id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__ereNzj6n4cohG1Hq | If the sum of the 4th term and the 12th term of an arithmetic progression is 24, what is the sum of the first 15 terms of the progression?
Choose the correct choice from the following options.
A) 300 B) 240 C) 220 D) 200 E) 180 | <gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * 24</gadget>
<output>180</output>
<result>E</result> | E | 180 | If the sum of the 4th term and the 12th term of an arithmetic progression is 24, what is the sum of the first 15 terms of the progression? | {
"A": "300",
"B": "240",
"C": "220",
"D": "200",
"E": "180"
} | multiply(divide(15, const_2), 24) | divide(n3,const_2)|multiply(n2,#0)| | "4 th term + 12 th term = 24 i . e . , ( a + 3 d ) + ( a + 11 d ) = 24 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 24 - - - - - - - - - - - - - - - from ( 1 ) = 180 answer : e" | general |
math_qa__LmuThdjEs43hdcvq | How many 4-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same? Choose one:
A) 1236
B) 3528
C) 4096
D) 4608
E) 6561 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">8 * 9</gadget>
<output>72</output>
<gadget id="calculator">49 * 72</gadget>
<output>3_528</output>
<result>B</result> | B | 3,528 | How many 4-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same? | {
"A": "1236",
"B": "3528",
"C": "4096",
"D": "4608",
"E": "6561"
} | multiply(multiply(add(const_4, const_3), add(const_4, const_3)), multiply(add(4, 4), multiply(3, 3))) | add(const_3,const_4)|add(n0,n0)|multiply(n1,n1)|multiply(#0,#0)|multiply(#1,#2)|multiply(#3,#4) | first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 7 possibilities . 9 * 8 * 7 * 7 = 3528 . b | general |
math_qa__xliapEkGEOxkiBLQ | 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 W? Select the correct option.
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 W? | {
"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__ZIPELSguwi3Xi4hh | A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price S per t-shirt that the vendor paid for these purchases?
Select the correct option.
A) $ 12.20 B) $ 12.50 C) $ 12.55 D) $ 12.70 E) $ 13.00 | <gadget id="calculator">10 + 14</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">12 + (1/2)</gadget>
<output>25/2 = around 12.5</output>
<result>A</result> | A | 12.2 | A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price S per t-shirt that the vendor paid for these purchases? | {
"A": "$ 12.20",
"B": "$ 12.50",
"C": "$ 12.55",
"D": "$ 12.70",
"E": "$ 13.00"
} | add(divide(add(10, 14), const_2), add(const_0_25, const_0_25)) | add(const_0_25,const_0_25)|add(n0,n1)|divide(#1,const_2)|add(#0,#2)| | "correct answer : a explanation : the relevant formula for this problem is average s = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ." | general |
math_qa__za8Rg17wDGM4WqMx | Of the families in City X in 1904, 50 percent owned a personal computer. The number of families in City X owning a computer in 1908 was 30 percent greater than it was in 1904, and the total number of families in City X was 5 percent greater in 1908 than it was in 1904. what percent of the families in City X owned a personal computer in 1908?
Choose the correct choice from the following options:
A) 61.90 %
B) 52.20 %
C) 56.20 %
D) 70.45 %
E) 74.41 % | <gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">130 * 50</gadget>
<output>6_500</output>
<gadget id="calculator">6_500 / 100</gadget>
<output>65</output>
<gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">65 / 105</gadget>
<output>13/21 = around 0.619048</output>
<gadget id="calculator">100 * (13/21)</gadget>
<output>1_300/21 = around 61.904762</output>
<result>A</result> | A | 61.9 | Of the families in City X in 1904, 50 percent owned a personal computer. The number of families in City X owning a computer in 1908 was 30 percent greater than it was in 1904, and the total number of families in City X was 5 percent greater in 1908 than it was in 1904. what percent of the families in City X owned a personal computer in 1908? | {
"A": "61.90 %",
"B": "52.20 %",
"C": "56.20 %",
"D": "70.45 %",
"E": "74.41 %"
} | multiply(const_100, divide(divide(multiply(add(30, const_100), 50), const_100), add(const_100, 5))) | add(n3,const_100)|add(n5,const_100)|multiply(n1,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)| | "say a 100 families existed in 1904 then the number of families owning a computer in 1904 - 50 number of families owning computer in 1908 = 50 * 130 / 100 = 65 number of families in 1908 = 105 the percentage = 65 / 105 * 100 = 61.90 % . option : a" | general |
math_qa__qlep60oCbZUYDixj | A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
Select.
A) 21 % B) 25 % C) 69 % D) 31 % E) 12 % | <gadget id="calculator">40 + 100</gadget>
<output>140</output>
<gadget id="calculator">140 * 20</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>
<gadget id="calculator">140 - 28</gadget>
<output>112</output>
<gadget id="calculator">112 - 100</gadget>
<output>12</output>
<result>E</result> | E | 12 | A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount? | {
"A": "21 %",
"B": "25 %",
"C": "69 %",
"D": "31 %",
"E": "12 %"
} | subtract(subtract(add(40, const_100), divide(multiply(add(40, const_100), 20), const_100)), const_100) | add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(#3,const_100)| | "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 20 % on 140 . profit = 112 - 100 12 % answer e" | gain |
math_qa__6WEjkjDf5QM3h5rB | The perimeter of a triangle is 36 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle? Choose the most appropriate option:
A) 76
B) 88
C) 66
D) 55
E) 45 | <gadget id="calculator">(2.5 * 36) / 2</gadget>
<output>45</output>
<result>E</result> | E | 45 | The perimeter of a triangle is 36 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle? | {
"A": "76",
"B": "88",
"C": "66",
"D": "55",
"E": "45"
} | triangle_area(2.5, 36) | triangle_area(n0,n1)| | "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : e" | geometry |
math_qa__OuPnKhcLCFAd0RgS | There were two candidates in an election. Winner candidate received 58% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? Choose the correct choice from the following:
A) 776
B) 1044
C) 299
D) 257
E) 125 | <gadget id="calculator">100 - 58</gadget>
<output>42</output>
<gadget id="calculator">58 - 42</gadget>
<output>16</output>
<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">288 / (4/25)</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 * 58</gadget>
<output>104_400</output>
<gadget id="calculator">104_400 / 100</gadget>
<output>1_044</output>
<result>B</result> | B | 1,044 | There were two candidates in an election. Winner candidate received 58% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? | {
"A": "776",
"B": "1044",
"C": "299",
"D": "257",
"E": "125"
} | divide(multiply(divide(288, divide(subtract(58, subtract(const_100, 58)), const_100)), 58), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | "w = 58 % l = 42 % 58 % - 42 % = 16 % 16 % - - - - - - - - 288 58 % - - - - - - - - ? = > 1044 answer : b" | gain |
math_qa__pBniu86MehCI4PqR | 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.
What is half of that number? Choose the correct choice from the following choices: A) 305 B) 315 C) 345 D) 325 E) 335 | <gadget id="calculator">4 / 15</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">5 / 7</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(4/15) * (5/7)</gadget>
<output>4/21 = around 0.190476</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">4 / 9</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">(2/5) * (4/9)</gadget>
<output>8/45 = around 0.177778</output>
<gadget id="calculator">(4/21) - (8/45)</gadget>
<output>4/315 = around 0.012698</output>
<gadget id="calculator">8 / (4/315)</gadget>
<output>630</output>
<gadget id="calculator">630 / 2</gadget>
<output>315</output>
<result>B</result> | B | 315 | 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.
What is half of that number? | {
"A": "305",
"B": "315",
"C": "345",
"D": "325",
"E": "335"
} | divide(divide(8, subtract(multiply(divide(4, 15), divide(5, 7)), multiply(divide(2, 5), divide(4, 9)))), 2) | divide(n0,n1)|divide(n2,n3)|divide(n6,n2)|divide(n0,n5)|multiply(#0,#1)|multiply(#2,#3)|subtract(#4,#5)|divide(n8,#6)|divide(#7,n6) | let the number be x . then 4 / 15 of 5 / 7 of x - 4 / 9 of 2 / 5 of x = 8 4 / 21 x - 8 / 45 x = 8 ( 4 / 21 - 8 / 45 ) x = 8 ( 60 - 56 ) / 315 x = 8 4 / 315 x = 8 x = ( 8 * 315 ) / 4 = 630 1 / 2 x = 315 hence required number = 315 answer is b . | general |
math_qa__08AnGVvWPEe6lBfF | A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 20 per kg, then his gain percent is Choices:
A) 7 % B) 13 % C) 14 % D) 15 % E) 16 % | <gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">20 * 8</gadget>
<output>160</output>
<gadget id="calculator">5 * 18</gadget>
<output>90</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
<gadget id="calculator">160 - 150</gadget>
<output>10</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 150</gadget>
<output>20/3 = around 6.666667</output>
<result>A</result> | A | 7 | A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 20 per kg, then his gain percent is | {
"A": "7 %",
"B": "13 %",
"C": "14 %",
"D": "15 %",
"E": "16 %"
} | divide(multiply(subtract(multiply(20, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20))) | add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|add(#1,#2)|multiply(n4,#0)|subtract(#4,#3)|multiply(#5,const_100)|divide(#6,#3)| | "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 20 ) = rs . 160 . profit = 160 - 150 = 10 so , profit % = ( 10 / 150 ) * 100 = 7 % option a" | gain |
math_qa__IiIoQgyvpmRspaJh | What is the total number of Y integers between 100 and 200 that are divisible by 3? Choose one
A) 33
B) 32
C) 31
D) 30
E) 29 | <gadget id="calculator">200 - 2</gadget>
<output>198</output>
<gadget id="calculator">100 + 2</gadget>
<output>102</output>
<gadget id="calculator">198 - 102</gadget>
<output>96</output>
<gadget id="calculator">96 / 3</gadget>
<output>32</output>
<gadget id="calculator">32 + 1</gadget>
<output>33</output>
<result>A</result> | A | 33 | What is the total number of Y integers between 100 and 200 that are divisible by 3? | {
"A": "33",
"B": "32",
"C": "31",
"D": "30",
"E": "29"
} | add(divide(subtract(subtract(200, const_2), add(100, const_2)), 3), const_1) | add(n0,const_2)|subtract(n1,const_2)|subtract(#1,#0)|divide(#2,n2)|add(#3,const_1) | yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33 | general |
math_qa__lT9NHGp3eKJ4dfdk | If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 136 games will be played during the tournament. Find the number of participants. Choose the correct choice from the following:
A) 15
B) 16
C) 17
D) 18
E) 19 | <gadget id="calculator">136 * 2</gadget>
<output>272</output>
<gadget id="calculator">272 * 4</gadget>
<output>1_088</output>
<gadget id="calculator">1_088 + 1</gadget>
<output>1_089</output>
<gadget id="calculator">1_089 ** (1/2)</gadget>
<output>33</output>
<gadget id="calculator">33 + 1</gadget>
<output>34</output>
<gadget id="calculator">34 / 2</gadget>
<output>17</output>
<result>C</result> | C | 17 | If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 136 games will be played during the tournament. Find the number of participants. | {
"A": "15",
"B": "16",
"C": "17",
"D": "18",
"E": "19"
} | divide(add(sqrt(add(multiply(multiply(136, const_2), const_4), const_1)), const_1), const_2) | multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2) | let p be the number of participants . pc 2 = 136 ( p ) ( p - 1 ) = 272 = 17 * 16 p = 17 the answer is c . | general |
math_qa__hWUNllcXScovxu1e | For the past n days, the average (arithmetic mean) daily production at a company was 40 units. If today's production of 90 units raises the average to 45 units per day, what is the value of n ?
