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__8dfv4fqTCZinaSph | A whale goes on a feeding frenzy that lasts for 12 hours. For the first hour he catches and eats 30 kilos of plankton. In every hour after the first, it consumes 2 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 600 kilos of plankton, how many kilos did he consume on the 10th hour? Choose one:
A) 36
B) 45
C) 28
D) 48
E) 52 | <gadget id="calculator">600 / 12</gadget>
<output>50</output>
<result>D</result> | D | 48 | A whale goes on a feeding frenzy that lasts for 12 hours. For the first hour he catches and eats 30 kilos of plankton. In every hour after the first, it consumes 2 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 600 kilos of plankton, how many kilos did he consume on the 10th hour? | {
"A": "36",
"B": "45",
"C": "28",
"D": "48",
"E": "52"
} | divide(600, 12) | divide(n3,n0) | therefor in 10 th hour he consume x + 2 * 9 = 30 + 18 = 48 correct option is d | general |
math_qa__1fY3j2iDjes5eL1r | Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce Choose the correct choice from the following answers:
A) 100
B) 65
C) 25
D) 11
E) 18 | <gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">1_080 / 60</gadget>
<output>18</output>
<result>E</result> | E | 18 | Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce | {
"A": "100",
"B": "65",
"C": "25",
"D": "11",
"E": "18"
} | divide(1080, multiply(divide(const_60.0, const_10), 10)) | divide(const_60.0,const_10)|multiply(n0,#0)|divide(n1,#1)| | "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 10 so , x = 10 . hence 6 x = 6 * 10 = 60 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 60 = 18 hence option ( e ) ." | general |
math_qa__P6qSTooMbCQjgB0x | A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 30 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans? Choose the correct option:
A) 65 %
B) 70 %
C) 75 %
D) 82 %
E) 95 % | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 * (7/5)</gadget>
<output>140</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">140 * (13/10)</gadget>
<output>182</output>
<gadget id="calculator">182 / 100</gadget>
<output>91/50 = around 1.82</output>
<gadget id="calculator">(91/50) - 1</gadget>
<output>41/50 = around 0.82</output>
<gadget id="calculator">(41/50) * 100</gadget>
<output>82</output>
<result>D</result> | D | 82 | A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 30 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans? | {
"A": "65 %",
"B": "70 %",
"C": "75 %",
"D": "82 %",
"E": "95 %"
} | multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(30, const_100))), const_100), const_1), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#3,const_100)|multiply(#2,#4)|divide(#5,const_100)|subtract(#6,const_1)|multiply(#7,const_100) | find the product of the two increases : ( 14 / 10 ) * ( 13 / 10 ) which is 1.82 and a 82 % increase . d | gain |
math_qa__AezmIPJZ8hCAWXKc | If 4% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is Choices:
A) 250 B) 231 C) 200 D) 288 E) 111 | <gadget id="calculator">350 - 340</gadget>
<output>10</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">10 / (1/25)</gadget>
<output>250</output>
<result>A</result> | A | 250 | If 4% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is | {
"A": "250",
"B": "231",
"C": "200",
"D": "288",
"E": "111"
} | divide(subtract(350, 340), divide(4, const_100)) | divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)| | "explanation : let c . p . be rs . x . then , 4 % of x = 350 - 340 = 10 x / 25 = 10 = > x = 250 answer : a" | gain |
math_qa__b6skS1C159xgIfqB | On increasing the price of T.V. sets by 50%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? Answers
A) 4 B) 5 C) 56 D) 20 E) 7 | <gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">150 * 20</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>
<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">150 - 130</gadget>
<output>20</output>
<result>D</result> | D | 20 | On increasing the price of T.V. sets by 50%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? | {
"A": "4",
"B": "5",
"C": "56",
"D": "20",
"E": "7"
} | subtract(add(const_100, 50), add(divide(multiply(add(const_100, 50), 20), const_100), const_100)) | add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|add(#2,const_100)|subtract(#0,#3)| | "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 150 × 80 ) = rs . 12000 increase % = 2000 / 10000 × 100 = 20 % answer : d" | gain |
math_qa__l8WYPgZwNa9dC5Wi | A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1600. The difference between the profit shares of A and C is? Choose the correct choice from the following
A) 288 B) 266 C) 155 D) 600 E) 640 | <gadget id="calculator">12_000 / 10_000</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">8_000 / 10_000</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(6/5) - (4/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 1_600</gadget>
<output>640</output>
<result>E</result> | E | 640 | A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1600. The difference between the profit shares of A and C is? | {
"A": "288",
"B": "266",
"C": "155",
"D": "600",
"E": "640"
} | multiply(subtract(divide(12000, 10000), divide(8000, 10000)), 1600) | divide(n2,n1)|divide(n0,n1)|subtract(#0,#1)|multiply(n3,#2) | ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1600 = > 5 parts out of 15 parts is rs . 1600 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1600 ) = rs . 640 answer : e | gain |
math_qa__EZxuZJ1NCMCpuNMZ | Machine A can finish a job in 4 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job? Select the correct option.
