
math_qa__Gc5x302G0XtCGRV0 | How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 12% solution? Choose the correct choice from the following answers.
A) 6.7 B) 2.3 C) 9.6 D) 12.5 E) 7.9 | <gadget id="calculator">12 - 10</gadget>
<output>2</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">1 - (3/25)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">2 / (22/25)</gadget>
<output>25/11 = around 2.272727</output>
<result>B</result> | B | 2.3 | How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 12% solution? | {
"A": "6.7",
"B": "2.3",
"C": "9.6",
"D": "12.5",
"E": "7.9"
} | divide(subtract(12, 10), subtract(const_1, divide(12, 100))) | divide(n2,n0)|subtract(n2,n1)|subtract(const_1,#0)|divide(#1,#2)| | "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 12 / 100 250 + 25 x = 300 + 3 x 22 x = 50 x = 2.3 answer is b" | general |
math_qa__7qt9h9A6qaaFjW7K | 350 is increased by 50%. Find the final number.
Choose the correct answer
A) 725
B) 625
C) 225
D) 525
E) 425 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">350 * (1/2)</gadget>
<output>175</output>
<gadget id="calculator">350 + 175</gadget>
<output>525</output>
<result>D</result> | D | 525 | 350 is increased by 50%. Find the final number. | {
"A": "725",
"B": "625",
"C": "225",
"D": "525",
"E": "425"
} | add(350, multiply(350, divide(50, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | explanation final number = initial number + 50 % ( original number ) = 350 + 50 % ( 350 ) = 350 + 175 = 525 . answer d | gain |
math_qa__ZHLnZ29Bnt3PcfCe | A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 2400. They completed the work in 3 days with the help of C. How much is to be paid to C?
Choose the correct answer:
A) s . 300
B) s . 600
C) s . 420
D) s . 400
E) s . 480 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/6) + (1/8)</gadget>
<output>7/24 = around 0.291667</output>
<gadget id="calculator">(1/3) - (7/24)</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">3 * (1/24)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 2_400</gadget>
<output>300</output>
<result>A</result> | A | 300 | A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 2400. They completed the work in 3 days with the help of C. How much is to be paid to C? | {
"A": "s . 300",
"B": "s . 600",
"C": "s . 420",
"D": "s . 400",
"E": "s . 480"
} | multiply(multiply(3, subtract(divide(const_1, 3), add(divide(const_1, 6), divide(const_1, 8)))), 2400) | divide(const_1,n3)|divide(const_1,n0)|divide(const_1,n1)|add(#1,#2)|subtract(#0,#3)|multiply(n3,#4)|multiply(n2,#5)| | "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 2400 × ( 1 / 8 ) = 300 answer : option a" | physics |
math_qa__ImDqKEJaSgkqAAq1 | Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 15% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate? Answers.
A) 19 % B) 21 % C) 23 % D) 25 % E) 27 % | <gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">4 * (3/20)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(9/20) + (3/5)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">(21/20) / 5</gadget>
<output>21/100 = around 0.21</output>
<gadget id="calculator">100 * (21/100)</gadget>
<output>21</output>
<result>B</result> | B | 21 | Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 15% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate? | {
"A": "19 %",
"B": "21 %",
"C": "23 %",
"D": "25 %",
"E": "27 %"
} | multiply(const_100, divide(add(divide(45, const_100), multiply(4, divide(15, const_100))), add(const_1, 4))) | add(n2,const_1)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#2)|add(#1,#3)|divide(#4,#0)|multiply(#5,const_100)| | "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 0.6 x = 1.05 x 1.05 x / 5 x = 0.21 the answer is b ." | gain |
math_qa__zO6ipcj3F1mNNWNz | PR is tangent to a circle at point P. Q is another point on circle such that PQ is diameter of circle and RQ cuts circle at M. if radius of circle is 4 units and PR=6units. find ratio of triangle PMR to PQR.
Choose the correct choice from the following answers:
A) 11 / 20
B) 3 / 5
C) 13 / 20
D) 18 / 25
E) 18 / 26 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">64 + 36</gadget>
<output>100</output>
<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">48 / 10</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 / 8</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">6 + (24/5) + (9/2)</gadget>
<output>153/10 = around 15.3</output>
<gadget id="calculator">8 + 6 + 10</gadget>
<output>24</output>
<gadget id="calculator">(153/10) / 24</gadget>
<output>51/80 = around 0.6375</output>
<result>C</result> | C | 0.65 | PR is tangent to a circle at point P. Q is another point on circle such that PQ is diameter of circle and RQ cuts circle at M. if radius of circle is 4 units and PR=6units. find ratio of triangle PMR to PQR. | {
"A": "11 / 20",
"B": "3 / 5",
"C": "13 / 20",
"D": "18 / 25",
"E": "18 / 26"
} | divide(triangle_perimeter(6, divide(multiply(multiply(4, const_2), 6), sqrt(add(power(multiply(4, const_2), const_2), power(6, const_2)))), divide(multiply(6, 6), multiply(4, const_2))), triangle_perimeter(multiply(4, const_2), 6, sqrt(add(power(multiply(4, const_2), const_2), power(6, const_2))))) | multiply(n0,const_2)|multiply(n1,n1)|power(n1,const_2)|divide(#1,#0)|multiply(n1,#0)|power(#0,const_2)|add(#5,#2)|sqrt(#6)|divide(#4,#7)|triangle_perimeter(n1,#0,#7)|triangle_perimeter(n1,#8,#3)|divide(#10,#9) | let pm = y qm = x mr = 10 - x in triangle pqm , pm ^ 2 + qm ^ 2 = pq ^ 2 = > x ^ 2 + y ^ 2 = 64 . . . . . ( 1 ) in triangle pmr , pm ^ 2 + mr ^ 2 = pr ^ 2 y ^ 2 + ( 10 - x ) ^ 2 = 36 . . . . . . ( 2 ) solving for x and y x = 6.4 y = 4.8 taking permineter of triangle pqr = 24 perimeter of triangle pmr = 14.4 take ratio 14.4 / 24 = 0.6 answer : c | geometry |
math_qa__mG0XZuvAYC94aCrW | The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 17. The larger of the two numbers is: Choose the correct choice from the following answers.
A) 276
B) 299
C) 391
D) 345
E) 355 | <gadget id="calculator">23 * 17</gadget>
<output>391</output>
<result>C</result> | C | 391 | The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 17. The larger of the two numbers is: | {
"A": "276",
"B": "299",
"C": "391",
"D": "345",
"E": "355"
} | multiply(23, 17) | multiply(n0,n2)| | "clearly , the numbers are ( 23 x 13 ) and ( 23 x 17 ) . larger number = ( 23 x 17 ) = 391 . answer : option c" | other |
math_qa__hLCQCoq0PtfTRKZs | A rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug? Choose the most appropriate option: A) a . 3 / 16 B) 1 / 4 C) c . 1 / 2 D) 25 / 32 E) 7 / 8 | <gadget id="calculator">2 * 7</gadget>
<output>14</output>
<gadget id="calculator">64 - 14</gadget>
<output>50</output>
<gadget id="calculator">50 / 64</gadget>
<output>25/32 = around 0.78125</output>
<result>D</result> | D | 0.78125 | A rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug? | {
"A": "a . 3 / 16",
"B": "1 / 4",
"C": "c . 1 / 2",
"D": "25 / 32",
"E": "7 / 8"
} | divide(subtract(64, multiply(2, 7)), 64) | multiply(n0,n1)|subtract(n2,#0)|divide(#1,n2) | area of the rectangular rug = 2 * 7 = 14 fraction not covered by the rug = ( total area - rug area ) / total area = ( 64 - 14 ) / 64 = 25 / 32 = d | geometry |
math_qa__x4Pl3puK5W4TBHKZ | Find the value of (55 + 113/78) × 78 Answers
A) 4423 B) 4403 C) 4413 D) 2403 E) 4375 | <gadget id="calculator">113 / 78</gadget>
<output>113/78 = around 1.448718</output>
<gadget id="calculator">(113/78) + 55</gadget>
<output>4_403/78 = around 56.448718</output>
<gadget id="calculator">(4_403/78) * 78</gadget>
<output>4_403</output>
<result>B</result> | B | 4,403 | Find the value of (55 + 113/78) × 78 | {
"A": "4423",
"B": "4403",
"C": "4413",
"D": "2403",
"E": "4375"
} | multiply(add(divide(113, 78), 55), 78) | divide(n1,n2)|add(n0,#0)|multiply(#1,n2)| | "= ( 55 + 113 / 78 ) × 78 = ( 4290 + 113 ) / 78 × 78 = 4403 / 78 × 78 = 4403 answer is b ." | general |
math_qa__R2CWtDVBmK0eLXIO | if two typists can type two pages in two minutes , how many typists will it take to type 25 pages in 5 minutes ?