Pick one: A) 30 B) 18 C) 10 D) 9 E) 7 | <gadget id="calculator">90 - 40</gadget>
<output>50</output>
<gadget id="calculator">45 - 40</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<result>D</result> | D | 9 | For the past n days, the average (arithmetic mean) daily production at a company was 40 units. If today's production of 90 units raises the average to 45 units per day, what is the value of n ? | {
"A": "30",
"B": "18",
"C": "10",
"D": "9",
"E": "7"
} | subtract(divide(subtract(90, 40), subtract(45, 40)), const_1) | subtract(n1,n0)|subtract(n2,n0)|divide(#0,#1)|subtract(#2,const_1)| | "( average production for n days ) * n = ( total production for n days ) - - > 40 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 40 n + 90 = 45 * ( n + 1 ) - - > n = 9 answer : d ." | general |
math_qa__jmiEuNoBXg8cmPQ0 | in the johnsons ' monthly budget , the dollar amounts allocated to household expenses , food , and miscellaneous items are in the ratio 5 : 4 : 1 , respectively . if the total amount allocated to these 3 categories is $ 1800 , what is the amount allocated to food ? Choose the most appropriate option
A) $ 900
B) $ 720
C) $ 675
D) $ 450
E) $ 225 | <gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">1_800 / 10</gadget>
<output>180</output>
<gadget id="calculator">180 * 4</gadget>
<output>720</output>
<result>B</result> | B | 720 | in the johnsons ' monthly budget , the dollar amounts allocated to household expenses , food , and miscellaneous items are in the ratio 5 : 4 : 1 , respectively . if the total amount allocated to these 3 categories is $ 1800 , what is the amount allocated to food ? | {
"A": "$ 900",
"B": "$ 720",
"C": "$ 675",
"D": "$ 450",
"E": "$ 225"
} | multiply(divide(1800, add(add(5, 4), 1)), 4) | add(n0,n1)|add(n2,#0)|divide(n4,#1)|multiply(n1,#2) | to solve this question , it will be best to first express the given ratio using variable multipliers . thus , we have : household expenses : food : miscellaneous = 5 x : 4 x : x since we are told that the total amount allocated to these categories is $ 1,800 we can set up the equation : 5 x + 4 x + x = 1,800 10 x = 1,800 x = 180 thus , the total amount allocated to food is 4 x 180 = $ 720 . answer b . | general |
math_qa__Jm1itwDMrIx7H95y | One ton has 2600 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons? Select the correct option
A) 2080
B) 1700
C) 2350
D) 2500
E) 8000 | <gadget id="calculator">13 * 2_600</gadget>
<output>33_800</output>
<gadget id="calculator">33_800 * 16</gadget>
<output>540_800</output>
<gadget id="calculator">16 * 16</gadget>
<output>256</output>
<gadget id="calculator">256 + 4</gadget>
<output>260</output>
<gadget id="calculator">540_800 / 260</gadget>
<output>2_080</output>
<result>A</result> | A | 2,080 | One ton has 2600 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons? | {
"A": "2080",
"B": "1700",
"C": "2350",
"D": "2500",
"E": "8000"
} | divide(multiply(multiply(13, 2600), 16), add(multiply(16, 16), 4)) | multiply(n0,n4)|multiply(n1,n1)|add(n3,#1)|multiply(n1,#0)|divide(#3,#2)| | "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2600 pound = 13 * 2600 * 16 ounces . hence the answer is ( 13 * 2600 * 16 ) / 260 = 2080 . answer : a ." | general |
math_qa__2pkt8mXssKvih5DU | The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is
Choose the correct choice from the following options:
A) 7 : 3 B) 2 : 3 C) 9 : 3 D) 6 : 3 E) 2 : 5 | <gadget id="calculator">15.8 - 15.4</gadget>
<output>0.4</output>
<gadget id="calculator">16.4 - 15.8</gadget>
<output>0.6</output>
<gadget id="calculator">0.4 / 0.6</gadget>
<output>0.666667</output>
<result>B</result> | B | 0.666667 | The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is | {
"A": "7 : 3",
"B": "2 : 3",
"C": "9 : 3",
"D": "6 : 3",
"E": "2 : 5"
} | divide(subtract(15.8, 15.4), subtract(16.4, 15.8)) | subtract(n0,n2)|subtract(n1,n0)|divide(#0,#1)| | "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) < = > k = 0.4 / 0.6 = 2 / 3 . required ratio = 2 / 3 : 1 = 2 : 3 . answer : b" | general |
math_qa__ETI6FloItCQ6IpQi | In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 35 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? Answers
A) 70
B) 245
C) 150
D) 35
E) 250 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(7/10) * (1/5)</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">35 / (7/50)</gadget>
<output>250</output>
<result>E</result> | E | 250 | In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 35 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? | {
"A": "70",
"B": "245",
"C": "150",
"D": "35",
"E": "250"
} | divide(35, multiply(divide(subtract(const_100, 30), const_100), divide(20, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)|divide(n2,#3)| | "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 35 , so 0.14 * { total } = 35 - - > { total } = 250 . answer : e ." | gain |
math_qa__up5AW9SY1GETBzQZ | Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 2/5 of the students are female, what fraction of all the students are on the honor roll? Choose the correct answer
A) 5 / 9 B) 3 / 15 C) 23 / 30 D) 22 / 30 E) 53 / 90 | <gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<gadget id="calculator">22 / 30</gadget>
<output>11/15 = around 0.733333</output>
<result>D</result> | D | 0.733333 | Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 2/5 of the students are female, what fraction of all the students are on the honor roll? | {
"A": "5 / 9",
"B": "3 / 15",
"C": "23 / 30",
"D": "22 / 30",
"E": "53 / 90"
} | divide(add(multiply(multiply(5, 2), 2), 2), multiply(2, multiply(3, 5))) | multiply(n0,n2)|multiply(n0,n3)|multiply(n2,#0)|multiply(n2,#1)|add(n2,#2)|divide(#4,#3) | let the total students be 30 given 2 / 5 of the students are females = 12 then males = 3 / 5 = 18 5 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 3 = 12 total students on honor roll = 12 + 10 = 22 fraction = 22 / 30 d | general |
math_qa__PCdxtiZhQF2LQHbA | A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train.
Choose the correct answer.
A) 150 B) 278 C) 179 D) 300 E) 191 | <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) * 18</gadget>
<output>300</output>
<result>D</result> | D | 300 | A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train. | {
"A": "150",
"B": "278",
"C": "179",
"D": "300",
"E": "191"
} | multiply(divide(multiply(60, const_1000), const_3600), 18) | 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 ) * 18 = 300 meter answer : d" | physics |
math_qa__6kalwJZJznVISlmQ | The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle? Pick.
A) 432 sq m B) 363 sq m C) 452 sq m D) 428 sq m E) 525 sq m | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">88 / 8</gadget>
<output>11</output>
<gadget id="calculator">11 * 3</gadget>
<output>33</output>
<gadget id="calculator">33 * 11</gadget>
<output>363</output>
<result>B</result> | B | 363 | The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle? | {
"A": "432 sq m",
"B": "363 sq m",
"C": "452 sq m",
"D": "428 sq m",
"E": "525 sq m"
} | multiply(multiply(divide(88, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(88, add(multiply(const_3, const_2), multiply(const_1, const_2)))) | multiply(const_2,const_3)|multiply(const_1,const_2)|add(#0,#1)|divide(n0,#2)|multiply(#3,const_3)|multiply(#3,#4) | 2 ( 3 x + x ) = 88 l = 33 b = 11 lb = 33 * 11 = 363 answer : b | geometry |
math_qa__fWIjDaTNeDTfojAy | A can run 256 metre in 28 seconds and B in 32 seconds. By what distance A beat B? Choose the correct option: A) 32 metre B) 28 metre C) 23 metre D) 15 metre E) 28 metre | <gadget id="calculator">256 / 32</gadget>
<output>8</output>
<gadget id="calculator">8 * 28</gadget>
<output>224</output>
<gadget id="calculator">256 - 224</gadget>
<output>32</output>
<result>A</result> | A | 32 | A can run 256 metre in 28 seconds and B in 32 seconds. By what distance A beat B? | {
"A": "32 metre",
"B": "28 metre",
"C": "23 metre",
"D": "15 metre",
"E": "28 metre"
} | subtract(256, multiply(divide(256, 32), 28)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)| | "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 256 / 32 = 8 m / s distance covered by b in 4 seconds = speed ã — time = 8 ã — 4 = 32 metre i . e . , a beat b by 32 metre answer is a" | physics |
math_qa__tT7rTs04hxCKOVqp | two circular signs are to be painted . if the diameter of the larger sign is 7 times that of the smaller sign , how many times more paint is needed to paint the larger sign ? ( we can assume that a given amount of paint covers the same area on both signs . ) Options.
A) 7 B) 14 C) 42 D) 49 E) 98 | <gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<result>D</result> | D | 49 | two circular signs are to be painted . if the diameter of the larger sign is 7 times that of the smaller sign , how many times more paint is needed to paint the larger sign ? ( we can assume that a given amount of paint covers the same area on both signs . ) | {
"A": "7",
"B": "14",
"C": "42",
"D": "49",
"E": "98"
} | power(7, const_2) | power(n0,const_2) | let r be the radius of the smaller sign . then the diameter of the smaller sign is 2 r , the diameter of the larger sign is 14 r , and the radius of the larger sign is 7 r . the area a of the smaller sign is a = pir ^ 2 . the area of the larger sign is pi ( 7 r ) ^ 2 = 49 pir ^ 2 = 49 a . since the area is 49 times larger , we need 49 times more paint for the larger sign . the answer is d . | geometry |
math_qa__9otnVUHwTdSrZHl9 | A man swims downstream 40 km and upstream 30 km taking 5 hours each time, what is the speed of the man in still water?