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/4) + (1/12)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/3) + (1/6)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / (1/2)</gadget>
<output>2</output>
<result>B</result> | B | 2 | Machine A can finish a job in 4 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | inverse(add(add(inverse(4), inverse(12)), inverse(6))) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)| | "the combined rate is 1 / 4 + 1 / 12 + 1 / 6 = 1 / 2 of the job per hour . the time to complete the job is 2 / 1 = 2 hours . the answer is b ." | physics |
math_qa__b0qyp5lUs2T7Tg2C | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required? Choose the correct option
A) 34
B) 92
C) 68
D) 88
E) none | <gadget id="calculator">720 / 20</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">72 + 20</gadget>
<output>92</output>
<result>B</result> | B | 92 | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required? | {
"A": "34",
"B": "92",
"C": "68",
"D": "88",
"E": "none"
} | add(multiply(divide(720, 20), const_2), 20) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | "explanation we have : l = 20 ft and lb = 720 sq . ft . so , b = 36 ft . length of fencing = ( l + 2 b ) = ( 20 + 72 ) ft = 92 ft . answer b" | geometry |
math_qa__otG2CmLb2YnlelJc | Walking with 3/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Choose the correct choice:
A) 16 min B) 26 min C) 34 min D) 20 min E) 15 min | <gadget id="calculator">5 / 3</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">5 / (5/3)</gadget>
<output>3</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<result>E</result> | E | 15 | Walking with 3/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time? | {
"A": "16 min",
"B": "26 min",
"C": "34 min",
"D": "20 min",
"E": "15 min"
} | multiply(divide(5, divide(5, 3)), 5) | divide(n1,n0)|divide(n2,#0)|multiply(n1,#1)| | "speed ratio = 1 : 3 / 5 = 5 : 3 time ratio = 3 : 5 1 - - - - - - - - 5 3 - - - - - - - - - ? è 15 answer : e" | physics |
math_qa__AMZ1ZFeuqQN5kJio | [( 3.241 x 14 ) / 100] = ? Options.
A) 0.045374 B) 4.5388 C) 453.88 D) 473.88 E) none of these | <gadget id="calculator">3.241 * 14</gadget>
<output>45.374</output>
<gadget id="calculator">45.374 / 100</gadget>
<output>0.45374</output>
<gadget id="calculator">0.45374 / 10</gadget>
<output>0.045374</output>
<result>A</result> | A | 0.045374 | [( 3.241 x 14 ) / 100] = ? | {
"A": "0.045374",
"B": "4.5388",
"C": "453.88",
"D": "473.88",
"E": "none of these"
} | divide(divide(multiply(3.241, 14), 100), const_10) | multiply(n0,n1)|divide(#0,n2)|divide(#1,const_10)| | "answer multiplying 3.241 x 14 = 4.5374 now divide 4.5374 by 100 so , 4.5374 ÷ 100 = 0.045374 ∴ shift the decimal two places to the left as 100 correct option : a" | general |
math_qa__aYZKFLSnNDRK8wiP | A person borrows Rs. 4000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year. Choose the correct choice from the following choices:
A) 100 rs B) 80 rs C) 160 rs D) 180 rs E) 200 rs | <gadget id="calculator">4_000 * 6</gadget>
<output>24_000</output>
<gadget id="calculator">24_000 * 2</gadget>
<output>48_000</output>
<gadget id="calculator">48_000 / 100</gadget>
<output>480</output>
<gadget id="calculator">4_000 * 4</gadget>
<output>16_000</output>
<gadget id="calculator">16_000 * 2</gadget>
<output>32_000</output>
<gadget id="calculator">32_000 / 100</gadget>
<output>320</output>
<gadget id="calculator">480 - 320</gadget>
<output>160</output>
<gadget id="calculator">160 / 2</gadget>
<output>80</output>
<result>B</result> | B | 80 | A person borrows Rs. 4000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year. | {
"A": "100 rs",
"B": "80 rs",
"C": "160 rs",
"D": "180 rs",
"E": "200 rs"
} | divide(subtract(divide(multiply(multiply(4000, 6), 2), const_100), divide(multiply(multiply(4000, 4), 2), const_100)), 2) | multiply(n0,n3)|multiply(n0,n2)|multiply(n1,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,#5)|divide(#6,n1)| | "gain in 2 years = [ ( 4000 * 6 * 2 ) / 100 ] - [ ( 4000 * 4 * 2 ) / 100 ] 480 - 320 = 160 gain in 1 year = ( 160 / 2 ) = 80 rs answer : b" | gain |
math_qa__Z0JtITmNv6HRF53Y | Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?