Pick one
A) 3 B) 4 C) 10 D) 12 E) 36 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">25 / (1/2)</gadget>
<output>50</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<result>C</result> | C | 10 | if two typists can type two pages in two minutes , how many typists will it take to type 25 pages in 5 minutes ? | {
"A": "3",
"B": "4",
"C": "10",
"D": "12",
"E": "36"
} | divide(divide(25, divide(const_1, const_2)), 5) | divide(const_1,const_2)|divide(n0,#0)|divide(#1,n1) | in 2 minutes 2 typists type 2 pages which means that in 5 minutes they will type 5 pages but to type 25 pages ( 5 times ) we need 5 times more typists i . e . 2 x 5 = 10 typists . c | physics |
math_qa__0AOoS4qE3VuMkqFG | The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than
Choose the correct choice from the following options:
A) 14 years B) 12 years C) 56 years D) 66 years E) 11 years | <gadget id="calculator">11 * 1</gadget>
<output>11</output>
<result>E</result> | E | 11 | The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than | {
"A": "14 years",
"B": "12 years",
"C": "56 years",
"D": "66 years",
"E": "11 years"
} | multiply(11, const_1) | multiply(n0,const_1)| | "given that a + b = 11 + b + c = > a â € “ c = 11 + b â € “ b = 11 = > c is younger than a by 11 years answer : e" | general |
math_qa__tnJm4ryR0JYgJhKs | n^(n/2)=2 is true when n=2 in the same way what is the value of n if n^(n/2) =12? Answers
A) 12 B) 6 C) 14 D) 16 E) 10 | <gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">144 / 12</gadget>
<output>12</output>
<result>A</result> | A | 12 | n^(n/2)=2 is true when n=2 in the same way what is the value of n if n^(n/2) =12? | {
"A": "12",
"B": "6",
"C": "14",
"D": "16",
"E": "10"
} | divide(power(12, 2), 12) | power(n4,n0)|divide(#0,n4)| | n ^ ( n / 2 ) = 12 apply log n / 2 logn = log 12 nlogn = 2 log 12 = log 12 ^ 2 = log 144 logn = log 144 now apply antilog n = 144 / n now n = 12 answer : a | general |
math_qa__rCpMfApsfado2n2Z | If y is the smallest positive integer such that 4410 multiplied by y is the square of an integer, then y must be Choose the correct answer
A) 2 B) 5 C) 6 D) 7 E) 10 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<result>E</result> | E | 10 | If y is the smallest positive integer such that 4410 multiplied by y is the square of an integer, then y must be | {
"A": "2",
"B": "5",
"C": "6",
"D": "7",
"E": "10"
} | multiply(add(const_2, const_3), const_2) | add(const_2,const_3)|multiply(#0,const_2) | 4410 = 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 2 * 5 = 10 . the answer is e . | geometry |
math_qa__bXg6IXmjxniRRjyN | If p and q are positive integers each greater than 1, and 17(p+1)=20(q+1), what is the least possible value of p+q? Choose the correct choice from the following options
A) 35 B) 42 C) 44 D) 46 E) none | <gadget id="calculator">20 + 17</gadget>
<output>37</output>
<gadget id="calculator">37 - 2</gadget>
<output>35</output>
<result>A</result> | A | 35 | If p and q are positive integers each greater than 1, and 17(p+1)=20(q+1), what is the least possible value of p+q? | {
"A": "35",
"B": "42",
"C": "44",
"D": "46",
"E": "none"
} | subtract(add(20, 17), const_2) | add(n1,n3)|subtract(#0,const_2)| | "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 20 / 17 - - > the least positive value of p + 1 is 20 , so the least value of p is 19 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 19 + 16 = 35 . answer : a" | general |
math_qa__Yc9ehVuxIUORqE6O | A portion of the 80% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 50% solution of chemicals resulted. What part of the original solution was replaced?
Options:
A) 1 / 3 B) 1 / 2 C) 1 / 4 D) 1 / 5 E) 1 / 6 | <gadget id="calculator">80 - 50</gadget>
<output>30</output>
<gadget id="calculator">80 - 20</gadget>
<output>60</output>
<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<result>B</result> | B | 0.5 | A portion of the 80% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 50% solution of chemicals resulted. What part of the original solution was replaced? | {
"A": "1 / 3",
"B": "1 / 2",
"C": "1 / 4",
"D": "1 / 5",
"E": "1 / 6"
} | divide(subtract(80, 50), subtract(80, 20)) | subtract(n0,n2)|subtract(n0,n1)|divide(#0,#1)| | "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.8 ( 1 - x ) + 0.2 * x = 0.5 - - > x = 1 / 2 . answer : b ." | gain |
math_qa__Lff4zkP7HfsH6NbQ | The maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? Choose the correct option
A) 16 B) 18 C) 36 D) 19 E) 32 | <gadget id="calculator">gcd(1_008, 928)</gadget>
<output>16</output>
<result>A</result> | A | 16 | The maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? | {
"A": "16",
"B": "18",
"C": "36",
"D": "19",
"E": "32"
} | gcd(1008, 928) | gcd(n0,n1)| | "number of pens = 1008 number of pencils = 928 required number of students = h . c . f . of 1008 and 928 = 16 answer is a" | general |
math_qa__EjaODj9SSM5ynAtH | Lilly has 10 fish and Rosy has 12 fish. In total, how many fish do they have in all? Choose the correct choice from the following
A) 18 B) 20 C) 22 D) 24 E) 26 | <gadget id="calculator">10 + 12</gadget>
<output>22</output>
<result>C</result> | C | 22 | Lilly has 10 fish and Rosy has 12 fish. In total, how many fish do they have in all? | {
"A": "18",
"B": "20",
"C": "22",
"D": "24",
"E": "26"
} | add(10, 12) | add(n0,n1) | 10 + 12 = 22 the answer is c . | general |
math_qa__TNjJQu3so755WxMN | A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
Answers: A) 2 / 27 B) 1 / 9 C) 1 / 3 D) 4 / 27 E) 2 / 9 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(1/3) * (2/9)</gadget>
<output>2/27 = around 0.074074</output>
<gadget id="calculator">(2/27) * 2</gadget>
<output>4/27 = around 0.148148</output>
<result>D</result> | D | 0.148148 | A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn? | {
"A": "2 / 27",
"B": "1 / 9",
"C": "1 / 3",
"D": "4 / 27",
"E": "2 / 9"
} | multiply(multiply(divide(3, add(add(3, 4), 2)), divide(2, add(add(3, 4), 2))), const_2) | add(n0,n1)|add(n2,#0)|divide(n0,#1)|divide(n2,#1)|multiply(#2,#3)|multiply(#4,const_2) | p = 2 ∗ 39 ∗ 29 = 427 p = 2 ∗ 39 ∗ 29 = 427 we are multiplying by 2 as there are two possible wining scenarios rw and wr . answer : d . | probability |
math_qa__qDvyy5zakB0FTpeo | Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? Choose the correct answer:
A) 142 % B) 150 % C) 165 % D) 176 % E) 188 % | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">(3/20) * 110</gadget>
<output>33/2 = around 16.5</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 100</gadget>
<output>10</output>
<gadget id="calculator">(33/2) / 10</gadget>
<output>33/20 = around 1.65</output>
<gadget id="calculator">(33/20) * 100</gadget>
<output>165</output>
<result>C</result> | C | 165 | Last year Sandy saved 10% of her annual salary. This year, she made 10% more money than last year, and she saved 15% of her salary. The amount saved this year was what percent of the amount she saved last year? | {
"A": "142 %",
"B": "150 %",
"C": "165 %",
"D": "176 %",
"E": "188 %"
} | multiply(divide(multiply(divide(15, const_100), add(const_100, 10)), divide(multiply(10, const_100), const_100)), const_100) | add(n1,const_100)|divide(n2,const_100)|multiply(n0,const_100)|divide(#2,const_100)|multiply(#0,#1)|divide(#4,#3)|multiply(#5,const_100)| | "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.15 * 1.1 x = 0.165 x 0.165 x / 0.1 x = 1.65 = 165 % the answer is c ." | gain |
math_qa__G3XrsIkxuZ3d8Xx3 | 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container M? Choose one.
A) a : 45 B) b : 25 C) c : 37.5 D) d : 36 E) e : 42 | <gadget id="calculator">9 + 16</gadget>
<output>25</output>
<gadget id="calculator">9 / 25</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) ** (1/2)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">15 / (2/5)</gadget>
<output>75/2 = around 37.5</output>
<result>C</result> | C | 37.5 | 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container M? | {
"A": "a : 45",
"B": "b : 25",
"C": "c : 37.5",
"D": "d : 36",
"E": "e : 42"
} | divide(15, subtract(const_1, sqrt(divide(9, add(9, 16))))) | add(n2,n3)|divide(n2,#0)|sqrt(#1)|subtract(const_1,#2)|divide(n0,#3)| | "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ." | general |
math_qa__mbKXKexFMrAewYXV | List K consists of 12 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K? Options
A) 5 B) 6 C) 7 D) 11 E) 12 | <gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<result>C</result> | C | 7 | List K consists of 12 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K? | {
"A": "5",
"B": "6",
"C": "7",
"D": "11",
"E": "12"
} | subtract(subtract(subtract(12, 3), const_1), const_1) | subtract(n0,n1)|subtract(#0,const_1)|subtract(#1,const_1)| | "answer = c = 7 if least = - 3 , then largest = 8 range = 8 - 1 = 7" | general |
math_qa__6Ub4YRr785zbOm1i | let a , b , c be distinct digits . consider a two - digit number ‘ ab ’ and a 3 - digit number ‘ ccb ’ , both defined under the usual decimal number system , if ( ab ) 2 = ccb > 300 , then the value of b is Choose one.