Choose the correct choice from the following options
A) 12 B) 8 C) 36 D) 5 E) 7 | <gadget id="calculator">30 / 5</gadget>
<output>6</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>E</result> | E | 7 | A man swims downstream 40 km and upstream 30 km taking 5 hours each time, what is the speed of the man in still water? | {
"A": "12",
"B": "8",
"C": "36",
"D": "5",
"E": "7"
} | divide(add(divide(30, 5), divide(40, 5)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | "40 - - - 5 ds = 8 ? - - - - 1 30 - - - - 5 us = 6 ? - - - - 1 m = ? m = ( 8 + 6 ) / 2 = 7 answer : e" | physics |
math_qa__vqOvTUs5cApc9V7z | If x is 20 percent greater than 88, then x = Choices: A) 68 B) 70.4 C) 86 D) 105.6 E) 108 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 88</gadget>
<output>88/5 = around 17.6</output>
<gadget id="calculator">88 + (88/5)</gadget>
<output>528/5 = around 105.6</output>
<result>D</result> | D | 105.6 | If x is 20 percent greater than 88, then x = | {
"A": "68",
"B": "70.4",
"C": "86",
"D": "105.6",
"E": "108"
} | add(88, multiply(divide(20, const_100), 88)) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | "x is 20 % greater than 88 means x is 1.2 times 88 ( in other words 88 + 20 / 100 * 88 = 1.2 * 88 ) therefore , x = 1.2 * 88 = 105.6 answer : d" | general |
math_qa__0E80vh70Ie8kqbx6 | Set A consists of all the prime numbers between 15 and 36. What is the range of set A? Choose the most appropriate option:
A) 12
B) 13
C) 14
D) 17
E) 23 | <gadget id="calculator">36 - 2</gadget>
<output>34</output>
<gadget id="calculator">15 + 4</gadget>
<output>19</output>
<gadget id="calculator">19 + 1</gadget>
<output>20</output>
<gadget id="calculator">34 - 20</gadget>
<output>14</output>
<result>C</result> | C | 14 | Set A consists of all the prime numbers between 15 and 36. What is the range of set A? | {
"A": "12",
"B": "13",
"C": "14",
"D": "17",
"E": "23"
} | subtract(subtract(36, const_2), add(add(15, const_4), const_1)) | add(n0,const_4)|subtract(n1,const_2)|add(#0,const_1)|subtract(#1,#2)| | "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 31 lowest number = 17 range = highest - lowest = 31 - 17 = 14 option c" | general |
math_qa__YALRSOCpt3b4bPHw | In one hour,a boat goes 21 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is : Choose the correct option:
A) 3 B) 5 C) 10 D) 9 E) 15 | <gadget id="calculator">21 + 9</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>E</result> | E | 15 | In one hour,a boat goes 21 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is : | {
"A": "3",
"B": "5",
"C": "10",
"D": "9",
"E": "15"
} | divide(add(21, 9), const_2) | add(n0,n1)|divide(#0,const_2)| | "solution speed in still water = 1 / 2 ( 21 + 9 ) kmph . = 15 kmph . answer e" | physics |
math_qa__zIco7GPwRroMkxub | 5% 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 3294, how much was it in the beginning? Answers:
A) 2988 B) 2776 C) 4079 D) 2871 E) 881 | <gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</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">(19/20) * (17/20)</gadget>
<output>323/400 = around 0.8075</output>
<gadget id="calculator">3_294 / (323/400)</gadget>
<output>1_317_600/323 = around 4_079.256966</output>
<gadget id="calculator">floor(1_317_600/323)</gadget>
<output>4_079</output>
<result>C</result> | C | 4,079 | 5% 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 3294, how much was it in the beginning? | {
"A": "2988",
"B": "2776",
"C": "4079",
"D": "2871",
"E": "881"
} | floor(divide(3294, multiply(divide(subtract(const_100, 5), 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 * ( 95 / 100 ) * ( 85 / 100 ) = 3294 x = 4079 answer : c | general |
math_qa__v868OAKnikL6y8lG | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 6 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? Choose the correct choice: A) 48 % B) 80 % C) 100 % D) 120 % E) 125 % | <gadget id="calculator">8 / 10</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) ** 2</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">6 / 8</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(16/25) * (3/4)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">(12/25) * 100</gadget>
<output>48</output>
<result>A</result> | A | 48 | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 6 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? | {
"A": "48 %",
"B": "80 %",
"C": "100 %",
"D": "120 %",
"E": "125 %"
} | multiply(multiply(power(divide(8, 10), const_2), divide(6, 8)), const_100) | divide(n0,n2)|divide(n1,n3)|power(#1,const_2)|multiply(#0,#2)|multiply(#3,const_100)| | "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 6 = 96 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 96 pi / 200 pi = 0.48 a" | physics |
math_qa__C8lFoN7szli2iy5w | On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 350 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? Choose the correct choice from the following answers.
A) 237 B) 287 C) 197 D) 287 E) 700 | <gadget id="calculator">350 * 2</gadget>
<output>700</output>
<result>E</result> | E | 700 | On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 350 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school? | {
"A": "237",
"B": "287",
"C": "197",
"D": "287",
"E": "700"
} | multiply(350, const_2) | multiply(n0,const_2)| | "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 350 ) = 2 + 2 ( extra ) = > 2 x - 700 = x = > x = 700 . answer : e" | general |
math_qa__rTmqNjwmkG8wyNYu | Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 10010000 and 100100000 ?
Choose the correct choice from the following choices:
A) 10
B) 11
C) 1001
D) 1011
E) 10001 | <gadget id="calculator">100_100_000 / 10_010_000</gadget>
<output>10</output>
<gadget id="calculator">10 + 1_000</gadget>
<output>1_010</output>
<result>C</result> | C | 1,001 | Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 10010000 and 100100000 ? | {
"A": "10",
"B": "11",
"C": "1001",
"D": "1011",
"E": "10001"
} | add(divide(100100000, 10010000), const_1000) | divide(n5,n4)|add(#0,const_1000) | binary divison can provide a quick answer if you are comfortable with it . as option e is the biggest binary number we try with it first : 100010000 / 1001 = 10000 1000100000 / 1001 = 100000 so answer is option is c | general |
math_qa__sDi4T6BQKSoo7JTS | A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? Answers
A) 27
B) 20
C) 40
D) 73
E) 72 | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/8) - (1/10)</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / (1/40)</gadget>
<output>40</output>
<result>C</result> | C | 40 | A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? | {
"A": "27",
"B": "20",
"C": "40",
"D": "73",
"E": "72"
} | inverse(subtract(divide(const_1, 8), divide(const_1, add(8, const_2)))) | add(n0,const_2)|divide(const_1,n0)|divide(const_1,#0)|subtract(#1,#2)|inverse(#3)| | "1 / 8 - 1 / x = 1 / 10 x = 40 answer : c" | physics |
math_qa__69zqgLe6SHTda1TS | Find the distance covered by a man walking for 24min at a speed of 10km/hr?
Choices.
A) 1 km B) 3 km C) 4 km D) 5 km E) 6 km | <gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 60</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">24 * (500/3)</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 1_000</gadget>
<output>4</output>
<result>C</result> | C | 4 | Find the distance covered by a man walking for 24min at a speed of 10km/hr? | {
"A": "1 km",
"B": "3 km",
"C": "4 km",
"D": "5 km",
"E": "6 km"
} | divide(multiply(24, divide(multiply(10, const_1000), const_60)), const_1000) | multiply(n1,const_1000)|divide(#0,const_60)|multiply(n0,#1)|divide(#2,const_1000)| | "distance = 10 * 24 / 60 = 4 km answer is c" | physics |
math_qa__lSSznBJNoF2506is | The diagonals of a rhombus are 30 cm and 20 cm. Find its area? Choose the correct choice from the following answers.
A) 176 B) 190 C) 150 D) 278 E) 300 | <gadget id="calculator">(30 * 20) / 2</gadget>
<output>300</output>
<result>E</result> | E | 300 | The diagonals of a rhombus are 30 cm and 20 cm. Find its area? | {
"A": "176",
"B": "190",
"C": "150",
"D": "278",
"E": "300"
} | rhombus_area(30, 20) | rhombus_area(n0,n1)| | "1 / 2 * 30 * 20 = 300 answer : e" | geometry |
math_qa__A4n0848S6vTuIjeQ | At what price must an article costing Rs.50 be marked in order that after deducting 10% 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) 69.44 B) 62.0 C) 62.6 D) 62.1 E) 62.2 | <gadget id="calculator">50 * 25</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 100</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">50 + (25/2)</gadget>
<output>125/2 = around 62.5</output>
<gadget id="calculator">(125/2) * 100</gadget>
<output>6_250</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">6_250 / 90</gadget>
<output>625/9 = around 69.444444</output>
<result>A</result> | A | 69.44 | At what price must an article costing Rs.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price? | {
"A": "69.44",
"B": "62.0",
"C": "62.6",
"D": "62.1",
"E": "62.2"
} | divide(multiply(add(50, divide(multiply(50, 25), const_100)), const_100), subtract(const_100, 10)) | multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)| | "cp = 50 sp = 50 * ( 125 / 100 ) = 62.50 mp * ( 90 / 100 ) = 62.50 mp = 69.44 answer : a" | gain |
math_qa__dTCfwdwNgIQ7USTt | A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? Choose the most appropriate option:
A) 10 % B) 5 % C) 12 % D) 6 % E) 4 % | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 / 120</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(5/6) * 512_456</gadget>
<output>1_281_140/3 = around 427_046.666667</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 / 80</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 512_456</gadget>
<output>640_570</output>
<gadget id="calculator">(1_281_140/3) + 640_570</gadget>
<output>3_202_850/3 = around 1_067_616.666667</output>
<gadget id="calculator">512_456 + 512_456</gadget>
<output>1_024_912</output>
<gadget id="calculator">(3_202_850/3) - 1_024_912</gadget>
<output>128_114/3 = around 42_704.666667</output>
<gadget id="calculator">(128_114/3) / (3_202_850/3)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) * 100</gadget>
<output>4</output>
<result>E</result> | E | 4 | A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? | {
"A": "10 %",
"B": "5 %",
"C": "12 %",
"D": "6 %",
"E": "4 %"
} | multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 20)), 512456), multiply(divide(const_100, subtract(const_100, 20)), 512456)), add(512456, 512456)), add(multiply(divide(const_100, add(const_100, 20)), 512456), multiply(divide(const_100, subtract(const_100, 20)), 512456))), const_100) | add(n1,const_100)|add(n0,n0)|subtract(const_100,n1)|divide(const_100,#0)|divide(const_100,#2)|multiply(n0,#3)|multiply(n0,#4)|add(#5,#6)|subtract(#7,#1)|divide(#8,#7)|multiply(#9,const_100) | in such a case there is always a loss loss % = ( 20 / 10 ) ^ 2 = 4 % answer is e | gain |
math_qa__98RInvotUPurJI1v | A train travels 225 km in 3.5 hours and 370 km in 5 hours.find the average speed of train.
Options:
A) 80 kmph B) 60 kmph C) 70 kmph D) 90 kmph E) none of these | <gadget id="calculator">225 + 370</gadget>
<output>595</output>
<gadget id="calculator">3.5 + 5</gadget>
<output>8.5</output>
<gadget id="calculator">595 / 8.5</gadget>
<output>70</output>
<result>C</result> | C | 70 | A train travels 225 km in 3.5 hours and 370 km in 5 hours.find the average speed of train. | {
"A": "80 kmph",
"B": "60 kmph",
"C": "70 kmph",
"D": "90 kmph",
"E": "none of these"
} | divide(add(225, 370), add(3.5, 5)) | add(n0,n2)|add(n1,n3)|divide(#0,#1)| | "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 225 + 370 = 595 km thus , total speed = 8.5 hrs or , average speed = 595 / 8.5 or , 70 kmph . answer : c" | physics |
math_qa__HKMtDkYfYqaiwGml | The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is Choose the correct choice: A) 51 : 52 B) 52 : 54 C) 53 : 54 D) 54 : 55 E) none of these | <gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">104 / 108</gadget>
<output>26/27 = around 0.962963</output>
<result>B</result> | B | 0.962963 | The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is | {
"A": "51 : 52",
"B": "52 : 54",
"C": "53 : 54",
"D": "54 : 55",
"E": "none of these"
} | divide(add(const_100, 4), add(const_100, 8)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | "explanation : let the cost price of article is rs . x required ratio = ( 104 % of x ) / ( 108 % of x ) = 104 / 108 = 52 / 54 = 52 : 54 . answer : b" | gain |
math_qa__cmXyDEUW1jSuhVfT | The speed of a boat in still water in 42 km/hr and the rate of current is 8 km/hr. The distance travelled downstream in 44 minutes is:
Choose the correct choice from the following choices
A) 86.6 km B) 46.6 km C) 36.6 km D) 35.6 km E) 26.6 km | <gadget id="calculator">42 + 8</gadget>
<output>50</output>
<gadget id="calculator">44 / 60</gadget>
<output>11/15 = around 0.733333</output>
<gadget id="calculator">50 * (11/15)</gadget>
<output>110/3 = around 36.666667</output>
<result>C</result> | C | 36.6 | The speed of a boat in still water in 42 km/hr and the rate of current is 8 km/hr. The distance travelled downstream in 44 minutes is: | {
"A": "86.6 km",
"B": "46.6 km",
"C": "36.6 km",
"D": "35.6 km",
"E": "26.6 km"
} | multiply(add(42, 8), divide(44, const_60)) | add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)| | "speed downstream = ( 42 + 8 ) = 50 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 50 = 36.6 km answer : c" | physics |
math_qa__rn0JctbiAPchJbVU | An article is sold at a certain price. By selling it at 2/3 of that price one loses 10%. Find the gain percent at original price. Choose the correct choice from the following.