Choose the correct choice from the following answers.
A) 0 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<result>D</result> | D | 5 | Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ? | {
"A": "0",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | subtract(add(add(2, 2), 2), 1) | add(n0,n0)|add(n0,#0)|subtract(#1,n2) | explanation : p + q = α – 2 and pq = – α – 1 ( p + q ) 2 = p 2 + q 2 + 2 pq , thus ( α – 2 ) 2 = p 2 + q 2 + 2 ( – α – 1 ) p 2 + q 2 = α 2 – 4 α + 4 + 2 α + 2 p 2 + q 2 = α 2 – 2 α + 6 p 2 + q 2 = α 2 – 2 α + 1 + 5 p 2 + q 2 = ( α – 1 ) 2 + 5 thus , minimum value of p 2 + q 2 is 5 . answer : d | general |
math_qa__ru9zSU0laNNzl5N6 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (9, 0), (0, -3.5), (-9, 0)?
Choose the correct choice from the following options:
A) 63
B) 88
C) 112
D) 116
E) 120 | <gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">3.5 * 2</gadget>
<output>7</output>
<gadget id="calculator">(18 * 7) / 2</gadget>
<output>63</output>
<result>A</result> | A | 63 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (9, 0), (0, -3.5), (-9, 0)? | {
"A": "63",
"B": "88",
"C": "112",
"D": "116",
"E": "120"
} | rhombus_area(multiply(9, const_2), multiply(3.5, 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 = 9 + 9 = 18 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 18 * 7 = 63 a is the answer" | geometry |
math_qa__O00oEjRyHBC3vWPj | Each of the 35 points is placed either inside or on the surface of a perfect sphere. If 88% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere? Choose the correct choice from the following choices
A) 7 B) 11 C) 13 D) 14 E) 15 | <gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">35 * (22/25)</gadget>
<output>154/5 = around 30.8</output>
<gadget id="calculator">(154/5) / 2</gadget>
<output>77/5 = around 15.4</output>
<result>E</result> | E | 15 | Each of the 35 points is placed either inside or on the surface of a perfect sphere. If 88% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere? | {
"A": "7",
"B": "11",
"C": "13",
"D": "14",
"E": "15"
} | divide(multiply(35, divide(88, const_100)), const_2) | divide(n1,const_100)|multiply(n0,#0)|divide(#1,const_2)| | "maximum number of points on the surface is 88 % * 35 = 30.8 . . . or 30 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 30 points , so at best we can form 15 pairs ( 30 ) . so , answer is ( e )" | geometry |
math_qa__n7sV9YwIthvfceO5 | 6 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Pick one.
A) 21 B) 34 C) 45 D) 25 E) 26 | <gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">3 * 12</gadget>
<output>36</output>
<gadget id="calculator">36 / 4</gadget>
<output>9</output>
<gadget id="calculator">12 + 9</gadget>
<output>21</output>
<result>A</result> | A | 21 | 6 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages | {
"A": "21",
"B": "34",
"C": "45",
"D": "25",
"E": "26"
} | add(multiply(const_2, 6), divide(multiply(3, multiply(const_2, 6)), 4)) | multiply(n0,const_2)|multiply(n1,#0)|divide(#1,n2)|add(#2,#0) | explanation : let the present age of p and q be 3 x and 4 x respectively . six years ago , p was half of q in age = > 2 ( 3 x – 6 ) = ( 4 x – 6 ) = > 6 x – 12 = 4 x – 6 = > 2 x = 6 = > x = 3 7 x = 7 * 3 = 21 answer : option a | general |
math_qa__mDkkyHcJHa51dL9Q | A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 3/4 of the current inventory is Speedsters, of which 3/5 are convertibles. If there are 30 vehicles that are not Speedsters, how many Speedster convertibles are there? Choose the most appropriate option: A) 30 B) 54 C) 60 D) 70 E) 90 | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">30 / (1/4)</gadget>
<output>120</output>
<gadget id="calculator">120 * (3/4)</gadget>
<output>90</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">90 * (3/5)</gadget>
<output>54</output>