A) 1 B) 0 C) 5 D) 6 E) 7 | <gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">21 ** 2</gadget>
<output>441</output>
<gadget id="calculator">441 % 10</gadget>
<output>1</output>
<result>A</result> | A | 1 | let a , b , c be distinct digits . consider a two - digit number ‘ ab ’ and a 3 - digit number ‘ ccb ’ , both defined under the usual decimal number system , if ( ab ) 2 = ccb > 300 , then the value of b is | {
"A": "1",
"B": "0",
"C": "5",
"D": "6",
"E": "7"
} | reminder(power(add(multiply(2, const_10), const_1), const_2), const_10) | multiply(n1,const_10)|add(#0,const_1)|power(#1,const_2)|reminder(#2,const_10) | explanation : given , ( ab ) 2 = ccb . [ only 1 , 5 and 6 on squaring will result with same digits in units place . ] taking a = 2 , b = 1 , = > ( 21 ) ^ 2 = 441 > 300 . hence , the required value of b = 1 answer : a | general |
math_qa__aiYpvSYzs2mXrKbR | A train running at the speed of 60 km/hr crosses a pole in 21 seconds. Find the length of the train. Choose the correct choice from the following answers.
A) 350 m B) 145 m C) 240 m D) 135 m E) 255 m | <gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 21</gadget>
<output>350</output>
<result>A</result> | A | 350 | A train running at the speed of 60 km/hr crosses a pole in 21 seconds. Find the length of the train. | {
"A": "350 m",
"B": "145 m",
"C": "240 m",
"D": "135 m",
"E": "255 m"
} | multiply(divide(multiply(60, const_1000), const_3600), 21) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 350 meter answer : a" | physics |
math_qa__I5zkYo6G1LLXvUk1 | Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ?
Choose the correct option:
A) 97.959 % B) 98.959 % C) 99.959 % D) 96.959 % E) 95.959 % | <gadget id="calculator">7 / 7</gadget>
<output>1</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">1 / 49</gadget>
<output>1/49 = around 0.020408</output>
<gadget id="calculator">(1/49) * 100</gadget>
<output>100/49 = around 2.040816</output>
<gadget id="calculator">100 - (100/49)</gadget>
<output>4_800/49 = around 97.959184</output>
<result>A</result> | A | 97.959 | Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ? | {
"A": "97.959 %",
"B": "98.959 %",
"C": "99.959 %",
"D": "96.959 %",
"E": "95.959 %"
} | subtract(const_100, multiply(divide(divide(7, 7), multiply(7, 7)), const_100)) | divide(n1,n1)|multiply(n0,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)| | "let the number be x the right number is 7 x the wrong number is x / 7 error is ( 7 x - x / 7 ) = 48 x / 7 percentage of error is ( ( 48 x / 7 ) / 7 x ) * 100 = 97.959 % answer : a" | general |
math_qa__MRn3osj7VtxxvAbU | find how many 4 digits no. is less then 1239 such that all 4 digits are distinct. Choices:
A) 68
B) 69
C) 70
D) 71
E) 72 | <gadget id="calculator">1_239 % 10</gadget>
<output>9</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">56 + 7</gadget>
<output>63</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">63 + 6</gadget>
<output>69</output>
<result>B</result> | B | 69 | find how many 4 digits no. is less then 1239 such that all 4 digits are distinct. | {
"A": "68",
"B": "69",
"C": "70",
"D": "71",
"E": "72"
} | add(add(multiply(subtract(reminder(1239, const_10), const_1), subtract(subtract(reminder(1239, const_10), const_1), const_1)), subtract(reminder(1239, const_10), const_2)), subtract(reminder(1239, const_10), const_3)) | reminder(n1,const_10)|subtract(#0,const_1)|subtract(#0,const_2)|subtract(#0,const_3)|subtract(#1,const_1)|multiply(#1,#4)|add(#5,#2)|add(#6,#3) | case 1 - 1000 - 1099 - there are 56 distinct digits case 2 - 1200 - 1209 - there are 7 distinct digits case 3 - 1230 - 1239 ( excluding 1239 ) - there are 6 distinct digits hence , 56 + 7 + 6 = 69 answer : b | general |
math_qa__hI8eFmrwA9sNstlI | If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 3 times, what is the probability that it will land tails up on the first flip and not on the last 2 flips? Pick one.
A) 1 / 8 B) 1 / 4 C) 1 / 3 D) 1 / 2 E) 3 / 4 | <gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<result>A</result> | A | 0.125 | If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 3 times, what is the probability that it will land tails up on the first flip and not on the last 2 flips? | {
"A": "1 / 8",
"B": "1 / 4",
"C": "1 / 3",
"D": "1 / 2",
"E": "3 / 4"
} | inverse(power(2, const_3)) | power(n1,const_3)|inverse(#0) | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 8 answer : a | probability |
math_qa__jljSI6u6r0YGsqmI | A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton, how many kilos did he consume on the sixth hour? Options: A) 38 B) 43 C) 50 D) 53 E) 62 | <gadget id="calculator">360 / 9</gadget>
<output>40</output>
<gadget id="calculator">40 + 3</gadget>
<output>43</output>
<result>B</result> | B | 43 | A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton, how many kilos did he consume on the sixth hour? | {
"A": "38",
"B": "43",
"C": "50",
"D": "53",
"E": "62"
} | add(divide(360, 9), 3) | divide(n2,n0)|add(n1,#0)| | "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 360 / 9 = 40 , so the median is also 40 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 43 . option b" | general |
math_qa__LAJxCF8yYGcDS7Bm | A factory produces 4340 toys per week. If the workers at this factory work 2 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? Choose the correct choice from the following answers:
A) 1375 toys
B) 2170 toys
C) 2375 toys
D) 2175 toys
E) 5375 toys | <gadget id="calculator">4_340 / 2</gadget>
<output>2_170</output>
<result>B</result> | B | 2,170 | A factory produces 4340 toys per week. If the workers at this factory work 2 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? | {
"A": "1375 toys",
"B": "2170 toys",
"C": "2375 toys",
"D": "2175 toys",
"E": "5375 toys"
} | divide(4340, 2) | divide(n0,n1)| | "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 2 days ) by 2 . 4340 / 2 = 2170 toys correct answer b" | physics |
math_qa__GWHurNm3OMq28aOT | At what price must an article costing Rs.47.50 be marked in order that after deducting 9% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice from the following choices:
A) 65.25 B) 62.6 C) 62.1 D) 62.7 E) 62.2 | <gadget id="calculator">47.5 * 25</gadget>
<output>1_187.5</output>
<gadget id="calculator">1_187.5 / 100</gadget>
<output>11.875</output>
<gadget id="calculator">47.5 + 11.875</gadget>
<output>59.375</output>
<gadget id="calculator">59.375 * 100</gadget>
<output>5_937.5</output>
<gadget id="calculator">100 - 9</gadget>
<output>91</output>
<gadget id="calculator">5_937.5 / 91</gadget>
<output>65.247253</output>
<result>A</result> | A | 65.25 | At what price must an article costing Rs.47.50 be marked in order that after deducting 9% from the list price. It may be sold at a profit of 25% on the cost price? | {
"A": "65.25",
"B": "62.6",
"C": "62.1",
"D": "62.7",
"E": "62.2"
} | divide(multiply(add(47.50, divide(multiply(47.50, 25), const_100)), const_100), subtract(const_100, 9)) | multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)| | "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 91 / 100 ) = 59.375 mp = 65.25 answer : a" | gain |
math_qa__OordeEwMKtnhfoH1 | The mean of 50 observations was 36. It was found later that an observation 34 was wrongly taken as 23. The corrected new mean is : Choose one:
A) 36.0 B) 36.5 C) 36.24 D) 36.12 E) 36.22 | <gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>E</result> | E | 36.22 | The mean of 50 observations was 36. It was found later that an observation 34 was wrongly taken as 23. The corrected new mean is : | {
"A": "36.0",
"B": "36.5",
"C": "36.24",
"D": "36.12",
"E": "36.22"
} | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)| | "explanation : correct sum = ( 36 * 50 + 434 - 23 ) = 1825 . correct mean = = 1811 / 50 = 36.5 answer : e ) 36.22" | general |
math_qa__7PaY0Xckbj0YDUjL | If -11 and -8 are negative integers, then -11*-8 + 5 is Choose the correct choice from the following choices
A) - 14 B) 14 C) 33 D) 83 E) 93 | <gadget id="calculator">-11</gadget>
<output>-11</output>
<gadget id="calculator">-8</gadget>
<output>-8</output>
<gadget id="calculator">(-11) * (-8)</gadget>
<output>88</output>
<gadget id="calculator">88 + 5</gadget>
<output>93</output>
<result>E</result> | E | 93 | If -11 and -8 are negative integers, then -11*-8 + 5 is | {
"A": "- 14",
"B": "14",
"C": "33",
"D": "83",
"E": "93"
} | add(multiply(negate(11), negate(8)), 5) | negate(n0)|negate(n1)|multiply(#0,#1)|add(n4,#2)| | answer : e | general |
math_qa__eJrhgJOXn3irHBcv | If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added? Choose the correct option
A) 1
B) 2
C) 3
D) 4
E) 5 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 - 20</gadget>
<output>1</output>