A) 15 % B) 35 % C) 25 % D) 50 % E) 30 % | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">90 / (2/3)</gadget>
<output>135</output>
<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>B</result> | B | 35 | An article is sold at a certain price. By selling it at 2/3 of that price one loses 10%. Find the gain percent at original price. | {
"A": "15 %",
"B": "35 %",
"C": "25 %",
"D": "50 %",
"E": "30 %"
} | subtract(divide(subtract(const_100, 10), divide(2, 3)), const_100) | divide(n0,n1)|subtract(const_100,n2)|divide(#1,#0)|subtract(#2,const_100)| | "let the original s . p be rs . x . then new s . p = rs . 2 / 3 x , loss = 10 % so c . p = rs . [ 100 / 90 * 2 / 3 x ] = 20 x / 27 . now c . p = rs . 20 x / 27 , s . p = rs . x , gain = rs . [ x - 20 x / 27 ] = rs . 7 x / 27 . gain % = [ 7 x / 27 * 27 / 20 x * 100 ] % = 35 % answer : b" | gain |
math_qa__s8m16plvzOpMbDTv | If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 6 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? Pick:
A) 1 / 9 B) 29 / 180 C) 26 / 143 D) 2 / 15 E) 39 / 121 | <gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">200 / 10</gadget>
<output>20</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">30 * 6</gadget>
<output>180</output>
<gadget id="calculator">180 / 15</gadget>
<output>12</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/20) + (1/12)</gadget>
<output>2/15 = around 0.133333</output>
<result>D</result> | D | 0.133333 | If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 6 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour? | {
"A": "1 / 9",
"B": "29 / 180",
"C": "26 / 143",
"D": "2 / 15",
"E": "39 / 121"
} | add(divide(const_1, divide(multiply(50, 4), const_10)), divide(const_1, divide(multiply(30, 6), 15))) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_10)|divide(#1,n5)|divide(const_1,#2)|divide(const_1,#3)|add(#4,#5) | 50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 6 * 2 = 12 hours ; in 1 hour 15 journeymen can finish 1 / 12 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 12 = 2 / 15 of the job . answer : d . | physics |
math_qa__ZfbPLxazRSN5yBKE | A shopkeeper sells 600 metres of cloth for Rs. 36000 at a loss of Rs.10 per metre. Find his cost price for one metre of cloth? Choose the correct choice from the following options.
A) s . 59
B) s . 58
C) s . 09
D) s . 70
E) s . 13 | <gadget id="calculator">36_000 / 600</gadget>
<output>60</output>
<gadget id="calculator">60 + 10</gadget>
<output>70</output>
<result>D</result> | D | 70 | A shopkeeper sells 600 metres of cloth for Rs. 36000 at a loss of Rs.10 per metre. Find his cost price for one metre of cloth? | {
"A": "s . 59",
"B": "s . 58",
"C": "s . 09",
"D": "s . 70",
"E": "s . 13"
} | add(divide(36000, 600), 10) | divide(n1,n0)|add(n2,#0)| | "sp per metre = 36000 / 600 = rs . 60 loss per metre = rs . 10 cp per metre = 60 + 10 = rs . 70 answer : d" | gain |
math_qa__yU6J450Nzq4A4iuq | How long will take a leak at the bottom of a tank to empty it if it will take
8 hours to fill it without the leak, but due to the leak it will take 9 hours to be filled? Choose the most appropriate option
A) 50 hours B) 33 hours C) 72 hours D) 82 hours E) 92 hours | <gadget id="calculator">8 * 9</gadget>
<output>72</output>
<result>C</result> | C | 72 | How long will take a leak at the bottom of a tank to empty it if it will take
8 hours to fill it without the leak, but due to the leak it will take 9 hours to be filled? | {
"A": "50 hours",
"B": "33 hours",
"C": "72 hours",
"D": "82 hours",
"E": "92 hours"
} | multiply(8, 9) | multiply(n0,n1) | part filled without leak in 1 hour = 1 / 8 part filled with leak in 1 hour = 1 / 9 work done by leak in 1 hour = 1 / 8 â ˆ ’ 1 / 9 = 72 hours answer : c | physics |
math_qa__BITX476S9HwRTlLr | On a sum of money, the simple interest for 2 years is Rs. 325, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is Choose the correct choice from the following answers.
A) 15 % B) 14.25 % C) 9.23 % D) 10.5 % E) 11.5 % | <gadget id="calculator">325 / 2</gadget>
<output>325/2 = around 162.5</output>
<gadget id="calculator">340 - (325/2)</gadget>
<output>355/2 = around 177.5</output>
<gadget id="calculator">(355/2) - (325/2)</gadget>
<output>15</output>
<gadget id="calculator">100 * 15</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / (325/2)</gadget>
<output>120/13 = around 9.230769</output>
<result>C</result> | C | 9.23 | On a sum of money, the simple interest for 2 years is Rs. 325, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is | {
"A": "15 %",
"B": "14.25 %",
"C": "9.23 %",
"D": "10.5 %",
"E": "11.5 %"
} | divide(multiply(const_100, subtract(subtract(340, divide(325, 2)), divide(325, 2))), divide(325, 2)) | divide(n1,n0)|subtract(n2,#0)|subtract(#1,#0)|multiply(#2,const_100)|divide(#3,#0)| | "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 325 = 15 ( r ã — si ) / ( 2 ã — 100 ) = 15 ( r ã — 325 ) / ( 2 ã — 100 ) = 15 r = 9.23 % answer : option c" | gain |
math_qa__99uXtyLhSnBbkPAn | A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.400, find the original price per kg? Choose the correct choice from the following choices.
A) s . 7 B) s . 9 C) s . 10 D) s . 11 E) s . 19 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 400</gadget>
<output>80</output>
<gadget id="calculator">80 / 10</gadget>
<output>8</output>
<gadget id="calculator">8 / 80</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>C</result> | C | 10 | A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.400, find the original price per kg? | {
"A": "s . 7",
"B": "s . 9",
"C": "s . 10",
"D": "s . 11",
"E": "s . 19"
} | multiply(divide(divide(multiply(divide(20, const_100), 400), 10), multiply(divide(20, const_100), 400)), const_100) | divide(n0,const_100)|multiply(n2,#0)|divide(#1,n1)|divide(#2,#1)|multiply(#3,const_100) | 100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 400 - - - 80 ? - - - 2 = > rs . 10 answer : c | gain |
math_qa__BhIr0ITvYZHTjXJS | The product of a and b is equal to 1 more than twice the sum of a and b. If b = 7, what is the value of b - a? Select the correct option
A) 2
B) 5
C) 4
D) 24
E) 35 | <gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">14 + 1</gadget>
<output>15</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<result>C</result> | C | 4 | The product of a and b is equal to 1 more than twice the sum of a and b. If b = 7, what is the value of b - a? | {
"A": "2",
"B": "5",
"C": "4",
"D": "24",
"E": "35"
} | subtract(7, divide(add(multiply(7, const_2), 1), subtract(7, const_2))) | multiply(n1,const_2)|subtract(n1,const_2)|add(n0,#0)|divide(#2,#1)|subtract(n1,#3)| | "ab = 1 + 2 ( a + b ) 7 a = 1 + 2 a + 14 5 a = 15 a = 3 b - a = 7 - 3 = 4 c is the answer" | general |
math_qa__POUXXvC8iSJQmYo7 | he greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is: Select the correct option: A) 15 cm B) 25 cm C) 35 cm D) 42 cm E) 45 cm | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<result>C</result> | C | 35 | he greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is: | {
"A": "15 cm",
"B": "25 cm",
"C": "35 cm",
"D": "42 cm",
"E": "45 cm"
} | multiply(add(const_4, const_1), 7) | add(const_1,const_4)|multiply(n0,#0) | required length = h . c . f . of 700 cm , 385 cm and 1295 cm = 35 cm . answer : option c | physics |
math_qa__svoVhkGjmlShNpCK | 12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? Answers:
A) 1 / 2
B) 1 / 3
C) 1 / 4
D) 1 / 6
E) 1 / 12 | <gadget id="calculator">6 / 12</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<gadget id="calculator">12 / 6</gadget>
<output>2</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">50 / 200</gadget>
<output>1/4 = around 0.25</output>
<result>C</result> | C | 0.25 | 12 is 6% of a, and 6 is 12% of b. c equals b/a. What is the value of c? | {
"A": "1 / 2",
"B": "1 / 3",
"C": "1 / 4",
"D": "1 / 6",
"E": "1 / 12"
} | divide(multiply(divide(6, 12), const_100), multiply(divide(12, 6), const_100)) | divide(n1,n0)|divide(n0,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,#3) | 6 a / 100 = 12 a = 200 12 b / 100 = 6 b = 50 c = b / a = 50 / 200 = 1 / 4 the answer is c . | general |
math_qa__baBGnrjGqTuqL3Pf | Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 15, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates? Choose the correct choice from the following
A) 5 / 2 B) 8 / 3 C) 9 / 4 D) 10 / 3 E) 12 / 5 | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/10) + (1/20)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 / (3/20)</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">15 / (20/3)</gadget>
<output>9/4 = around 2.25</output>
<result>C</result> | C | 2.25 | Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 15, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates? | {
"A": "5 / 2",
"B": "8 / 3",
"C": "9 / 4",
"D": "10 / 3",
"E": "12 / 5"
} | divide(15, divide(const_1, add(divide(const_1, 10), divide(const_1, 20)))) | divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|divide(const_1,#2)|divide(n0,#3)| | "the time it takes printer x is 15 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 15 / ( 20 / 3 ) = 3 * 15 / 20 = 9 / 4 the answer is c ." | general |
math_qa__PXfs6PIfzgUaSBiy | Excluding stoppages, the speed of a train is 35 kmph and including stoppages it is 22 kmph. Of how many minutes does the train stop per hour? Choose the correct choice:
A) 82
B) 17
C) 22
D) 82
E) 18 | <gadget id="calculator">22 / 35</gadget>
<output>22/35 = around 0.628571</output>
<gadget id="calculator">60 * (22/35)</gadget>
<output>264/7 = around 37.714286</output>
<gadget id="calculator">60 - (264/7)</gadget>
<output>156/7 = around 22.285714</output>
<result>C</result> | C | 22 | Excluding stoppages, the speed of a train is 35 kmph and including stoppages it is 22 kmph. Of how many minutes does the train stop per hour? | {
"A": "82",
"B": "17",
"C": "22",
"D": "82",
"E": "18"
} | subtract(const_60, multiply(const_60, divide(22, 35))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "explanation : t = 13 / 35 * 60 = 22 answer : option c" | physics |
math_qa__aMdr123278HZxcyw | A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was Choose the correct choice from the following options
A) 665 B) 127 C) 272 D) 287 E) 227 | <gadget id="calculator">84 * 8</gadget>
<output>672</output>
<gadget id="calculator">672 + 85</gadget>
<output>757</output>
<gadget id="calculator">757 - 92</gadget>
<output>665</output>
<result>A</result> | A | 665 | A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was | {
"A": "665",
"B": "127",
"C": "272",
"D": "287",
"E": "227"
} | subtract(add(multiply(84, 8), 85), 92) | multiply(n0,n3)|add(n1,#0)|subtract(#1,n2)| | "let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a" | general |
math_qa__UW1yjJcfSTqOJrlf | If Tim had lunch at $50.50 and he gave 15% tip, how much did he spend? Choose the correct choice from the following answers:
A) $ 58 B) $ 60.60 C) $ 70.60 D) $ 40.60 E) $ 50.60 | <gadget id="calculator">50.5 * 15</gadget>
<output>757.5</output>
<gadget id="calculator">757.5 / 100</gadget>
<output>7.575</output>
<gadget id="calculator">50.5 + 7.575</gadget>
<output>58.075</output>
<result>A</result> | A | 58 | If Tim had lunch at $50.50 and he gave 15% tip, how much did he spend? | {
"A": "$ 58",
"B": "$ 60.60",
"C": "$ 70.60",
"D": "$ 40.60",
"E": "$ 50.60"
} | add(50.50, divide(multiply(50.50, 15), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | "the tip is 20 % of what he paid for lunch . hence tip = 15 % of 50.50 = ( 15 / 100 ) * 50.50 = $ 7.575 total spent 50.50 + 7.575 = $ 58 correct answer a" | gain |
math_qa__S5pVGsBNPVGmmkiG | If the numbers 1 to 98 are written on 98 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
Pick: A) 1 / 50 B) 1 / 25 C) 1 / 98 D) 1 E) 2 | <gadget id="calculator">1 / 98</gadget>
<output>1/98 = around 0.010204</output>
<result>C</result> | C | 0.010204 | If the numbers 1 to 98 are written on 98 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite? | {
"A": "1 / 50",
"B": "1 / 25",
"C": "1 / 98",
"D": "1",
"E": "2"
} | divide(1, 98) | divide(n0,n1)| | "there are 25 primes , 72 composite numbers from 1 to 98 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 98 . answer : c" | other |
math_qa__mEBYZgSFlKn27Qxp | If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 70? Choose the correct choice from the following answers: A) 11 B) 12 C) 13 D) 14 E) 17 | <gadget id="calculator">70 - 2</gadget>
<output>68</output>
<gadget id="calculator">68 / 4</gadget>
<output>17</output>
<result>E</result> | E | 17 | If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 70? | {
"A": "11",
"B": "12",
"C": "13",
"D": "14",
"E": "17"
} | divide(subtract(70, 2), 4) | subtract(n3,n0)|divide(#0,n1)| | "four wheeler = 17 * 4 = 68 ( max ) 2 wheel = 1 so no of 4 wheeler = 17 answer : e" | general |
math_qa__pORrDRPkJ9G7ztLP | On a purchase of $112, a store offered a payment plan consisting of a $12 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan? Choose the correct answer: A) 10.7 % B) 11.7 % C) 12.7 % D) 13.7 % E) 14.7 % | <gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">120 + 12</gadget>
<output>132</output>
<gadget id="calculator">132 - 120</gadget>
<output>12</output>
<gadget id="calculator">12 / 112</gadget>
<output>3/28 = around 0.107143</output>
<gadget id="calculator">(3/28) * 100</gadget>
<output>75/7 = around 10.714286</output>
<result>A</result> | A | 10.7 | On a purchase of $112, a store offered a payment plan consisting of a $12 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan? | {
"A": "10.7 %",
"B": "11.7 %",
"C": "12.7 %",
"D": "13.7 %",
"E": "14.7 %"
} | multiply(divide(subtract(add(multiply(10, 12), 12), multiply(10, 12)), 112), const_100) | multiply(n2,n3)|add(n1,#0)|subtract(#1,#0)|divide(#2,n0)|multiply(#3,const_100)| | "12 * 10 + 12 = 132 ( 12 / 112 ) * 100 = 10.7 answer : a" | gain |
math_qa__fj34BaSM6PXC3Vx2 | John bought 9.25m of cloth for $425.50. Find the cost price per metre. Choose the most appropriate option.