<result>B</result> | B | 54 | A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 3/4 of the current inventory is Speedsters, of which 3/5 are convertibles. If there are 30 vehicles that are not Speedsters, how many Speedster convertibles are there? | {
"A": "30",
"B": "54",
"C": "60",
"D": "70",
"E": "90"
} | multiply(multiply(divide(30, subtract(const_1, divide(3, 4))), divide(3, 4)), divide(3, 5)) | divide(n2,n3)|divide(n0,n1)|subtract(const_1,#1)|divide(n4,#2)|multiply(#3,#1)|multiply(#0,#4)| | "total vehicle = 3 / 4 of speedster + 1 / 4 of others . speedster convertibles = 3 / 4 total vehicle * 3 / 5 given : 1 / 4 constitutes 30 vehicles . hence 3 / 4 constitutes 90 speedster convertibls = 90 * 3 / 5 = 54 b" | physics |
math_qa__ZlpufuNm97vpYG0Y | A rower can row 6 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
Choose the correct option
A) 2.66 B) 2.78 C) 2.8 D) 2.87 E) 2.92 | <gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 + 5</gadget>
<output>12</output>
<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">(5/12) * 7</gadget>
<output>35/12 = around 2.916667</output>
<result>E</result> | E | 2.92 | A rower can row 6 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock? | {
"A": "2.66",
"B": "2.78",
"C": "2.8",
"D": "2.87",
"E": "2.92"
} | multiply(divide(subtract(6, 1), add(add(6, 1), subtract(6, 1))), add(6, 1)) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(#1,#2)|multiply(#0,#3)| | "let x be the distance to big rock . time = x / 5 + x / 7 = 1 x = 35 / 12 = 2.92 the answer is e ." | physics |
math_qa__zpBrBiLv11BSMWBt | in a stockpile of products produced by 3 machines m 1 , m 2 and m 3 , 40 % and 30 % were manufactured by m 1 and m 2 respectively . 3 % of the products of m 1 are defective , 1 % of products of m 2 defective , while 93 % of the products of m 3 iii are not defective . what is the percentage of defective in the stockpile ? Select.
A) 3 %
B) 5 %
C) 2.5 %
D) 4 %
E) 3.6 % | <gadget id="calculator">100 - 93</gadget>
<output>7</output>
<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">40 + 30</gadget>
<output>70</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">(7/100) * 30</gadget>
<output>21/10 = around 2.1</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(1/100) * 30</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(21/10) + (3/10)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(3/100) * 40</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(12/5) + (6/5)</gadget>
<output>18/5 = around 3.6</output>
<result>E</result> | E | 3.6 | in a stockpile of products produced by 3 machines m 1 , m 2 and m 3 , 40 % and 30 % were manufactured by m 1 and m 2 respectively . 3 % of the products of m 1 are defective , 1 % of products of m 2 defective , while 93 % of the products of m 3 iii are not defective . what is the percentage of defective in the stockpile ? | {
"A": "3 %",
"B": "5 %",
"C": "2.5 %",
"D": "4 %",
"E": "3.6 %"
} | add(add(multiply(divide(subtract(const_100, 93), const_100), subtract(const_100, add(40, 30))), multiply(divide(1, const_100), 30)), multiply(divide(3, const_100), 40)) | add(n4,n5)|divide(n1,const_100)|divide(n0,const_100)|subtract(const_100,n12)|divide(#3,const_100)|multiply(n5,#1)|multiply(n4,#2)|subtract(const_100,#0)|multiply(#4,#7)|add(#8,#5)|add(#9,#6) | explanation : let there be 100 products in the stockpile . 40 % and 30 % were manufactured by m 1 and m 2 respectively . so , 30 % are manufactured by m 3 . products from m 1 = 40 , from m 2 = 30 and from m 3 = 30 . number of defective products from m 1 = 0.03 x 40 = 1.2 , from m 2 = 0.01 x 30 = 0.3 and from m 3 = 0.07 x 30 = 2.1 therefore , total number of defective products = 3.6 answer : e | gain |
math_qa__tE1xGFh5U6rVuR17 | the average mark obtained by 22 candidates in an examination is 48 . the average of the first 10 is 55 while the last 11 is 40 . the marks obtained by the 11 th candidate is ? Choose the correct option.