<result>A</result> | A | 1 | If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | subtract(multiply(add(const_4, const_3), 3), 20) | add(const_3,const_4)|multiply(n1,#0)|subtract(#1,n0) | given there are 20 apples . if 1 extra apple is added , then it becomes 21 which can be divided equally that is 7 apples to each baby . option a is correct . | general |
math_qa__8apVLQGeKKwgsnCa | 8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ? Select
A) 1 / 9
B) 1 / 8
C) 1 / 7
D) 7 / 8
E) 8 / 7 | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<result>B</result> | B | 0.125 | 8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ? | {
"A": "1 / 9",
"B": "1 / 8",
"C": "1 / 7",
"D": "7 / 8",
"E": "8 / 7"
} | divide(const_1, 8) | divide(const_1,n0) | when there are eight people , the share of each person is 1 / 8 th the total cost answer : b | general |
math_qa__j2sRbOlyiUp8Yrrz | A box contains 3 red balls and 4 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
Choose the correct choice from the following choices:
A) 7 / 4 B) 1 / 2 C) 1 / 2 D) 5 / 8 E) 2 / 3 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 / 4</gadget>
<output>7/4 = around 1.75</output>
<result>A</result> | A | 1.75 | A box contains 3 red balls and 4 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black? | {
"A": "7 / 4",
"B": "1 / 2",
"C": "1 / 2",
"D": "5 / 8",
"E": "2 / 3"
} | divide(add(3, 4), const_4) | add(n0,n1)|divide(#0,const_4) | my complicated version of your simple approach let the 5 black balls be bbbbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 4 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 3 red ( rrr ) they can be arranged in ( 6 ! ) / ( 3 ! x 3 ! ) hence required probability = [ ( 7 ! ) / ( 4 ! x 3 ! ) ] / [ ( 6 ! ) / ( 3 ! x 3 ! ) ] ans = 7 / 4 a | probability |
math_qa__9C5o6iaDuTJzWlv0 | In Kaya's teacher's desk there are 4 pink highlighters, 2 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all? Choose the correct choice from the following options:
A) 11
B) 22
C) 77
D) 33
E) 88 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<result>A</result> | A | 11 | In Kaya's teacher's desk there are 4 pink highlighters, 2 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all? | {
"A": "11",
"B": "22",
"C": "77",
"D": "33",
"E": "88"
} | add(add(4, 2), 5) | add(n0,n1)|add(n2,#0)| | "add the numbers of highlighters . 4 + 2 + 5 = 11 . answer is a ." | general |
math_qa__RTQqxqKGrsVGH7S6 | The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person? Pick
A) 75 kg B) 50 kg C) 85 kg D) 90 kg E) 60 kg | <gadget id="calculator">10 * 2.5</gadget>
<output>25</output>
<gadget id="calculator">25 + 65</gadget>
<output>90</output>
<result>D</result> | D | 90 | The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person? | {
"A": "75 kg",
"B": "50 kg",
"C": "85 kg",
"D": "90 kg",
"E": "60 kg"
} | add(multiply(10, 2.5), 65) | multiply(n0,n1)|add(n2,#0)| | "explanation : total increase in weight = 10 ã — 2.5 = 25 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 25 = x - 65 = > x = 25 + 65 = 90 answer : option d" | general |
math_qa__KttkR1SfKP2qPtWA | On a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles? Select the correct option.
A) 5.2 B) 7.4 C) 13.7 D) 21.2 E) 28.7 | <gadget id="calculator">383.6 / 28</gadget>
<output>13.7</output>
<result>C</result> | C | 13.7 | On a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles? | {
"A": "5.2",
"B": "7.4",
"C": "13.7",
"D": "21.2",
"E": "28.7"
} | divide(383.6, 28) | divide(n2,n1)| | "z inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c" | physics |
math_qa__Ien6h194gNcHNCkT | A train 150 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Pick one.
A) 5 B) 6 C) 7 D) 9 E) 8 | <gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">66 * (5/18)</gadget>
<output>55/3 = around 18.333333</output>
<gadget id="calculator">150 / (55/3)</gadget>
<output>90/11 = around 8.181818</output>
<result>E</result> | E | 8 | A train 150 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? | {
"A": "5",
"B": "6",
"C": "7",
"D": "9",
"E": "8"
} | divide(150, multiply(add(60, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 150 * 3 / 55 = 8 sec . answer : e" | physics |
math_qa__r7xdrQO3lASK0uZn | The H.C.F. of two numbers is 40 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is: Select the correct option.
A) 276
B) 600
C) 699
D) 722
E) 745 | <gadget id="calculator">40 * 15</gadget>
<output>600</output>
<result>B</result> | B | 600 | The H.C.F. of two numbers is 40 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is: | {
"A": "276",
"B": "600",
"C": "699",
"D": "722",
"E": "745"
} | multiply(40, 15) | multiply(n0,n2)| | "the numbers are ( 40 x 11 ) and ( 40 x 15 ) . larger number = ( 40 x 15 ) = 600 . answer : b" | other |
math_qa__iHRPxg43HAy04cQX | Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
Choose the correct answer: A) 13.55 B) 14.55 C) 15.55 D) 16.55 E) 17.55 | <gadget id="calculator">40 / 54</gadget>
<output>20/27 = around 0.740741</output>
<gadget id="calculator">60 * (20/27)</gadget>
<output>400/9 = around 44.444444</output>
<gadget id="calculator">60 - (400/9)</gadget>
<output>140/9 = around 15.555556</output>
<result>C</result> | C | 15.55 | Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? | {
"A": "13.55",
"B": "14.55",
"C": "15.55",
"D": "16.55",
"E": "17.55"
} | subtract(const_60, multiply(const_60, divide(40, 54))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "explanation : t = 14 / 54 * 60 = 15.55 answer : option c" | physics |
math_qa__YUUeFoqAvETK47rl | A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the correct choice from the following options.
A) 5
B) 21
C) 7
D) 8
E) 9 | <gadget id="calculator">385 / 1_000</gadget>
<output>77/200 = around 0.385</output>
<gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">(77/200) / 66</gadget>
<output>7/1_200 = around 0.005833</output>
<gadget id="calculator">3_600 * (7/1_200)</gadget>
<output>21</output>
<result>B</result> | B | 21 | A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? | {
"A": "5",
"B": "21",
"C": "7",
"D": "8",
"E": "9"
} | multiply(const_3600, divide(divide(385, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 385 * 3 / 55 ] sec = 21 sec answer : option b" | physics |
math_qa__gHDpAi1ZFXeU3b99 | A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 15 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans? Pick.
A) 61 %
B) 70 %
C) 75 %
D) 85 %
E) 95 % | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 * (7/5)</gadget>
<output>140</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">140 * (23/20)</gadget>
<output>161</output>
<gadget id="calculator">161 / 100</gadget>
<output>161/100 = around 1.61</output>
<gadget id="calculator">(161/100) - 1</gadget>
<output>61/100 = around 0.61</output>
<gadget id="calculator">(61/100) * 100</gadget>
<output>61</output>
<result>A</result> | A | 61 | A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 15 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans? | {
"A": "61 %",
"B": "70 %",
"C": "75 %",
"D": "85 %",
"E": "95 %"
} | multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(15, const_100))), const_100), const_1), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#3,const_100)|multiply(#2,#4)|divide(#5,const_100)|subtract(#6,const_1)|multiply(#7,const_100)| | "find the product of the two increases : ( 1.4 ) * ( . 15 ) , which is 1.61 and a 61 % increase . a" | gain |
math_qa__S5iR4LhwFVgOpRel | If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 39 women together do the work? Select:
A) 10 days
B) 30 days
C) 20 days
D) 80 days
E) 40 days | <gadget id="calculator">12 * 54</gadget>
<output>648</output>
<gadget id="calculator">9 / 648</gadget>
<output>1/72 = around 0.013889</output>
<gadget id="calculator">20 * 54</gadget>
<output>1_080</output>
<gadget id="calculator">39 / 1_080</gadget>
<output>13/360 = around 0.036111</output>
<gadget id="calculator">(1/72) + (13/360)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / (1/20)</gadget>
<output>20</output>
<result>C</result> | C | 20 | If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 39 women together do the work? | {
"A": "10 days",
"B": "30 days",
"C": "20 days",
"D": "80 days",
"E": "40 days"
} | inverse(add(divide(9, multiply(12, 54)), divide(39, multiply(20, 54)))) | multiply(n0,n2)|multiply(n1,n2)|divide(n3,#0)|divide(n4,#1)|add(#2,#3)|inverse(#4) | c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 39 women = 15 women + 39 women = 54 women 20 women can do the work in 54 days . so , 54 women can do it in ( 20 * 54 ) / 54 = 20 days . | physics |
math_qa__GmMDkIVDR0mzm7Xx | If a car had traveled 35 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 105 km, at what speed did it travel? Choose one.