A) 46
B) 47
C) 58
D) 56
E) 54 | <gadget id="calculator">425.5 / 9.25</gadget>
<output>46</output>
<result>A</result> | A | 46 | John bought 9.25m of cloth for $425.50. Find the cost price per metre. | {
"A": "46",
"B": "47",
"C": "58",
"D": "56",
"E": "54"
} | divide(425.5, 9.25) | divide(n1,n0) | cloth bought by john = 9.25 m cost of 9.25 m = $ 425.50 cost per metre = 425.50 ÷ 9.25 the cost of the cloth per metre = $ 46 answers : a | physics |
math_qa__MdZrMkFEI2ef2YXy | A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord E, in feet? Select the correct option:
A) 30 B) 25 C) 15 D) 10 E) 5 | <gadget id="calculator">30 / 3</gadget>
<output>10</output>
<result>D</result> | D | 10 | A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord E, in feet? | {
"A": "30",
"B": "25",
"C": "15",
"D": "10",
"E": "5"
} | divide(30, const_3) | divide(n0,const_3)| | "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . e = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d" | general |
math_qa__IdZwNTaL9oi0bLeJ | A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before is Choices: A) 20 min B) 35 min C) 50 min D) 70 min E) none | <gadget id="calculator">40 * 10</gadget>
<output>400</output>
<gadget id="calculator">400 / 8</gadget>
<output>50</output>
<result>C</result> | C | 50 | A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before is | {
"A": "20 min",
"B": "35 min",
"C": "50 min",
"D": "70 min",
"E": "none"
} | divide(multiply(40, 10), 8) | multiply(n1,n2)|divide(#0,n0) | solution let original diameter be d metres . then , its circumference = ( π d ) metres . time taken to cover ( 8 π d ) m = 40 min . new diameter = ( 10 d ) m . then , its circumference = ( π x 10 d ) m . time taken to go round it once ‹ = › [ 40 / 8 π d x 10 π d ] m ‹ = › 50 min . answer c | physics |
math_qa__VRLUxRLXd6whFR2g | a will was written such that an estate would be divided among 3 guys with the remainder donated to charity . one stipulation in the will is that no one from the guys can receive an amount within 30 % of another ' s amount . if one of the guys received $ 20000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 3 guys ? Choose the most appropriate option:
A) $ 4096 B) $ 5904 C) $ 7892 D) $ 10052 E) $ 20736 | <gadget id="calculator">20_000 / 2</gadget>
<output>10_000</output>
<result>D</result> | D | 10,052 | a will was written such that an estate would be divided among 3 guys with the remainder donated to charity . one stipulation in the will is that no one from the guys can receive an amount within 30 % of another ' s amount . if one of the guys received $ 20000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 3 guys ? | {
"A": "$ 4096",
"B": "$ 5904",
"C": "$ 7892",
"D": "$ 10052",
"E": "$ 20736"
} | divide(20000, const_2) | divide(n2,const_2) | 1 st - 20000 . 2 nd - 0.7 * 20000 = 14000 3 rd - 0.7 * 14000 = 9800 range = 20000 - 9800 = 10200 . answer : d . | general |
math_qa__hAIpBZRMkmzUANpA | Mukesh borrowed a sum of Rs. 10000 at simple interest from a bank. After two years he takes Rs. 12000 more as loan and discharge all the debt at the end of next 3 years depositing Rs. 27160 to the bank. What is the rate of interest per annum?
Choose one:
A) 5 %
B) 6 %
C) 8 %
D) 10 %
E) none of these | <gadget id="calculator">10_000 + 12_000</gadget>
<output>22_000</output>
<gadget id="calculator">27_160 - 22_000</gadget>
<output>5_160</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">10_000 * 5</gadget>
<output>50_000</output>
<gadget id="calculator">12_000 * 3</gadget>
<output>36_000</output>
<gadget id="calculator">50_000 + 36_000</gadget>
<output>86_000</output>
<gadget id="calculator">5_160 / 86_000</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 100</gadget>
<output>6</output>
<result>B</result> | B | 6 | Mukesh borrowed a sum of Rs. 10000 at simple interest from a bank. After two years he takes Rs. 12000 more as loan and discharge all the debt at the end of next 3 years depositing Rs. 27160 to the bank. What is the rate of interest per annum? | {
"A": "5 %",
"B": "6 %",
"C": "8 %",
"D": "10 %",
"E": "none of these"
} | multiply(divide(subtract(27160, add(10000, 12000)), add(multiply(10000, add(3, const_2)), multiply(12000, 3))), const_100) | add(n0,n1)|add(n2,const_2)|multiply(n1,n2)|multiply(n0,#1)|subtract(n3,#0)|add(#3,#2)|divide(#4,#5)|multiply(#6,const_100) | si = 27160 - ( principal amount ) = 27160 - 22000 = 5160 . now , ( 10000 * 5 * r / 100 ) + ( 12000 * 3 * r / 100 ) = 5160 . 500 r + 360 r = 5160 . . . . . rate = 6 % . answer : b | general |
math_qa__KEDEUvU3r2h5F07n | a player holds 13 cards of 4 suits , of which 7 are black and 6 are red . there are twice as many diamonds as spades and twice as many hearts as diamonds . how many clubs does he hold
Choices:
A) 4
B) 5
C) 6
D) 7
E) 8 | <gadget id="calculator">13 - 7</gadget>
<output>6</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 6</gadget>
<output>1</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<result>C</result> | C | 6 | a player holds 13 cards of 4 suits , of which 7 are black and 6 are red . there are twice as many diamonds as spades and twice as many hearts as diamonds . how many clubs does he hold | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | subtract(7, divide(subtract(13, 7), add(4, const_2))) | add(n1,const_2)|subtract(n0,n2)|divide(#1,#0)|subtract(n2,#2) | explanation : clearly , the black cards are either clubs or spades while the red cards are either diamonds or hearts . let the number of spades be x . then , number of clubs = ( 7 - x ) . number of diamonds = 2 x number of spades = 2 x ; number of hearts = 2 x number of diamonds = 4 x . total number of cards = x + 2 x + 4 x + 7 - x = 6 x + 7 . therefore 6 x + 7 = 13 6 x = 6 x - 1 . hence , number of clubs = ( 7 - x ) = 6 . answer : c | probability |
math_qa__t9y8KsI5OqTm6JLt | A worker can load one truck in 6 hours. A second worker can load the same truck in 8 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck? Answers:
A) 2.6
B) 2.8
C) 3.0
D) 3.2
E) 3.4 | <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 / (7/24)</gadget>
<output>24/7 = around 3.428571</output>
<result>E</result> | E | 3.4 | A worker can load one truck in 6 hours. A second worker can load the same truck in 8 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck? | {
"A": "2.6",
"B": "2.8",
"C": "3.0",
"D": "3.2",
"E": "3.4"
} | inverse(add(divide(const_1, 6), divide(const_1, 8))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2)| | "the workers fill the truck at a rate of 1 / 6 + 1 / 8 = 14 / 48 = 7 / 24 of the truck per hour . then the time to fill one truck is 24 / 7 which is about 3.4 hours . the answer is e ." | physics |
math_qa__xH4sGihqa3jaK8MU | here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ? Choose the correct choice from the following answers: A) 11 B) 15 C) 18 D) 17 E) 19 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/5) + (1/3)</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">(1/3) - (1/5)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(2/15) * 3</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(8/15) + (2/5)</gadget>
<output>14/15 = around 0.933333</output>
<gadget id="calculator">1 - (14/15)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / (1/15)</gadget>
<output>15</output>
<result>B</result> | B | 15 | here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ? | {
"A": "11",
"B": "15",
"C": "18",
"D": "17",
"E": "19"
} | divide(const_1, subtract(const_1, add(add(divide(const_1, add(const_1, const_4)), divide(const_1, const_3)), multiply(subtract(divide(const_1, const_3), divide(const_1, add(const_1, const_4))), 3)))) | add(const_1,const_4)|divide(const_1,const_3)|divide(const_1,#0)|add(#2,#1)|subtract(#1,#2)|multiply(n0,#4)|add(#3,#5)|subtract(const_1,#6)|divide(const_1,#7) | b 15 the number of bees was 15 | general |
math_qa__7cNc1kwOFTWqWhHy | Product of two co-prime numbers is 117. Their L.C.M should be Choose the correct option
A) 222 B) 117 C) 278 D) 767 E) 298 | <gadget id="calculator">117 * 1</gadget>
<output>117</output>
<result>B</result> | B | 117 | Product of two co-prime numbers is 117. Their L.C.M should be | {
"A": "222",
"B": "117",
"C": "278",
"D": "767",
"E": "298"
} | multiply(117, const_1) | multiply(n0,const_1) | h . c . f of co - prime numbers is 1 . so , l . c . m = \ inline \ fn _ jvn \ frac { 117 } { 1 } = 117 answer : b | general |
math_qa__vtcOAh8HS5uUt3nB | If to a certain number, 720 be added, and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462. What is that number?