A) 22
B) 0
C) 49
D) 58
E) 66 | <gadget id="calculator">22 * 48</gadget>
<output>1_056</output>
<gadget id="calculator">10 * 55</gadget>
<output>550</output>
<gadget id="calculator">11 * 40</gadget>
<output>440</output>
<gadget id="calculator">550 + 440</gadget>
<output>990</output>
<gadget id="calculator">1_056 - 990</gadget>
<output>66</output>
<result>E</result> | E | 66 | the average mark obtained by 22 candidates in an examination is 48 . the average of the first 10 is 55 while the last 11 is 40 . the marks obtained by the 11 th candidate is ? | {
"A": "22",
"B": "0",
"C": "49",
"D": "58",
"E": "66"
} | subtract(multiply(22, 48), add(multiply(10, 55), multiply(11, 40))) | multiply(n0,n1)|multiply(n2,n3)|multiply(n4,n5)|add(#1,#2)|subtract(#0,#3) | it is clear that 22 x 48 = 10 x 55 + k + 11 x 40 ⇒ ⇒ k = 66 answer : e | general |
math_qa__TeiCsRHSzu0DvQRH | A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? Choose the correct choice from the following answers: A) 20 % B) 40 % C) 35 % D) 32 % E) 29 % | <gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(9/5) - (3/2)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) / (3/2)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>A</result> | A | 20 | A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? | {
"A": "20 %",
"B": "40 %",
"C": "35 %",
"D": "32 %",
"E": "29 %"
} | multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(50, const_100))), add(const_1, divide(50, const_100))), const_100) | divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(#2,#3)|divide(#4,#3)|multiply(#5,const_100)| | "assume the revenue in 2000 to be 100 . then in 2003 it would be 150 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 150 ) / 150 = 30 / 150 = ~ 20 % . answer : a" | gain |
math_qa__NPMbifWrOzAJgCyb | If 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? Choose one.
A) 150 B) 170 C) 190 D) 210 E) 230 | <gadget id="calculator">factorial(21)</gadget>
<output>51_090_942_171_709_440_000</output>
<gadget id="calculator">21 - 2</gadget>
<output>19</output>
<gadget id="calculator">factorial(19)</gadget>
<output>121_645_100_408_832_000</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">121_645_100_408_832_000 * 2</gadget>
<output>243_290_200_817_664_000</output>
<gadget id="calculator">51_090_942_171_709_440_000 / 243_290_200_817_664_000</gadget>
<output>210</output>
<result>D</result> | D | 210 | If 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? | {
"A": "150",
"B": "170",
"C": "190",
"D": "210",
"E": "230"
} | divide(factorial(21), multiply(factorial(subtract(21, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 21 lines is 21 c 2 = 210 the answer is d ." | physics |
math_qa__UQo93J1nStzZrYfa | Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 22 square meters. What is the area that is covered with three layers of rug ?
Select the correct option:
A) 18 square meters
B) 20 square meters
C) 24 square meters
D) 19 square meters
E) 30 square meters | <gadget id="calculator">200 - 140</gadget>
<output>60</output>
<gadget id="calculator">60 - 22</gadget>
<output>38</output>
<gadget id="calculator">38 / 2</gadget>
<output>19</output>
<result>D</result> | D | 19 | Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 22 square meters. What is the area that is covered with three layers of rug ? | {
"A": "18 square meters",
"B": "20 square meters",
"C": "24 square meters",
"D": "19 square meters",
"E": "30 square meters"
} | divide(subtract(subtract(200, 140), 22), const_2) | subtract(n0,n1)|subtract(#0,n2)|divide(#1,const_2) | total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 200 - 22 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : d . | geometry |
math_qa__66tMG0dJri4Sj1gz | If a person walks at 12 km/hr instead of 8 km/hr, he would have walked 20 km more. The actual distance traveled by him is? Choose the most appropriate option
A) 50 km B) 58 km C) 60 km D) 40 km E) 65 km | <gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>D</result> | D | 40 | If a person walks at 12 km/hr instead of 8 km/hr, he would have walked 20 km more. The actual distance traveled by him is? | {
"A": "50 km",
"B": "58 km",
"C": "60 km",
"D": "40 km",
"E": "65 km"
} | multiply(8, divide(20, subtract(12, 8))) | subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)| | "let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 12 3 x - 2 x = 40 = > x = 40 km . answer : d" | general |
math_qa__WclLt4zHenBIEzFh | Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer E between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? Choose the correct choice from the following choices:
A) 12
B) 15
C) 17
D) e = 18
E) 20 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>D</result> | D | 18 | Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer E between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? | {
"A": "12",
"B": "15",
"C": "17",
"D": "e = 18",
"E": "20"
} | multiply(multiply(3, const_2), 3) | multiply(const_2,n0)|multiply(n0,#0)| | "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ." | physics |
math_qa__VeOdqU3BpOaYWZHv | A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? Choose the correct answer:
A) $ 0
B) $ 3
C) $ 4
D) $ 12
E) $ 15 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">60 / (3/4)</gadget>
<output>80</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">80 * (4/5)</gadget>
<output>64</output>
<gadget id="calculator">64 - 60</gadget>
<output>4</output>
<result>C</result> | C | 4 | A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? | {
"A": "$ 0",
"B": "$ 3",
"C": "$ 4",
"D": "$ 12",
"E": "$ 15"
} | subtract(multiply(divide(60, subtract(const_1, divide(25, const_100))), subtract(const_1, divide(20, const_100))), 60) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|divide(n0,#2)|multiply(#4,#3)|subtract(#5,n0)| | "markup = x x = 0.25 ( 60 + x ) = > 3 x / 4 = 15 = > x = 20 so sp = 80 but actual sp = 0.8 * 80 = 64 so profit = $ 4 answer - c" | gain |
math_qa__Xb2YkEIi1ilLnrAx | A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours? Pick one.