A) 50 kmh
B) 55 kmh
C) 60 kmh
D) 65 kmh
E) 70 kmh | <gadget id="calculator">105 * 35</gadget>
<output>3_675</output>
<gadget id="calculator">2 * 3_675</gadget>
<output>7_350</output>
<gadget id="calculator">7_350 * 4</gadget>
<output>29_400</output>
<gadget id="calculator">35 ** 2</gadget>
<output>1_225</output>
<gadget id="calculator">29_400 + 1_225</gadget>
<output>30_625</output>
<gadget id="calculator">30_625 ** (1/2)</gadget>
<output>175</output>
<gadget id="calculator">175 - 35</gadget>
<output>140</output>
<gadget id="calculator">140 / 2</gadget>
<output>70</output>
<result>E</result> | E | 70 | If a car had traveled 35 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 105 km, at what speed did it travel? | {
"A": "50 kmh",
"B": "55 kmh",
"C": "60 kmh",
"D": "65 kmh",
"E": "70 kmh"
} | divide(subtract(sqrt(add(multiply(multiply(const_2, multiply(105, 35)), const_4), power(35, const_2))), 35), const_2) | multiply(n0,n2)|power(n0,const_2)|multiply(#0,const_2)|multiply(#2,const_4)|add(#3,#1)|sqrt(#4)|subtract(#5,n0)|divide(#6,const_2)| | "time = distance / speed difference in time = 1 / 2 hrs 105 / x - 105 / ( x + 35 ) = 1 / 2 substitute the value of x from the options . - - > x = 70 - - > 105 / 70 - 105 / 105 = 3 / 2 - 1 = 1 / 2 answer : e" | physics |
math_qa__JnoKgwmeRArfl00T | The base of pyramid P is an isosceles right triangle whose leg is 3. If the height of P is 4, what is the volume of P? Choose the correct choice from the following
A) 36 B) 18 C) 12 D) 8 E) 6 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) * 4</gadget>
<output>18</output>
<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<result>E</result> | E | 6 | The base of pyramid P is an isosceles right triangle whose leg is 3. If the height of P is 4, what is the volume of P? | {
"A": "36",
"B": "18",
"C": "12",
"D": "8",
"E": "6"
} | divide(multiply(divide(power(3, const_2), const_2), 4), const_3) | power(n0,const_2)|divide(#0,const_2)|multiply(n1,#1)|divide(#2,const_3) | volume of a pyramid is given by v = 1 / 3 ah , where a is the area of the triangular base and h is the height of the pyramid . area of triangular base = 1 / 2 * 3 * 3 = 9 / 2 so , v = 1 / 3 * 9 / 2 * 4 = 6 option e | geometry |
math_qa__Nw2krViimhAvCx8W | 10% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 6514, how much was it in the beginning?
Choose the correct choice from the following
A) 8545 B) 8770 C) 8515 D) 7999 E) 7989 | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(9/10) * (17/20)</gadget>
<output>153/200 = around 0.765</output>
<gadget id="calculator">6_514 / (153/200)</gadget>
<output>1_302_800/153 = around 8_515.03268</output>
<gadget id="calculator">floor(1_302_800/153)</gadget>
<output>8_515</output>
<result>C</result> | C | 8,515 | 10% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 6514, how much was it in the beginning? | {
"A": "8545",
"B": "8770",
"C": "8515",
"D": "7999",
"E": "7989"
} | floor(divide(6514, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 15), const_100)))) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|divide(n2,#4)|floor(#5)| | "x * ( 90 / 100 ) * ( 85 / 100 ) = 6514 x = 8515 answer : c" | general |
math_qa__gQApXafurrDNm0Yd | If each year the population of the country grows by 10%, how many years will elapse before the population of the country doubles? Choose the correct answer:
A) 3 B) 4 C) 5 D) 7 E) 8 | <gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>E</result> | E | 8 | If each year the population of the country grows by 10%, how many years will elapse before the population of the country doubles? | {
"A": "3",
"B": "4",
"C": "5",
"D": "7",
"E": "8"
} | add(const_4, const_4) | add(const_4,const_4) | till year 2000 , population is 100 . year 2001 : population becomes 110 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 121 . . . . . . . . . . . . . 2 year elapsed year 2003 : population becomes > 133 . . . . . . . . . . . . . 3 year elapsed year 2004 : population becomes > 146 . . . . . . . . . . . . . . . . . . 4 year elapsed year 2005 : population becomes > 160 . . . . . . . . . . . . . . . . . . 5 year elapsed year 2006 : population becomes > 176 . . . . . . . . . . . . . . . . . . 6 year elapsed year 2007 : population becomes > 193 . . . . . . . . . . . . . . . . . . 7 year elapsed year 2008 : population > 200 . . . . . . . . . . . . . . . . . . 8 year elapsed answer : e | gain |
math_qa__hLXqHlNBdZxU91CB | 5 percent of a certain grass seed is timothy . if the amount of the mixture needed to plant one acre contains 2 pounds of timothy , how many acres can be planted with 600 pounds of the seed mixture ? Options:
A) 12 B) 15 C) 20 D) 24 E) 120 | <gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">600 / 40</gadget>
<output>15</output>
<result>B</result> | B | 15 | 5 percent of a certain grass seed is timothy . if the amount of the mixture needed to plant one acre contains 2 pounds of timothy , how many acres can be planted with 600 pounds of the seed mixture ? | {
"A": "12",
"B": "15",
"C": "20",
"D": "24",
"E": "120"
} | divide(600, multiply(2, divide(const_100, 5))) | divide(const_100,n0)|multiply(n1,#0)|divide(n2,#1) | if the mixture contains 2 pounds of timothy , the mixture must be 40 pounds . thus we need 40 pounds of mixture per acre . 600 / 40 = 15 acres the answer is b . | gain |
math_qa__NGeDs30uQ45CTdwk | A cistern 8 m long and 6 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: Choose one:
A) 80 m 2 B) 50 m 2 C) 83 m 2 D) 86 m 2 E) 55 m 2 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 6</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(5/4) * 8</gadget>
<output>10</output>
<gadget id="calculator">(15/2) + 10</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">2 * (35/2)</gadget>
<output>35</output>
<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">35 + 48</gadget>
<output>83</output>
<result>C</result> | C | 83 | A cistern 8 m long and 6 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: | {
"A": "80 m 2",
"B": "50 m 2",
"C": "83 m 2",
"D": "86 m 2",
"E": "55 m 2"
} | add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 6), multiply(add(divide(25, const_100), 1), 8))), multiply(6, 8)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1) | area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 6 x 1.25 + 8 x 1.25 ) + 8 x 6 ] m 2 = 83 m 2 . answer : c | physics |
math_qa__iG7Kugzvff6V1SwV | In a certain accounting class of 90 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 60%, and the students on the make-up date had an average score of 70%, what was the average score for the entire class? Choices: A) 63 % B) 64 % C) 65 % D) 66 % E) 67 % | <gadget id="calculator">70 * 60</gadget>
<output>4_200</output>
<gadget id="calculator">90 - 70</gadget>
<output>20</output>
<gadget id="calculator">70 * 20</gadget>
<output>1_400</output>
<gadget id="calculator">4_200 + 1_400</gadget>
<output>5_600</output>
<gadget id="calculator">5_600 / 90</gadget>
<output>560/9 = around 62.222222</output>
<result>A</result> | A | 63 | In a certain accounting class of 90 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 60%, and the students on the make-up date had an average score of 70%, what was the average score for the entire class? | {
"A": "63 %",
"B": "64 %",
"C": "65 %",
"D": "66 %",
"E": "67 %"
} | divide(add(multiply(70, 60), multiply(70, subtract(90, 70))), 90) | multiply(n1,n2)|subtract(n0,n1)|multiply(n3,#1)|add(#0,#2)|divide(#3,n0)| | "70 % of the class scored 60 % and 30 % of the class scored 70 % . the difference between 60 % and 70 % is 10 % . the average will be 60 % + 0.3 ( 10 % ) = 63 % . the answer is a ." | general |
math_qa__DwOJid1QfvXxZNMK | A sum fetched a total simple interest of 4016.25 at the rate of 9 %.p.a. in 5 years. What is the sum? Choose the most appropriate option: A) 4462.5 B) 8032.5 C) 8925 D) none of these E) can not be determined | <gadget id="calculator">4_016.25 * 100</gadget>
<output>401_625</output>
<gadget id="calculator">401_625 / 9</gadget>
<output>44_625</output>
<gadget id="calculator">44_625 / 5</gadget>
<output>8_925</output>
<result>C</result> | C | 8,925 | A sum fetched a total simple interest of 4016.25 at the rate of 9 %.p.a. in 5 years. What is the sum? | {
"A": "4462.5",
"B": "8032.5",
"C": "8925",
"D": "none of these",
"E": "can not be determined"
} | divide(divide(multiply(4016.25, const_100), 9), 5) | multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)| | "explanation : principal = ( 100 x 4016.25 ) / ( 9 x 5 ) = 401625 / 45 = 8925 answer : option c" | gain |
math_qa__KHzODWeQ4ptBPPDW | A bag consists of 20 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white? Choices:
A) 3 / 4
B) 2 / 4
C) 1 / 4
D) 1 / 8
E) 1 / 16 | <gadget id="calculator">5 + 9</gadget>
<output>14</output>
<gadget id="calculator">20 - 14</gadget>
<output>6</output>
<gadget id="calculator">6 + 9</gadget>
<output>15</output>
<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<result>A</result> | A | 0.75 | A bag consists of 20 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white? | {
"A": "3 / 4",
"B": "2 / 4",
"C": "1 / 4",
"D": "1 / 8",
"E": "1 / 16"
} | divide(add(subtract(20, add(5, 9)), 9), 20) | add(n1,n2)|subtract(n0,#0)|add(n2,#1)|divide(#2,n0)| | "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 20 - 5 - 9 = 6 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 20 + 6 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ." | probability |
math_qa__l1UfMH3vopATcM7R | A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is:
Choose the correct choice.