Choose the correct choice from the following answers
A) 1280 B) 1270 C) 1260 D) 1250 E) none | <gadget id="calculator">125 * 7_392</gadget>
<output>924_000</output>
<gadget id="calculator">462 * 720</gadget>
<output>332_640</output>
<gadget id="calculator">924_000 - 332_640</gadget>
<output>591_360</output>
<gadget id="calculator">591_360 / 462</gadget>
<output>1_280</output>
<result>A</result> | A | 1,280 | If to a certain number, 720 be added, and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462. What is that number? | {
"A": "1280",
"B": "1270",
"C": "1260",
"D": "1250",
"E": "none"
} | divide(subtract(multiply(125, 7392), multiply(462, 720)), 462) | multiply(n1,n2)|multiply(n0,n3)|subtract(#0,#1)|divide(#2,n3) | solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a | general |
math_qa__Jyu0eXCLkJVY8JII | A cricket player whose bowling average was 22.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match? Answers
A) 64 B) 72 C) 121 D) 984 E) 108 | <gadget id="calculator">22.5 - 0.5</gadget>
<output>22</output>
<gadget id="calculator">22 * 5</gadget>
<output>110</output>
<gadget id="calculator">110 - 52</gadget>
<output>58</output>
<gadget id="calculator">58 / 0.5</gadget>
<output>116</output>
<result>C</result> | C | 121 | A cricket player whose bowling average was 22.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match? | {
"A": "64",
"B": "72",
"C": "121",
"D": "984",
"E": "108"
} | divide(subtract(multiply(subtract(22.5, 0.5), 5), 52), 0.5) | subtract(n0,n3)|multiply(n1,#0)|subtract(#1,n2)|divide(#2,n3) | average = total runs / total wickets total runs after last match = 22.5 w + 52 total wickets after last match = w + 5 ( 22.5 w + 52 ) / ( w + 5 ) = 22.5 - 0.5 = 22 w = 116 so total wickets aftr last match = w + 5 = 121 answer : c | general |
math_qa__1U2yT77pQ9XYTCgB | The radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is Select the correct option.
A) 200 B) 250 C) 300 D) 500 E) none of these | <gadget id="calculator">1_000 * 66</gadget>
<output>66_000</output>
<gadget id="calculator">100 * 66_000</gadget>
<output>6_600_000</output>
<gadget id="calculator">60 * 1</gadget>
<output>60</output>
<gadget id="calculator">6_600_000 / 60</gadget>
<output>110_000</output>
<gadget id="calculator">2 * 35</gadget>
<output>70</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">2 + 12</gadget>
<output>14</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 + 8</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">3 + (7/50)</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">70 * (157/50)</gadget>
<output>1_099/5 = around 219.8</output>
<gadget id="calculator">110_000 / (1_099/5)</gadget>
<output>550_000/1_099 = around 500.454959</output>
<result>D</result> | D | 500 | The radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is | {
"A": "200",
"B": "250",
"C": "300",
"D": "500",
"E": "none of these"
} | divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 35), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2))))) | multiply(n1,const_1000)|multiply(const_1,const_60)|multiply(const_3,const_4)|multiply(const_2,const_4)|multiply(n0,const_2)|add(#2,const_2)|add(#3,const_2)|multiply(#0,const_100)|divide(#7,#1)|power(#6,const_2)|divide(#5,#9)|add(#10,const_3)|multiply(#11,#4)|divide(#8,#12) | radius of the wheel of bus = 35 cm . then , circumference of wheel = 2 ï € r = 70 ï € = 220 cm distance covered by bus in 1 minute = 66 â „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 220 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 220 = 500 answer d | physics |
math_qa__Z3D7Lyb8HaeLayMw | A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? Choose the correct answer.
A) 14 B) 13 C) 11 D) 9 E) 7 | <gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/24) / 2</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(1/24) + (1/48)</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/16) + (1/30)</gadget>
<output>23/240 = around 0.095833</output>
<gadget id="calculator">(1/30) / 2</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(23/240) + (1/60)</gadget>
<output>9/80 = around 0.1125</output>
<gadget id="calculator">1 / (9/80)</gadget>
<output>80/9 = around 8.888889</output>
<result>D</result> | D | 9 | A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? | {
"A": "14",
"B": "13",
"C": "11",
"D": "9",
"E": "7"
} | inverse(add(add(add(divide(const_1, multiply(12, const_2)), divide(divide(const_1, multiply(12, const_2)), const_2)), divide(const_1, multiply(15, const_2))), divide(divide(const_1, multiply(15, const_2)), const_2))) | multiply(n0,const_2)|multiply(n1,const_2)|divide(const_1,#0)|divide(const_1,#1)|divide(#2,const_2)|divide(#3,const_2)|add(#2,#4)|add(#6,#3)|add(#7,#5)|inverse(#8) | machine e finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of e = 5 shifts / day rate of b = 4 shifts / day rate of ( e + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d | physics |
math_qa__rugTu30jxc76jZaL | A train 110 m long is running with a speed of 84 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? Answers.
A) 7 sec B) 6 sec C) 8 sec D) 4.4 sec E) 2 sec | <gadget id="calculator">84 + 6</gadget>
<output>90</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>
<gadget id="calculator">110 / 25</gadget>
<output>22/5 = around 4.4</output>
<result>D</result> | D | 4.4 | A train 110 m long is running with a speed of 84 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": "7 sec",
"B": "6 sec",
"C": "8 sec",
"D": "4.4 sec",
"E": "2 sec"
} | divide(110, multiply(add(84, 6), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | "speed of train relative to man = 84 + 6 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . time taken to pass the men = 110 / 25 = 4.4 sec . answer : d" | physics |
math_qa__tekAAwcA2u9nE5OR | A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 25 payments is to be $500; each of the remaining payments is to be $100 more than each of the first 25 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year? Options:
A) 500 B) 450 C) 552 D) 600 E) 400 | <gadget id="calculator">25 * 500</gadget>
<output>12_500</output>
<gadget id="calculator">500 + 100</gadget>
<output>600</output>
<gadget id="calculator">52 - 25</gadget>
<output>27</output>
<gadget id="calculator">600 * 27</gadget>
<output>16_200</output>
<gadget id="calculator">12_500 + 16_200</gadget>
<output>28_700</output>
<gadget id="calculator">28_700 / 52</gadget>
<output>7_175/13 = around 551.923077</output>
<result>C</result> | C | 552 | A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 25 payments is to be $500; each of the remaining payments is to be $100 more than each of the first 25 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year? | {
"A": "500",
"B": "450",
"C": "552",
"D": "600",
"E": "400"
} | divide(add(multiply(25, 500), multiply(add(500, 100), subtract(52, 25))), 52) | add(n4,n5)|multiply(n3,n4)|subtract(n0,n3)|multiply(#0,#2)|add(#1,#3)|divide(#4,n0)| | "total = 500 ( 25 ) + 600 ( 27 ) number of installments = 52 average = total / number of installments = 552 approximately answer : c" | general |
math_qa__mPHiaxU07KT7xBxA | There are 6 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? Choose the correct choice:
A) 90
B) 120
C) 225
D) 180
E) 200 | <gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">24 * 36</gadget>
<output>864</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">864 / 4</gadget>
<output>216</output>
<result>C</result> | C | 225 | There are 6 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? | {
"A": "90",
"B": "120",
"C": "225",
"D": "180",
"E": "200"
} | divide(multiply(multiply(6, const_4), multiply(6, 6)), power(factorial(2), 2)) | factorial(n2)|multiply(n0,const_4)|multiply(n0,n1)|multiply(#1,#2)|power(#0,n2)|divide(#3,#4)| | "number of ways of selecting 2 fiction books = 6 c 2 number of ways of selecting 2 non fiction books = 6 c 2 6 c 2 * 6 c 2 = 15 * 15 = 225 answer : c" | general |
math_qa__CiLQXKSi5DlBACC1 | A certain school implemented a reading program for its students, with the goal of getting each student to read 4 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
Choose the correct choice from the following:
A) 20 cs B) cs / 2 C) 48 cs D) ( 2 cs ) / 12 E) ( 24 c ) / s | <gadget id="calculator">4 * 12</gadget>
<output>48</output>
<result>C</result> | C | 48 | A certain school implemented a reading program for its students, with the goal of getting each student to read 4 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year? | {
"A": "20 cs",
"B": "cs / 2",
"C": "48 cs",
"D": "( 2 cs ) / 12",
"E": "( 24 c ) / s"
} | multiply(4, const_12) | multiply(n0,const_12)| | "ans : c solution : simple multiplication s students , c classes , 4 books / month = 48 books a year total number of books = 48 cs" | general |
math_qa__3npk3xIs52KCDoe9 | How many natural numbers are there between 43 and 200 which are exactly divisible by 6? Select: A) 26 B) 25 C) 24 D) 22 E) 23 | <gadget id="calculator">200 - 4</gadget>
<output>196</output>
<gadget id="calculator">43 + 1</gadget>
<output>44</output>
<gadget id="calculator">196 - 44</gadget>
<output>152</output>
<gadget id="calculator">152 / 6</gadget>
<output>76/3 = around 25.333333</output>
<gadget id="calculator">(76/3) + 1</gadget>
<output>79/3 = around 26.333333</output>
<result>A</result> | A | 26 | How many natural numbers are there between 43 and 200 which are exactly divisible by 6? | {
"A": "26",
"B": "25",
"C": "24",
"D": "22",
"E": "23"
} | add(divide(subtract(subtract(200, const_4), add(43, const_1)), 6), const_1) | add(n0,const_1)|subtract(n1,const_4)|subtract(#1,#0)|divide(#2,n2)|add(#3,const_1)| | "43 / 6 = 7 , remainder = 1 . hence 5 more should be added to 43 to get the minimum number divisible by 6 between 43 and 200 . = > minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48 200 / 6 = 33 , remainder = 2 . hence 2 should be decreased from 200 to get the maximum number divisible by 6 between 43 and 200 . = > maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198 hence , natural numbers numbers divisible by 6 between 43 and 200 are 48 , 54 , 60 , . . . 198 this is arithmetic progression with a = 48 , d = 6 , l = 198 number of terms = ( l − a ) / d + 1 = ( 198 − 48 ) / 6 + 1 = 150 / 6 + 1 = 25 + 1 = 26 answer is a" | general |
math_qa__LantUJKe7BTFhGzV | Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed? Select: A) 110 B) 1,100 C) 9,900 D) 10,000 E) 12,100 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">16 - 5</gadget>
<output>11</output>
<gadget id="calculator">10 * 11</gadget>
<output>110</output>
<gadget id="calculator">9 * 110</gadget>
<output>990</output>
<gadget id="calculator">990 * 10</gadget>
<output>9_900</output>
<result>C</result> | C | 9,900 | Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed? | {
"A": "110",
"B": "1,100",
"C": "9,900",
"D": "10,000",
"E": "12,100"
} | multiply(multiply(subtract(const_10, const_1), multiply(add(6, 4), subtract(16, 5))), const_10) | add(n0,n2)|subtract(n3,n1)|subtract(const_10,const_1)|multiply(#0,#1)|multiply(#3,#2)|multiply(#4,const_10)| | "p can take a total of 10 * 11 co - ordinates . for a given p , r can take a total of 9 co - ordinates and q can take a total of 10 co - ordinates . hence , total = 110 * 9 * 10 = 9900 ans : c" | general |
math_qa__xjzYvAUaPeFchEYx | In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 160 marks, the no of questions he attempts correctly is : Choose the correct choice from the following answers:
A) 35 B) 38 C) 40 D) 42 E) 44 | <gadget id="calculator">160 + 60</gadget>
<output>220</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">220 / 5</gadget>
<output>44</output>
<result>E</result> | E | 44 | In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 160 marks, the no of questions he attempts correctly is : | {
"A": "35",
"B": "38",
"C": "40",
"D": "42",
"E": "44"
} | divide(add(160, 60), add(4, 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)| | "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 160 = > 5 x = 220 = > x = 44 answer : e" | physics |
math_qa__ufyXtOXlywNI9pm0 | A batsman makes a score of 50 runs in the 17th inning and thus increases his averages by 2. What is his average after 17th inning?