A) 125 miles B) 225 miles C) 455 miles D) 425 miles E) 525 miles | <gadget id="calculator">65 * 7</gadget>
<output>455</output>
<result>C</result> | C | 455 | A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours? | {
"A": "125 miles",
"B": "225 miles",
"C": "455 miles",
"D": "425 miles",
"E": "525 miles"
} | multiply(65, 7) | multiply(n0,n1)| | "during each hour , the car travels 65 miles . for 7 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 = 7 × 65 = 455 miles correct answer is c ) 455 miles" | physics |
math_qa__vZKuiDFM5upR8lgx | The percentage profit earned by selling an article for Rs. 1720 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Choose the correct option
A) 3000
B) 1230
C) 1875
D) 5600
E) 3400 | <gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1_720 + 1_280</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 2</gadget>
<output>1_500</output>
<gadget id="calculator">(5/4) * 1_500</gadget>
<output>1_875</output>
<result>C</result> | C | 1,875 | The percentage profit earned by selling an article for Rs. 1720 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? | {
"A": "3000",
"B": "1230",
"C": "1875",
"D": "5600",
"E": "3400"
} | multiply(divide(add(const_100, 25), const_100), divide(add(1720, 1280), const_2)) | add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(#1,const_2)|multiply(#2,#3)| | "then , ( 1720 - x ) / x * 100 = ( x - 1280 ) / x * 100 1720 - x = x - 1280 2 x = 3000 = > x = 1500 required s . p . = 125 % of rs . 1500 = 125 / 100 * 1500 = rs . 1875 . answer c" | gain |
math_qa__UlmRjdSQopGNowEZ | Find the surface area of a 10 cm x 4 cm x 2 cm brick. Choose the correct choice from the following options
A) 136 cu cm
B) 124 cu cm
C) 164 cu cm
D) 180 cu cm
E) none | <gadget id="calculator">2 * (2 * 4 + 4 * 10 + 2 * 10)</gadget>
<output>136</output>
<result>A</result> | A | 136 | Find the surface area of a 10 cm x 4 cm x 2 cm brick. | {
"A": "136 cu cm",
"B": "124 cu cm",
"C": "164 cu cm",
"D": "180 cu cm",
"E": "none"
} | surface_rectangular_prism(2, 4, 10) | surface_rectangular_prism(n0,n1,n2)| | "sol . surface area = [ 2 ( 10 x 4 + 4 x 2 + 10 x 2 ) ] = ( 2 x 68 ) = 136 cu cm answer a" | geometry |
math_qa__gjK4i873cufSdNCr | A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? Pick one
A) 1 : 2 B) 1 : 3 C) 10 : 27 D) 5 : 4 E) 10 : 40 | <gadget id="calculator">192 / 32</gadget>
<output>6</output>
<gadget id="calculator">192 / 6</gadget>
<output>32</output>
<gadget id="calculator">6 - 3</gadget>
<output>3</output>
<gadget id="calculator">192 / 3</gadget>
<output>64</output>
<gadget id="calculator">32 / 64</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? | {
"A": "1 : 2",
"B": "1 : 3",
"C": "10 : 27",
"D": "5 : 4",
"E": "10 : 40"
} | divide(divide(192, divide(192, 32)), divide(192, subtract(divide(192, 32), const_3))) | divide(n0,n1)|divide(n0,#0)|subtract(#0,const_3)|divide(n0,#2)|divide(#1,#3)| | "explanation : t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2 answer is a" | physics |
math_qa__o7EEyQfJFPy7pgNe | A certain country is divided into 4 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/12 the total number of Progressives in the entire country, what fraction of the country is Traditionalist? Choose the correct option.
A) 1 / 5 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 3 / 4 | <gadget id="calculator">4 / 12</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) + 1</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(1/3) / (4/3)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<result>E</result> | E | 0.75 | A certain country is divided into 4 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/12 the total number of Progressives in the entire country, what fraction of the country is Traditionalist? | {
"A": "1 / 5",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "3 / 4"
} | subtract(1, divide(divide(4, 12), add(divide(4, 12), 1))) | divide(n0,n2)|add(n1,#0)|divide(#0,#1)|subtract(n1,#2)| | "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 4 p / 12 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ." | general |
math_qa__bOfVyFBQe9eYXYmB | Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ? Pick.