A) 16 : 15 B) 15 : 16 C) 15 : 8 D) 8 : 15 E) 8 : 17 | <gadget id="calculator">8 + 8</gadget>
<output>16</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">16 / 15</gadget>
<output>16/15 = around 1.066667</output>
<result>A</result> | A | 1.066667 | A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is: | {
"A": "16 : 15",
"B": "15 : 16",
"C": "15 : 8",
"D": "8 : 15",
"E": "8 : 17"
} | divide(add(8, 8), add(5, add(5, 5))) | add(n2,n2)|add(n1,n1)|add(n1,#1)|divide(#0,#2) | explanation : let the partial amount at 5 % be x and the partial amount at 8 % be ( 1550 - x ) interest on x at 5 % for 3 years + interest on ( 1550 - x ) at 8 % for 3 years = 300 x × 5 × 3 / 100 + ( 1550 - x ) × 8 × 3 / 100 = 300 x × 5 / 100 + ( 1550 - x ) × 8 / 100 = 100 5 x + 8 ( 1550 − x ) = 10000 5 x + 12400 − 8 x = 10000 3 x = 2400 x = 800 required ratio = x : ( 1550 - x ) = 800 : ( 1550 - 800 ) = 800 : 750 = 16 : 15 answer : option a | gain |
math_qa__elGSQgN6TThZ3oS5 | A part-time employee’s hourly wage was increased by 15%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased? Choose the correct choice from the following answers: A) 13 % B) 15 % C) 25 % D) 50 % E) 100 % | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">15 + 100</gadget>
<output>115</output>
<gadget id="calculator">115 / 100</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">(3/20) / (23/20)</gadget>
<output>3/23 = around 0.130435</output>
<gadget id="calculator">(3/23) * 100</gadget>
<output>300/23 = around 13.043478</output>
<result>A</result> | A | 13 | A part-time employee’s hourly wage was increased by 15%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased? | {
"A": "13 %",
"B": "15 %",
"C": "25 %",
"D": "50 %",
"E": "100 %"
} | multiply(divide(divide(15, const_100), divide(add(15, const_100), const_100)), const_100) | add(n0,const_100)|divide(n0,const_100)|divide(#0,const_100)|divide(#1,#2)|multiply(#3,const_100)| | "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 15 % wage increase , the employee makes $ 1.15 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.15 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.15 to get : new # of hours = 100 / 1.15 ≈ 87 hours so , the number of hours decreases from 100 hours to ( approximately ) 87 hours . this represents a 13 % decrease ( approximately ) . answer : a" | general |
math_qa__GhLKu0iagEBjszLU | If y is 60% greater than x, than x is what % less than y?
Choose the correct answer
A) 29.3 % B) 33.4 % C) 37.5 % D) 41.6 % E) 45.7 % | <gadget id="calculator">60 + 100</gadget>
<output>160</output>
<gadget id="calculator">60 / 160</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>C</result> | C | 37.5 | If y is 60% greater than x, than x is what % less than y? | {
"A": "29.3 %",
"B": "33.4 %",
"C": "37.5 %",
"D": "41.6 %",
"E": "45.7 %"
} | multiply(divide(60, add(60, const_100)), const_100) | add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100)| | "y = 1.6 x x = y / 1.6 = 10 y / 16 = 5 y / 8 x is 3 / 8 less which is 37.5 % less than y . the answer is c ." | general |
math_qa__nP9ePWUtkpPq5Y2i | A student gets 50% in one subject, 70% in the other. To get an overall of 70% how much should get in third subject. Choose the correct choice from the following options
A) 90 %
B) 25 %
C) 45 %
D) 55 %
E) 65 % | <gadget id="calculator">70 * 3</gadget>
<output>210</output>
<gadget id="calculator">50 + 70</gadget>
<output>120</output>
<gadget id="calculator">210 - 120</gadget>
<output>90</output>
<result>A</result> | A | 90 | A student gets 50% in one subject, 70% in the other. To get an overall of 70% how much should get in third subject. | {
"A": "90 %",
"B": "25 %",
"C": "45 %",
"D": "55 %",
"E": "65 %"
} | subtract(multiply(70, const_3), add(50, 70)) | add(n0,n1)|multiply(n2,const_3)|subtract(#1,#0)| | "let the 3 rd subject % = x 50 + 70 + x = 3 * 70 120 + x = 210 x = 210 - 120 = 90 answer : a" | gain |
math_qa__zdiUkJeu5iNBp4j2 | The product of two successive numbers is 2652. Which is the smaller of the two numbers? Choose the correct choice from the following answers:
A) 51
B) 68
C) 57
D) 55
E) 37 | <gadget id="calculator">2_652 ** (1/2)</gadget>
<output>2*sqrt(663) = around 51.497573</output>
<result>A</result> | A | 51 | The product of two successive numbers is 2652. Which is the smaller of the two numbers? | {
"A": "51",
"B": "68",
"C": "57",
"D": "55",
"E": "37"
} | sqrt(2652) | sqrt(n0)| | "a 51 from the given alternatives , 51 × 52 = 2652 ∴ smaller number = 51" | general |
math_qa__4bGCPR2bT4rLnUtz | A sum of money deposited at C.I. amounts to Rs.2560 in 3 years and to Rs.2989 in 4 years. Find the rate percent? Options.
A) 30 % B) 10 % C) 20 % D) 16 % E) 50 % | <gadget id="calculator">2_989 - 2_560</gadget>
<output>429</output>
<gadget id="calculator">429 / 2_560</gadget>
<output>429/2_560 = around 0.167578</output>
<gadget id="calculator">(429/2_560) * 100</gadget>
<output>2_145/128 = around 16.757812</output>
<result>D</result> | D | 16 | A sum of money deposited at C.I. amounts to Rs.2560 in 3 years and to Rs.2989 in 4 years. Find the rate percent? | {
"A": "30 %",
"B": "10 %",
"C": "20 %",
"D": "16 %",
"E": "50 %"
} | multiply(divide(subtract(2989, 2560), 2560), const_100) | subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)| | "2560 - - - 429 100 - - - ? = > 16 % answer : d" | gain |
math_qa__ulx1kpNRzswYUEpE | If k is a non-negative integer and 30^k is a divisor of 929,260 then 3^k - k^3 = Choose the correct choice from the following options:
A) 0
B) 1
C) 45
D) 130
E) 520 | <gadget id="calculator">1 - 1</gadget>
<output>0</output>
<gadget id="calculator">3 ** 0</gadget>
<output>1</output>
<gadget id="calculator">0 ** 3</gadget>
<output>0</output>
<gadget id="calculator">1 - 0</gadget>
<output>1</output>
<result>B</result> | B | 1 | If k is a non-negative integer and 30^k is a divisor of 929,260 then 3^k - k^3 = | {
"A": "0",
"B": "1",
"C": "45",
"D": "130",
"E": "520"
} | subtract(power(3, subtract(const_1, const_1)), power(subtract(const_1, const_1), 3)) | subtract(const_1,const_1)|power(n2,#0)|power(#0,n2)|subtract(#1,#2) | 9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b . | general |
math_qa__TJJgZ0gP3obz9P8I | A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 18%. What was its profit on the items sold in February? Answers:
A) 27.5 %
B) 30 %
C) 35 %
D) 23 %
E) 40 % | <gadget id="calculator">100 - 18</gadget>
<output>82</output>
<gadget id="calculator">82 / 100</gadget>
<output>41/50 = around 0.82</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">120 * (5/4)</gadget>
<output>150</output>
<gadget id="calculator">(41/50) * 150</gadget>
<output>123</output>
<gadget id="calculator">123 - 100</gadget>
<output>23</output>
<result>D</result> | D | 23 | A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 18%. What was its profit on the items sold in February? | {
"A": "27.5 %",
"B": "30 %",
"C": "35 %",
"D": "23 %",
"E": "40 %"
} | subtract(multiply(divide(subtract(const_100, 18), const_100), multiply(add(const_100, 20), divide(add(const_100, 25), const_100))), const_100) | add(n0,const_100)|add(n1,const_100)|subtract(const_100,n2)|divide(#2,const_100)|divide(#1,const_100)|multiply(#0,#4)|multiply(#3,#5)|subtract(#6,const_100)| | "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.82 * 150 x = 123 x hence total profit = 23 % option d" | gain |
math_qa__dz9DD142u9s7eW4t | In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 5500, the number of valid votes that the other candidate got, was: Choices:
A) 2800 B) 1980 C) 2900 D) 2200 E) 2300 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 5_500</gadget>
<output>1_980</output>
<result>B</result> | B | 1,980 | In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 5500, the number of valid votes that the other candidate got, was: | {
"A": "2800",
"B": "1980",
"C": "2900",
"D": "2200",
"E": "2300"
} | multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 5500) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(n2,#4)| | "b number of valid votes = 80 % of 5500 = 4400 . valid votes polled by other candidate = 45 % of 4400 = ( 45 / 100 x 4400 ) = 1980 ." | gain |
math_qa__5Si2wfVsmWUm0Wsc | There are 7 players in a bowling team with an average weight of 103 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? Choose the most appropriate option: A) 95 kg . B) 99 kg . C) 89 kg . D) 90 kg . E) 92 kg . | <gadget id="calculator">7 * 103</gadget>
<output>721</output>
<gadget id="calculator">110 + 60</gadget>
<output>170</output>
<gadget id="calculator">721 + 170</gadget>
<output>891</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">891 / 9</gadget>
<output>99</output>
<result>B</result> | B | 99 | There are 7 players in a bowling team with an average weight of 103 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? | {
"A": "95 kg .",
"B": "99 kg .",
"C": "89 kg .",
"D": "90 kg .",
"E": "92 kg ."