Choices: A) 39 B) 18 C) 42 D) 40.5 E) 41.5 | <gadget id="calculator">17 * 2</gadget>
<output>34</output>
<gadget id="calculator">50 - 34</gadget>
<output>16</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<result>B</result> | B | 18 | A batsman makes a score of 50 runs in the 17th inning and thus increases his averages by 2. What is his average after 17th inning? | {
"A": "39",
"B": "18",
"C": "42",
"D": "40.5",
"E": "41.5"
} | add(subtract(50, multiply(17, 2)), 2) | multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)| | "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b" | general |
math_qa__CAjZUE3yu94KWnwB | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 7.5), (8, 0), (0, -7.5), (-8, 0)? Answers.
A) 56
B) 88
C) 112
D) 116
E) 120 | <gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">7.5 * 2</gadget>
<output>15</output>
<gadget id="calculator">(16 * 15) / 2</gadget>
<output>120</output>
<result>E</result> | E | 120 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 7.5), (8, 0), (0, -7.5), (-8, 0)? | {
"A": "56",
"B": "88",
"C": "112",
"D": "116",
"E": "120"
} | rhombus_area(multiply(8, const_2), multiply(7.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)| | "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer" | geometry |
math_qa__b98iH5NNko0DSmhk | Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? Choose the correct choice from the following answers
A) 14 % B) 16 % C) 18 % D) 21.6 % E) of these | <gadget id="calculator">40_000 + 13_000</gadget>
<output>53_000</output>
<gadget id="calculator">64_900 - 53_000</gadget>
<output>11_900</output>
<gadget id="calculator">11_900 / 53_000</gadget>
<output>119/530 = around 0.224528</output>
<gadget id="calculator">(119/530) * 100</gadget>
<output>1_190/53 = around 22.45283</output>
<result>D</result> | D | 21.6 | Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? | {
"A": "14 %",
"B": "16 %",
"C": "18 %",
"D": "21.6 %",
"E": "of these"
} | multiply(divide(subtract(64900, add(40000, 13000)), add(40000, 13000)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | "total cp = rs . 40000 + rs . 13000 = rs . 53000 and sp = rs . 64900 profit ( % ) = ( 64900 - 53000 ) / 55000 * 100 = 21.6 % answer : d" | gain |
math_qa__QI1numBose5GvaL6 | On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 44 centimeters assuming that 1-inch is 2.54 centimeters? Pick one.
A) 174.2 B) 277 C) 288.1 D) 296 E) 282.4 | <gadget id="calculator">44 / 2.54</gadget>
<output>17.322835</output>
<gadget id="calculator">24 / 1.5</gadget>
<output>16</output>
<gadget id="calculator">17.322835 * 16</gadget>
<output>277.16536</output>
<result>B</result> | B | 277 | On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 44 centimeters assuming that 1-inch is 2.54 centimeters? | {
"A": "174.2",
"B": "277",
"C": "288.1",
"D": "296",
"E": "282.4"
} | multiply(divide(44, 2.54), divide(24, 1.5)) | divide(n2,n4)|divide(n1,n0)|multiply(#0,#1)| | "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 44 cm . : 44 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 44 / ( 3.81 ) = 277 answer will be b ." | physics |
math_qa__7dS67hFc0JbOdfVn | If 0.12 ÷ x2 = 12, than x = ? Select
A) 0.001 B) 0.01 C) 0.1 D) 1 E) 0 | <gadget id="calculator">0.12 / 12</gadget>
<output>0.01</output>
<gadget id="calculator">0.01 ** (1/2)</gadget>
<output>0.1</output>
<result>C</result> | C | 0.1 | If 0.12 ÷ x2 = 12, than x = ? | {
"A": "0.001",
"B": "0.01",
"C": "0.1",
"D": "1",
"E": "0"
} | sqrt(divide(0.12, 12)) | divide(n0,n2)|sqrt(#0) | explanation : 0.12 ÷ x 2 = 12 = > 0.12 / x 2 = 12 = > x 2 = 0.12 / 12 = 0.01 = > x = 0.1 answer : option c | general |
math_qa__qDbTI0MDc30mUBXC | A woman complete a journey in 30 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. Choose the correct choice from the following choices: A) 334 km . B) 216 km . C) 314 km . D) 224 km . E) 672 km . | <gadget id="calculator">30 * 24</gadget>
<output>720</output>
<gadget id="calculator">24 + 21</gadget>
<output>45</output>
<gadget id="calculator">720 / 45</gadget>
<output>16</output>
<gadget id="calculator">16 * 21</gadget>
<output>336</output>
<gadget id="calculator">336 * 2</gadget>
<output>672</output>
<result>E</result> | E | 672 | A woman complete a journey in 30 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. | {
"A": "334 km .",
"B": "216 km .",
"C": "314 km .",
"D": "224 km .",
"E": "672 km ."
} | multiply(multiply(divide(multiply(30, 24), add(24, 21)), 21), const_2) | add(n1,n2)|multiply(n0,n2)|divide(#1,#0)|multiply(n1,#2)|multiply(#3,const_2)| | "0.5 x / 21 + 0.5 x / 24 = 30 - - > x / 21 + x / 24 = 60 - - > x = 672 km . e" | physics |
math_qa__6dXA7hTziEljGGRK | In a class of 35 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
Choose one.
A) 6 B) 8 C) 10 D) 12 E) 14 | <gadget id="calculator">26 + 20</gadget>
<output>46</output>
<gadget id="calculator">46 - 17</gadget>
<output>29</output>
<gadget id="calculator">35 - 29</gadget>
<output>6</output>
<result>A</result> | A | 6 | In a class of 35 students 26 play football and play 20 long tennis, if 17 play above, many play neither? | {
"A": "6",
"B": "8",
"C": "10",
"D": "12",
"E": "14"
} | subtract(35, subtract(add(26, 20), 17)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)| | "26 + 20 - 17 = 29 35 - 29 = 6 play neither answer is a" | other |
math_qa__0n5UTWark0ZbzRHt | A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? Choose one:
A) 480
B) 488
C) 882
D) 269
E) 298 | <gadget id="calculator">24 * 20</gadget>
<output>480</output>
<result>A</result> | A | 480 | A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? | {
"A": "480",
"B": "488",
"C": "882",
"D": "269",
"E": "298"
} | multiply(24, 20) | multiply(n0,n2) | 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a | physics |
math_qa__n08JuhTFk0Iabotx | The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is? Answers: A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">21 * 6</gadget>
<output>126</output>
<gadget id="calculator">7 * 16</gadget>
<output>112</output>
<gadget id="calculator">126 - 112</gadget>
<output>14</output>
<gadget id="calculator">21 - 16</gadget>
<output>5</output>
<gadget id="calculator">14 / 5</gadget>
<output>14/5 = around 2.8</output>
<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(14/5) + (1/5)</gadget>
<output>3</output>
<result>A</result> | A | 3 | The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | add(divide(subtract(multiply(21, 6), multiply(7, 16)), subtract(21, 16)), divide(const_2, const_10)) | divide(const_2,const_10)|multiply(n0,n3)|multiply(n1,n2)|subtract(n3,n2)|subtract(#1,#2)|divide(#4,#3)|add(#5,#0) | let x be subtracted . then , 6 - x 7 - x < 16 21 21 ( 6 - x ) < 16 ( 7 - x ) 5 x > 14 x > 2.8 least such whole number is 3 . answer : a | other |
math_qa__hOZKnk3MIVRSgkq0 | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased? Choose the most appropriate option: A) 12.5 % B) 20 % C) 25 % D) 50 % E) 100 % | <gadget id="calculator">10 * 4</gadget>
<output>40</output>
<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">(4/5) * 10</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent should the number of hours worked be increased? | {
"A": "12.5 %",
"B": "20 %",
"C": "25 %",
"D": "50 %",
"E": "100 %"
} | multiply(divide(subtract(divide(multiply(const_10, const_4), multiply(divide(subtract(const_100, 20), const_100), const_10)), const_4), const_4), const_100) | multiply(const_10,const_4)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#2,const_10)|divide(#0,#3)|subtract(#4,const_4)|divide(#5,const_4)|multiply(#6,const_100)| | "assume hours worked : 10 hours hourly wage : 10 $ weekly wage : 100 $ after decrease of 20 % in hourly wage would become 8 $ hours worked would have to be 12.5 hours in order to maintain weekly wage of 100 $ % increase in number of hours worked = ( 12.5 - 10 ) / 10 = 0.25 * 100 = 25 % answer is c" | general |
math_qa__dAWXYL9uTAY7Jgu3 | Patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils. The cost of 60 pencils is how many times the selling price of 60 pencils? Pick one: A) 0.75 B) 0.8 C) 1 D) 1.33 E) 1.75 | <gadget id="calculator">60 + 20</gadget>
<output>80</output>
<gadget id="calculator">60 / 80</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / (3/4)</gadget>
<output>4/3 = around 1.333333</output>
<result>D</result> | D | 1.33 | Patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils. The cost of 60 pencils is how many times the selling price of 60 pencils? | {
"A": "0.75",
"B": "0.8",
"C": "1",
"D": "1.33",
"E": "1.75"
} | inverse(divide(60, add(60, 20))) | add(n0,n1)|divide(n0,#0)|inverse(#1)| | "say the cost price of 60 pencils was $ 60 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 60 - 60 p = 20 p - - > p = 3 / 4 . ( cost price ) / ( selling price ) = 1 / ( 3 / 4 ) = 4 / 3 = 1.33 . answer : d ." | general |
math_qa__1Ve2LfeMgw9izMR8 | In a group of 800 people, 1/5 play at least one instrument, 128 play two or more. What is the probability that one student play exactly one instrument?