A) 1287 B) 2887 C) 2100 D) 1129 E) 1192 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(9/10) * (11/10)</gadget>
<output>99/100 = around 0.99</output>
<gadget id="calculator">(99/100) + (9/10)</gadget>
<output>189/100 = around 1.89</output>
<gadget id="calculator">(189/100) + 1</gadget>
<output>289/100 = around 2.89</output>
<gadget id="calculator">6_069 / (289/100)</gadget>
<output>2_100</output>
<result>C</result> | C | 2,100 | Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ? | {
"A": "1287",
"B": "2887",
"C": "2100",
"D": "1129",
"E": "1192"
} | divide(6069, add(add(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))), const_1)) | divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#0)|multiply(#1,#2)|add(#3,#2)|add(#4,const_1)|divide(n2,#5)| | "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6069 = x = 6069 / 2.89 = 2100 therefore , amount invested by raghu is rs . 2100 . answer : c" | general |
math_qa__rskKJ8LDwshZ4skk | An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth? Choose the correct choice
A) 488 B) 204 C) 195 D) 178 E) 133 | <gadget id="calculator">25 / 0.128</gadget>
<output>195.3125</output>
<result>C</result> | C | 195 | An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth? | {
"A": "488",
"B": "204",
"C": "195",
"D": "178",
"E": "133"
} | divide(25, 0.128) | divide(n1,n0) | let the required time be x seconds . more metres , more time ( direct proportion ) 0.128 : 25 : : 1 : x 0.128 x = 25 x 1 x = 25 / 0.128 = ( 25 x 1000 ) / 128 x = 195.31 . required time = 195 sec ( approximately ) . answer is c . | physics |
math_qa__oYrSrF0hEHQJhyNm | The sum of two numbers is 45. The sum of their quotient and is reciprocal is 2.05, the product of the numbers is? Pick one.
A) 300 B) 400 C) 500 D) 600 E) 700 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">45 * 100</gadget>
<output>4_500</output>
<gadget id="calculator">4_500 / 10</gadget>
<output>450</output>
<gadget id="calculator">450 + 45</gadget>
<output>495</output>
<gadget id="calculator">5 + 495</gadget>
<output>500</output>
<result>C</result> | C | 500 | The sum of two numbers is 45. The sum of their quotient and is reciprocal is 2.05, the product of the numbers is? | {
"A": "300",
"B": "400",
"C": "500",
"D": "600",
"E": "700"
} | add(add(const_2, const_3), add(divide(multiply(45, const_100), const_10), 45)) | add(const_2,const_3)|multiply(n0,const_100)|divide(#1,const_10)|add(n0,#2)|add(#0,#3) | a + b = 45 a / b + b / a = 2.05 = > ( a ^ 2 + b ^ 2 ) / ab = 2.05 = > ( ( a + b ) ^ 2 − 2 ab ) / ab = 2.05 = > ( a + b ) ^ 2 = 2.05 ab + 2 ab = 4.05 ab = > ab = 45 ^ 2 / 4.05 = 500 answer : c | general |
math_qa__XfxaXnKcyZFHEqOR | daal is now being sold at rate Rs.20 a kg.During last month its rate was Rs 16 per kg.By How reduce percent should a family its consumption so as to keep the expenditure fixed? Choose the correct choice: A) 10 % B) 20 % C) 30 % D) 40 % E) 50 % | <gadget id="calculator">20 / 16</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1 / (5/4)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<result>B</result> | B | 20 | daal is now being sold at rate Rs.20 a kg.During last month its rate was Rs 16 per kg.By How reduce percent should a family its consumption so as to keep the expenditure fixed? | {
"A": "10 %",
"B": "20 %",
"C": "30 %",
"D": "40 %",
"E": "50 %"
} | subtract(const_100, multiply(inverse(divide(20, 16)), const_100)) | divide(n0,n1)|inverse(#0)|multiply(#1,const_100)|subtract(const_100,#2) | last month rate = 16 per kg this month rate = 20 per kg if 20 = 100 % then 16 = ? therefore % = ( 16 * 100 ) / 20 = 80 % to reduce consumption 100 - 80 = 20 % answer : b | gain |
math_qa__js72R2VLcQ8V2zm2 | A cricket bat is sold for $850, making a profit of $225. The profit percentage would be Choose the correct answer
A) 24 % B) 25 % C) 30 % D) 36 % E) 40 % | <gadget id="calculator">850 - 225</gadget>
<output>625</output>
<gadget id="calculator">225 / 625</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 100</gadget>
<output>36</output>
<result>D</result> | D | 36 | A cricket bat is sold for $850, making a profit of $225. The profit percentage would be | {
"A": "24 %",
"B": "25 %",
"C": "30 %",
"D": "36 %",
"E": "40 %"
} | multiply(divide(225, subtract(850, 225)), const_100) | subtract(n0,n1)|divide(n1,#0)|multiply(#1,const_100)| | "225 / ( 850 - 225 ) = 225 / 625 = 9 / 25 bit more than 33 % . answer : d" | gain |
math_qa__a1Z3fyImfJXAFlpq | Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 40. He was allowed to drop his lowest score. After doing so, his average test score improved to 45. What is the lowest test score that was dropped?