} | divide(add(multiply(7, 103), add(110, 60)), add(7, const_2)) | add(n2,n3)|add(n0,const_2)|multiply(n0,n1)|add(#0,#2)|divide(#3,#1)| | "the new average will be = ( 103 * 7 + 110 + 60 ) / 9 = 99 kgs b is the answer" | general |
math_qa__azvvEzXFhjOaS7tQ | If the annual increase in the population of a town is 10% and the present number of people is 14000, what will the population be in 2 years? Answers: A) 12100 B) 15240 C) 12456 D) 16940 E) 10002 | <gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) * 14_000</gadget>
<output>15_400</output>
<gadget id="calculator">15_400 * (11/10)</gadget>
<output>16_940</output>
<result>D</result> | D | 16,940 | If the annual increase in the population of a town is 10% and the present number of people is 14000, what will the population be in 2 years? | {
"A": "12100",
"B": "15240",
"C": "12456",
"D": "16940",
"E": "10002"
} | multiply(multiply(divide(add(10, const_100), const_100), 14000), divide(add(10, const_100), const_100)) | add(n0,const_100)|divide(#0,const_100)|multiply(n1,#1)|multiply(#1,#2)| | "the required population is = 14000 ( 1 + 10 / 100 ) ^ 2 = 14000 * 11 / 10 * 11 / 10 = 16940 answer is d" | gain |
math_qa__7l0M9EFTfmSxFz0w | The average of 21 numbers is 44. Average of the first 11 of them is 48 and that of the last 11 is 41. Find the 11th number? Options.
A) 48 B) 51 C) 47 D) 49 E) 55 | <gadget id="calculator">11 * 41</gadget>
<output>451</output>
<gadget id="calculator">21 * 44</gadget>
<output>924</output>
<gadget id="calculator">48 * 11</gadget>
<output>528</output>
<gadget id="calculator">924 - 528</gadget>
<output>396</output>
<gadget id="calculator">451 - 396</gadget>
<output>55</output>
<result>E</result> | E | 55 | The average of 21 numbers is 44. Average of the first 11 of them is 48 and that of the last 11 is 41. Find the 11th number? | {
"A": "48",
"B": "51",
"C": "47",
"D": "49",
"E": "55"
} | subtract(multiply(11, 41), subtract(multiply(21, 44), multiply(48, 11))) | multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)| | sum of all the 21 numbers = 21 * 44 = 924 sum of the first 11 of them = 11 * 48 = 528 sum of the last 11 of them = 11 * 41 = 451 so , the 11 th number = 528 + 451 - 924 = 55 . answer : e | general |
math_qa__6MR9DR9ODoG4C9NY | A train running at the speed of 30 km/hr crosses a pole in 9 sec. What is the length of the train? Choose the most appropriate option.
A) 75 m
B) 180 m
C) 324 m
D) can not be determined
E) none of these | <gadget id="calculator">30 * 1_000</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 3_600</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">(25/3) * 9</gadget>
<output>75</output>
<result>A</result> | A | 75 | A train running at the speed of 30 km/hr crosses a pole in 9 sec. What is the length of the train? | {
"A": "75 m",
"B": "180 m",
"C": "324 m",
"D": "can not be determined",
"E": "none of these"
} | multiply(divide(multiply(30, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 9 = 75 m answer : a" | physics |
math_qa__anAdNEoiyCPJVLf4 | In the next Cricket World Cup T-20, Team T has decided to score 200 runs only through 4s and 6s. In how many ways can the Team T score these 200 runs? Choices:
A) 13
B) 15
C) 16
D) 17
E) 18 | <gadget id="calculator">200 / 4</gadget>
<output>50</output>
<gadget id="calculator">200 / 6</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">50 - (100/3)</gadget>
<output>50/3 = around 16.666667</output>
<result>D</result> | D | 17 | In the next Cricket World Cup T-20, Team T has decided to score 200 runs only through 4s and 6s. In how many ways can the Team T score these 200 runs? | {
"A": "13",
"B": "15",
"C": "16",
"D": "17",
"E": "18"
} | subtract(divide(200, 4), divide(200, 6)) | divide(n1,n2)|divide(n1,n3)|subtract(#0,#1) | team t can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d | general |
math_qa__sfVmanrCrJC2msVF | The perimeter of an isosceles right triangle is 8 + 8 sq rt 2. What is the length of the hypotenuse of the triangle? Pick one
A) 4
B) 5.656
C) 5
D) 6
E) 7 | <gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">8 * (sqrt(2))</gadget>
<output>8*sqrt(2) = around 11.313708</output>
<gadget id="calculator">(8*sqrt(2)) / 2</gadget>
<output>4*sqrt(2) = around 5.656854</output>
<result>B</result> | B | 5.656 | The perimeter of an isosceles right triangle is 8 + 8 sq rt 2. What is the length of the hypotenuse of the triangle? | {
"A": "4",
"B": "5.656",
"C": "5",
"D": "6",
"E": "7"
} | divide(multiply(8, sqrt(2)), 2) | sqrt(n2)|multiply(n0,#0)|divide(#1,n2)| | "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 8 + 8 sqrt 2 or , a . ( 2 + sqrt 2 ) = 8 ( 1 + sqrt 2 ) , a = 8 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 8 * 2.414 / 3.414 = 0.707 * 8 then hypotenuse = 5.656 b" | geometry |
math_qa__F20hfIxE1nJ635he | When x is multiplied by 3, the result is 18 more than the result of subtracting x from 26. What is the value of x? Select.
A) - 4 B) - 2 C) 11 D) 13 E) 22 | <gadget id="calculator">26 + 18</gadget>
<output>44</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">44 / 4</gadget>
<output>11</output>
<result>C</result> | C | 11 | When x is multiplied by 3, the result is 18 more than the result of subtracting x from 26. What is the value of x? | {
"A": "- 4",
"B": "- 2",
"C": "11",
"D": "13",
"E": "22"
} | divide(add(26, 18), add(3, const_1)) | add(n1,n2)|add(const_1,n0)|divide(#0,#1)| | "the equation that can be formed is : 3 x - 18 = 26 - x or , 4 x = 44 or , x = 11 . c answer ." | general |
math_qa__Q011U4NpgCNxc3cQ | A bag contains 5 red, 6 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Choose one: A) 1 / 13 B) 2 / 23 C) 5 / 39 D) 4 / 27 E) 3 / 23 | <gadget id="calculator">binomial(5, 2)</gadget>
<output>10</output>
<gadget id="calculator">5 + 6</gadget>
<output>11</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<gadget id="calculator">binomial(13, 2)</gadget>
<output>78</output>
<gadget id="calculator">10 / 78</gadget>
<output>5/39 = around 0.128205</output>
<result>C</result> | C | 0.128205 | A bag contains 5 red, 6 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? | {
"A": "1 / 13",
"B": "2 / 23",
"C": "5 / 39",
"D": "4 / 27",
"E": "3 / 23"
} | divide(choose(5, 2), choose(add(add(5, 6), 2), 2)) | add(n0,n1)|choose(n0,n3)|add(n2,#0)|choose(#2,n3)|divide(#1,#3)| | "p ( both are red ) , 5 c 213 c 2 = 6 c 213 c 2 = 10 / 78 = 5 / 39 c" | other |
math_qa__wT3t7AU7ILJUpRcg | The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? Options:
A) 50
B) 75
C) 69
D) 79
E) 82 | <gadget id="calculator">gcd(100, 50)</gadget>
<output>50</output>
<result>A</result> | A | 50 | The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? | {
"A": "50",
"B": "75",
"C": "69",
"D": "79",
"E": "82"
} | gcd(100, 50) | gcd(n0,n1)| | "number of pens = 100 number of pencils = 50 required number of students = h . c . f . of 100 and 50 = 50 answer is a" | general |
math_qa__Z3ViwkcToR0l6gRo | Rahul travels from A to B a distance of 200 miles in 5 hours. He returns to A in 4 hours. Find his average speed?