Choices:
A) 2 / 125 B) 3 / 125 C) 2 / 25 D) 3 / 25 E) 1 / 25 | <gadget id="calculator">800 * 1</gadget>
<output>800</output>
<gadget id="calculator">800 / 5</gadget>
<output>160</output>
<gadget id="calculator">160 - 128</gadget>
<output>32</output>
<gadget id="calculator">32 / 800</gadget>
<output>1/25 = around 0.04</output>
<result>E</result> | E | 0.04 | In a group of 800 people, 1/5 play at least one instrument, 128 play two or more. What is the probability that one student play exactly one instrument? | {
"A": "2 / 125",
"B": "3 / 125",
"C": "2 / 25",
"D": "3 / 25",
"E": "1 / 25"
} | divide(subtract(divide(multiply(800, 1), 5), 128), 800) | multiply(n0,n1)|divide(#0,n2)|subtract(#1,n3)|divide(#2,n0)| | "p ( playing 2 or more instruments ) = 128 / 800 = 4 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 4 / 25 = 1 / 25 . answer e ." | general |
math_qa__cUMwqK1ioHJJOD3Z | The present worth of a sum due sometime hence is Rs. 576 and the banker’s gain is Rs. 16. The true discount is :
Select:
A) 36
B) 52
C) 66
D) 96
E) none | <gadget id="calculator">576 * 16</gadget>
<output>9_216</output>
<gadget id="calculator">9_216 ** (1/2)</gadget>
<output>96</output>
<result>D</result> | D | 96 | The present worth of a sum due sometime hence is Rs. 576 and the banker’s gain is Rs. 16. The true discount is : | {
"A": "36",
"B": "52",
"C": "66",
"D": "96",
"E": "none"
} | sqrt(multiply(576, 16)) | multiply(n0,n1)|sqrt(#0)| | "sol . t . d . = √ p . w . * b . g . = √ 576 * 16 = 96 . answer d" | gain |
math_qa__VQTyM6N4Jdskejco | The distance from City A to City B is 60 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob? Choose the correct option
A) 45 B) 48 C) 50 D) 52 E) 60 | <gadget id="calculator">60 / 40</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(3/2) - (1/2)</gadget>
<output>1</output>
<gadget id="calculator">60 / 1</gadget>
<output>60</output>
<result>E</result> | E | 60 | The distance from City A to City B is 60 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob? | {
"A": "45",
"B": "48",
"C": "50",
"D": "52",
"E": "60"
} | divide(60, subtract(divide(60, 40), divide(30, const_60))) | divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)| | "the time it takes bob to drive to city b is 60 / 40 = 1.5 hours . alice needs to take less than 1 hour for the trip . alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour . the answer is e ." | physics |
math_qa__FI2PWoXGd5sab1GV | If 18 persons can build a wall 140 m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is? Options:
A) 28 B) 18 C) 24 D) 21 E) 16 | <gadget id="calculator">18 * 100</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 * 42</gadget>
<output>75_600</output>
<gadget id="calculator">140 * 30</gadget>
<output>4_200</output>
<gadget id="calculator">75_600 / 4_200</gadget>
<output>18</output>
<result>B</result> | B | 18 | If 18 persons can build a wall 140 m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is? | {
"A": "28",
"B": "18",
"C": "24",
"D": "21",
"E": "16"
} | divide(multiply(multiply(18, 100), 42), multiply(140, 30)) | multiply(n0,n4)|multiply(n1,n3)|multiply(n2,#0)|divide(#2,#1)| | "explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x 140 x 30 x x = 100 x 18 x 42 or x = 18 answer : b" | physics |
math_qa__1FjI1xtCQqaUNJmV | A pharmaceutical company received $7 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Choose the correct choice: A) 8 % B) 15 % C) 45 % D) 52 % E) 76 % | <gadget id="calculator">7 / 20</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">35 - (25/3)</gadget>
<output>80/3 = around 26.666667</output>
<gadget id="calculator">(80/3) / 35</gadget>
<output>16/21 = around 0.761905</output>
<gadget id="calculator">(16/21) * 100</gadget>
<output>1_600/21 = around 76.190476</output>
<result>E</result> | E | 76 | A pharmaceutical company received $7 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales? | {
"A": "8 %",
"B": "15 %",
"C": "45 %",
"D": "52 %",
"E": "76 %"
} | multiply(divide(subtract(multiply(divide(7, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(7, 20), const_100)), const_100) | divide(n0,n1)|divide(n2,n3)|multiply(#0,const_100)|multiply(#1,const_100)|subtract(#2,#3)|divide(#4,#2)|multiply(#5,const_100)| | "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 7 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 7 / 20 ) x 60 = 21 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 9 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 21 ) / 21 ] x 100 - 1600 / 21 x 100 at this point we can stop and consider the answer choices . since we know that 1600 / 21 is just a bit less than ½ , we know that - 1600 / 21 x 100 is about a 76 % decrease . answer e ." | general |
math_qa__62OlNxuuobPwQ1dG | An error 6% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: Choose the most appropriate option.
A) 12.36 B) 8.36 C) 9.36 D) 10.36 E) 11.36 | <gadget id="calculator">100 + 6</gadget>
<output>106</output>
<gadget id="calculator">106 ** 2</gadget>
<output>11_236</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">11_236 - 10_000</gadget>
<output>1_236</output>
<gadget id="calculator">1_236 * 100</gadget>
<output>123_600</output>
<gadget id="calculator">123_600 / 10_000</gadget>
<output>309/25 = around 12.36</output>
<result>A</result> | A | 12.36 | An error 6% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: | {
"A": "12.36",
"B": "8.36",
"C": "9.36",
"D": "10.36",
"E": "11.36"
} | divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | "explanation : 100 cm is read as 106 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 106 × 106 ) cm 2 = 11236 ( a 2 - a 1 ) = 11236 - 10000 = 1236 = > 1236 / 10000 * 100 = 12.36 answer : a" | gain |
math_qa__LVuVCeJmn5Ra23Lh | What is the decimal equivalent of (1/9)^2? Select:
A) 0.0123 B) 0.0625 C) 0.16 D) 0.25 E) 0.5 | <gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/9) ** 2</gadget>
<output>1/81 = around 0.012346</output>
<result>A</result> | A | 0.0123 | What is the decimal equivalent of (1/9)^2? | {
"A": "0.0123",
"B": "0.0625",
"C": "0.16",
"D": "0.25",
"E": "0.5"
} | power(divide(1, 9), 2) | divide(n0,n1)|power(#0,n2)| | "( 1 / 9 ) ² = ( 1 / 9 ) ( 1 / 9 ) = 1 / 81 approach # 1 : use long division to divide 81 into 1 to get 1 / 81 = 0.0123 a" | general |
math_qa__g7c9DPHrtxWXbKzk | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 30 overs to reach the target of 282 runs?
Select the correct option
A) 6.25 B) 5.5 C) 7.4 D) 8.3 E) 6.2 | <gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 30</gadget>
<output>25/3 = around 8.333333</output>
<result>D</result> | D | 8.3 | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 30 overs to reach the target of 282 runs? | {
"A": "6.25",
"B": "5.5",
"C": "7.4",
"D": "8.3",
"E": "6.2"
} | divide(subtract(282, multiply(10, 3.2)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 30 run rate needed = 250 / 30 = 8.3 answer : option d" | gain |
math_qa__nvnVafuEoW5aIhHv | With a slope of 4, with a straight line in the xy- plane which has a point with x-coordinate of the point 14 and y-coordinate 19, find the y-intercept.
Select
A) - 19
B) 18
C) - 37
D) 50
E) 37 | <gadget id="calculator">14 * 4</gadget>
<output>56</output>
<gadget id="calculator">19 - 56</gadget>
<output>-37</output>
<result>C</result> | C | -37 | With a slope of 4, with a straight line in the xy- plane which has a point with x-coordinate of the point 14 and y-coordinate 19, find the y-intercept. | {
"A": "- 19",
"B": "18",
"C": "- 37",
"D": "50",
"E": "37"
} | subtract(19, multiply(14, 4)) | multiply(n0,n1)|subtract(n2,#0) | eq of line = y = mx + c m = 4 x = 14 y = 19 c = y - mx substitute given : c = 19 - ( 4 ) ( 14 ) c = - 37 correct option is c | general |
math_qa__Z8PkRNh5jKLQlOna | Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? Answers.
A) 1
B) 4
C) 9
D) 13
E) 16 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<result>E</result> | E | 16 | Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? | {
"A": "1",
"B": "4",
"C": "9",
"D": "13",
"E": "16"
} | multiply(4, 4) | multiply(n1,n2)| | "number of cups flour needed for 3 ounces of butter = 4 number of cups flour needed for 1 ounce of butter = 4 / 3 number of cups flour needed for 12 ounces of butter = 4 / 3 * 12 = 16 answer e" | general |
math_qa__pxU4j0yNkoTGCzPc | Excluding stoppages, the speed of a bus is 52 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Choose the correct choice from the following options.
A) 7 min
B) 6 min
C) 9 min
D) 8 min
E) 11 min | <gadget id="calculator">52 - 45</gadget>
<output>7</output>
<gadget id="calculator">7 / 52</gadget>
<output>7/52 = around 0.134615</output>
<gadget id="calculator">60 * (7/52)</gadget>
<output>105/13 = around 8.076923</output>
<result>D</result> | D | 8 | Excluding stoppages, the speed of a bus is 52 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? | {
"A": "7 min",
"B": "6 min",
"C": "9 min",
"D": "8 min",
"E": "11 min"
} | multiply(const_60, divide(subtract(52, 45), 52)) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_60)| | "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( 7 / 52 ) x 60 = 8 min answer : d" | physics |
math_qa__3upf6K12WckILO4o | A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? Answers.
A) 5729 B) 5760 C) 2889 D) 3600 E) 2799 | <gadget id="calculator">8 * 60</gadget>
<output>480</output>
<gadget id="calculator">2.5 * 480</gadget>
<output>1_200</output>
<gadget id="calculator">6 * 60</gadget>
<output>360</output>
<gadget id="calculator">480 / 360</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1_200 / (1/3)</gadget>
<output>3_600</output>
<result>D</result> | D | 3,600 | A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? | {
"A": "5729",
"B": "5760",
"C": "2889",
"D": "3600",
"E": "2799"
} | divide(multiply(2.5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 2.5 = 3600 . answer : d" | physics |
math_qa__s3mp4HkwXl83IxCd | The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 50 instead of 10 then find the correct average marks? Options
A) 78 B) 82 C) 96 D) 91 E) 85 | <gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 50</gadget>
<output>950</output>
<gadget id="calculator">950 + 10</gadget>
<output>960</output>
<gadget id="calculator">960 / 10</gadget>
<output>96</output>
<result>C</result> | C | 96 | The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 50 instead of 10 then find the correct average marks? | {
"A": "78",
"B": "82",
"C": "96",
"D": "91",
"E": "85"
} | divide(add(subtract(multiply(100, 10), 50), 10), 10) | multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)| | "correct avg marks = 100 + ( 10 - 50 ) / 10 avg = 100 - 4 = 96 answer is c" | general |
math_qa__nbhR9fSVgybakenu | P and Q can complete a work in 40 days and 24 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last? Choose the correct choice from the following answers
A) 5 days B) 10 days C) 14 days D) 22 days E) 25 days | <gadget id="calculator">16 / 40</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/40) + (1/24)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(3/5) / (1/15)</gadget>
<output>9</output>
<gadget id="calculator">16 + 9</gadget>
<output>25</output>
<result>E</result> | E | 25 | P and Q can complete a work in 40 days and 24 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last? | {
"A": "5 days",
"B": "10 days",
"C": "14 days",
"D": "22 days",
"E": "25 days"
} | add(16, divide(subtract(const_1, divide(16, 40)), add(inverse(40), inverse(24)))) | divide(n2,n0)|inverse(n0)|inverse(n1)|add(#1,#2)|subtract(const_1,#0)|divide(#4,#3)|add(n2,#5)| | "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 16 days = 16 ã — ( 1 / 40 ) = 2 / 5 remaining work = 1 â € “ 2 / 5 = 3 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 3 / 5 ) / ( 1 / 15 ) = 9 total days = 16 + 9 = 25 answer : option e" | physics |
math_qa__hkwXIaczxr7dL3Ij | In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 360 vote’s majority. What is the total number of votes polled? Answers.
A) 750 B) 700 C) 900 D) 850 E) none of these | <gadget id="calculator">100 * 360</gadget>
<output>36_000</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">70 - 30</gadget>
<output>40</output>
<gadget id="calculator">36_000 / 40</gadget>
<output>900</output>
<result>C</result> | C | 900 | In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 360 vote’s majority. What is the total number of votes polled? | {
"A": "750",
"B": "700",
"C": "900",
"D": "850",
"E": "none of these"
} | divide(multiply(const_100, 360), subtract(70, subtract(const_100, 70))) | multiply(n1,const_100)|subtract(const_100,n0)|subtract(n0,#1)|divide(#0,#2)| | "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c" | gain |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.