Select:
A) 52.2 mph B) 61.9 mph C) 44.4 mph D) 35.7 mph E) 65.6 mph | <gadget id="calculator">200 / 5</gadget>
<output>40</output>
<gadget id="calculator">200 / 4</gadget>
<output>50</output>
<gadget id="calculator">40 + 50</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<result>C</result> | C | 44.4 | Rahul travels from A to B a distance of 200 miles in 5 hours. He returns to A in 4 hours. Find his average speed? | {
"A": "52.2 mph",
"B": "61.9 mph",
"C": "44.4 mph",
"D": "35.7 mph",
"E": "65.6 mph"
} | divide(add(divide(200, 5), divide(200, 4)), const_2) | divide(n0,n1)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2) | speed from a to b = 200 / 5 = 40 mph speed from b to a = 200 / 4 = 50 mph average speed = 2 * 40 * 50 / 90 = 44.4 mph answer is c | physics |
math_qa__k4Y0WXiqaunW5zVq | if 5x*x+14*x+k=0 having two reciprocal roots find the value of k. Select: A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">14 - 5</gadget>
<output>9</output>
<gadget id="calculator">14 - 9</gadget>
<output>5</output>
<result>E</result> | E | 5 | if 5x*x+14*x+k=0 having two reciprocal roots find the value of k. | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | subtract(14, subtract(14, 5)) | subtract(n1,n0)|subtract(n1,#0) | product of reciprocal roots = 1 product of roots of quadratic eqn ax ^ 2 + bx + c = 0 is c / a . hence k / 5 = 1 k = 5 answer : e | general |
math_qa__cpig461sqjg1UtIV | The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:12. If P invested the money for 5 months, find for how much time did Q invest the money? Choose the correct choice:
A) 19
B) 17
C) 13
D) 10
E) 12 | <gadget id="calculator">7 / 5</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">12 / 7</gadget>
<output>12/7 = around 1.714286</output>
<gadget id="calculator">(7/5) * (12/7)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 5</gadget>
<output>12</output>
<result>E</result> | E | 12 | The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:12. If P invested the money for 5 months, find for how much time did Q invest the money? | {
"A": "19",
"B": "17",
"C": "13",
"D": "10",
"E": "12"
} | multiply(multiply(divide(7, 5), divide(12, 7)), 5) | divide(n0,n1)|divide(n3,n2)|multiply(#0,#1)|multiply(n4,#2)| | "7 * 5 : 5 * x = 7 : 12 x = 12 answer : e" | gain |
math_qa__IibxRpRsbNaPB1RE | Two employees X and Y are paid a total of Rs. 770 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Choose one: A) s . 150 B) s . 200 C) s . 250 D) s . 350 E) s . 400 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">770 * 10</gadget>
<output>7_700</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">7_700 / 22</gadget>
<output>350</output>
<result>D</result> | D | 350 | Two employees X and Y are paid a total of Rs. 770 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? | {
"A": "s . 150",
"B": "s . 200",
"C": "s . 250",
"D": "s . 350",
"E": "s . 400"
} | divide(multiply(770, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 770 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 770 â ‡ ’ y [ 12 / 10 + 1 ] = 770 â ‡ ’ 22 y / 10 = 770 â ‡ ’ 22 y = 7700 â ‡ ’ y = 700 / 22 = 700 / 2 = rs . 350 d )" | general |
math_qa__eBB8b42ig4qI6vjP | The tax on a commodity is diminished by 30% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? Options.
A) 20 %
B) 18 %
C) 15 %
D) 12 %
E) 14 % | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">115 * 70</gadget>
<output>8_050</output>
<gadget id="calculator">8_050 / 100</gadget>
<output>161/2 = around 80.5</output>
<gadget id="calculator">100 - (161/2)</gadget>
<output>39/2 = around 19.5</output>
<result>A</result> | A | 20 | The tax on a commodity is diminished by 30% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? | {
"A": "20 %",
"B": "18 %",
"C": "15 %",
"D": "12 %",
"E": "14 %"
} | subtract(const_100, divide(multiply(add(const_100, 15), subtract(const_100, 30)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | "100 * 100 = 10000 70 * 115 = 8050 10000 - - - - - - - 1950 100 - - - - - - - ? = 20 % answer : a" | general |
math_qa__r4c9w0MPQe3uX5Ty | Two trains 137 meters and 163 meters in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will they be clear of each other from the moment they meet Select
A) 8 sec
B) 10 sec
C) 12 sec
D) 14 sec
E) 16 sec | <gadget id="calculator">137 + 163</gadget>
<output>300</output>
<gadget id="calculator">48 + 42</gadget>
<output>90</output>
<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">300 / 25</gadget>
<output>12</output>
<result>C</result> | C | 12 | Two trains 137 meters and 163 meters in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will they be clear of each other from the moment they meet | {
"A": "8 sec",
"B": "10 sec",
"C": "12 sec",
"D": "14 sec",
"E": "16 sec"
} | divide(add(137, 163), divide(multiply(add(48, 42), const_1000), const_3600)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_1000)|divide(#2,const_3600)|divide(#0,#3) | explanation : relative speed of the trains = ( 42 + 48 ) kmph = 90 kmph = ( 90 × 5 / 18 ) m / sec = 25 m / sec . time taken by the trains to ‘ pass each other = time taken to cover ( 137 + 163 ) m at 25 m / sec = ( 300 / 25 ) sec = 12 sec answer : option c | physics |
math_qa__zZPeOQoq13zikaoi | Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 17 from the product of their ages a year from today. What is their age today? Pick one.
A) 2 . B) 4 . C) 5 . D) 7 . E) 8 . | <gadget id="calculator">17 - 1</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>E</result> | E | 8 | Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 17 from the product of their ages a year from today. What is their age today? | {
"A": "2 .",
"B": "4 .",
"C": "5 .",
"D": "7 .",
"E": "8 ."
} | divide(subtract(17, const_1), const_2) | subtract(n0,const_1)|divide(#0,const_2)| | "ad = ( a + 1 ) ( d + 1 ) - 17 0 = a + d - 16 a + d = 16 a = d ( as they are twin brothers ) a = d = 8 e is the answer" | general |
math_qa__l7AFYlg3znOVsZwL | A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30% of the original number. What percent of the red candies remain? Choose the most appropriate option:
A) 22.5 % B) 31.5 % C) 37.5 % D) 42.5 % E) 46.5 % | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">30 - 15</gadget>
<output>15</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) / 20</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>C</result> | C | 37.5 | A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30% of the original number. What percent of the red candies remain? | {
"A": "22.5 %",
"B": "31.5 %",
"C": "37.5 %",
"D": "42.5 %",
"E": "46.5 %"
} | multiply(divide(divide(subtract(30, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100) | add(const_2,const_3)|divide(const_100,#0)|divide(#1,const_2)|divide(#2,const_2)|add(#2,#3)|subtract(n0,#4)|divide(#5,const_2)|divide(#6,#1)|multiply(#7,const_100)| | "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.5 x red + yellow = 0.75 x red = 0.375 x , since red = yellow . the answer is c ." | general |
math_qa__80mfEVkvZuB5p549 | Rs.100 amounts to Rs.320 in 4 years at simple interest. If the interest is increased by 3%, it would amount to how much? Choose the correct choice
A) 246 B) 650 C) 110 D) 240 E) 360 | <gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">1 + (3/100)</gadget>
<output>103/100 = around 1.03</output>
<gadget id="calculator">(103/100) ** 4</gadget>
<output>112_550_881/100_000_000 = around 1.125509</output>
<gadget id="calculator">(112_550_881/100_000_000) * 100</gadget>
<output>112_550_881/1_000_000 = around 112.550881</output>
<result>C</result> | C | 110 | Rs.100 amounts to Rs.320 in 4 years at simple interest. If the interest is increased by 3%, it would amount to how much? | {
"A": "246",
"B": "650",
"C": "110",
"D": "240",
"E": "360"
} | multiply(power(add(const_1, divide(3, const_100)), 4), 100) | divide(n3,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | "( 100 * 4 * 3 ) / 100 = 12 100 + 12 = 112 answer : c" | gain |
math_qa__jTkkhAA2hSpYYMRJ | A family has two children. find the probability that both the children are girls given that at least
one of them is a girl? Choose the most appropriate option.
A) 1 / 5 B) 1 / 3 C) 3 / 7 D) 2 / 7 E) 3 / 7 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">3 * (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/4) / (3/4)</gadget>
<output>1/3 = around 0.333333</output>
<result>B</result> | B | 0.333333 | A family has two children. find the probability that both the children are girls given that at least
one of them is a girl? | {
"A": "1 / 5",
"B": "1 / 3",
"C": "3 / 7",
"D": "2 / 7",
"E": "3 / 7"
} | divide(const_0_25, multiply(const_3, const_0_25)) | multiply(const_0_25,const_3)|divide(const_0_25,#0) | let b stand for boy and g for girl . the sample space of the experiment is s = { ( g , g ) , ( g , b ) , ( b , g ) , ( b , b ) } let e and f denote the following events : e : ‘ both the children are girls ’ f : ‘ at least one of the child is a girl ’ then e = { ( g , g ) } and f = { ( g , g ) , ( g , b ) , ( b , g ) } now e n f = { ( g , g ) } thus p ( f ) = 3 / 4 and p ( e n f ) = 1 / 4 therefore p ( e | f ) = p ( e ∩ f ) / p ( f ) = ( 1 / 4 ) / ( 3 / 4 ) = 1 / 3 b ) | other |
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