Choose the most appropriate option:
A) 20
B) 25
C) 55
D) 65
E) 80 | <gadget id="calculator">40 * 4</gadget>
<output>160</output>
<gadget id="calculator">45 * 3</gadget>
<output>135</output>
<gadget id="calculator">160 - 135</gadget>
<output>25</output>
<result>B</result> | B | 25 | Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 40. He was allowed to drop his lowest score. After doing so, his average test score improved to 45. What is the lowest test score that was dropped? | {
"A": "20",
"B": "25",
"C": "55",
"D": "65",
"E": "80"
} | subtract(multiply(40, 4), multiply(45, const_3)) | multiply(n0,n1)|multiply(n2,const_3)|subtract(#0,#1)| | "the arithmetic mean of 4 equally weighted tests was 40 . so what we can assume is that we have 4 test scores , each 40 . he dropped his lowest score and the avg went to 45 . this means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 40 . so the lowest score = 40 - 15 = 25 answer ( b )" | general |
math_qa__dQTfB78BJwqzwkFw | The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica?
Choices:
A) 48 B) 47 C) 46 D) 49 E) 52 | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">9 + 15</gadget>
<output>24</output>
<gadget id="calculator">24 + 25</gadget>
<output>49</output>
<gadget id="calculator">147 / 49</gadget>
<output>3</output>
<gadget id="calculator">25 * 3</gadget>
<output>75</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">75 - 27</gadget>
<output>48</output>
<result>A</result> | A | 48 | The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 147, what is the difference between the ages of Patrick and Monica? | {
"A": "48",
"B": "47",
"C": "46",
"D": "49",
"E": "52"
} | subtract(multiply(multiply(5, 5), divide(147, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(147, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5))))) | multiply(n0,n0)|multiply(n1,n0)|multiply(n1,n3)|add(#0,#1)|add(#3,#2)|divide(n4,#4)|multiply(#5,#2)|multiply(#5,#0)|subtract(#6,#7)| | "let their ages are 9 x , 15 x and 25 x respectively . difference between the ages of patrick and monica = 25 x - 9 x = 16 x where 49 x = 147 or x = 3 so diff in ages = 16 x = 16 * 3 = 48 yrs answer : a" | general |
math_qa__Dk9LnW1Rw6gENFMF | If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? Select:
A) 50 % B) 75 % C) 120 % D) 133 1 / 3 % E) 150 % | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">50 * (1/3)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">100 + (1/3)</gadget>
<output>301/3 = around 100.333333</output>
<gadget id="calculator">(50/3) + (301/3)</gadget>
<output>117</output>
<result>C</result> | C | 120 | If the price of a certain bond on May 1st was 2/3 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st? | {
"A": "50 %",
"B": "75 %",
"C": "120 %",
"D": "133 1 / 3 %",
"E": "150 %"
} | add(multiply(50, const_0_33), add(const_100, const_0_33)) | add(const_0_33,const_100)|multiply(n5,const_0_33)|add(#0,#1)| | "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 2 / 3 * 12 = 8 ; the price on july 1 st = 8 * 1.50 = 12 . the average price of the bond on may 1 st and july 1 st = ( 8 + 12 ) / 2 = 10 . the price of the bond on june 1 st ( 12 ) is 6 / 5 times ( 120 % ) the average price of the bond on may 1 st and july 1 st . answer : c ." | general |
math_qa__rmxrxiWyeHIiggMX | Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 252 runs?
Choose the correct choice from the following choices:
A) 6 B) 6.25 C) 7.25 D) 5.5 E) 8 | <gadget id="calculator">3.2 * 10</gadget>
<output>32</output>
<gadget id="calculator">252 - 32</gadget>
<output>220</output>
<gadget id="calculator">220 / 40</gadget>
<output>11/2 = around 5.5</output>
<result>D</result> | D | 5.5 | Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 252 runs? | {
"A": "6",
"B": "6.25",
"C": "7.25",
"D": "5.5",
"E": "8"
} | divide(subtract(252, multiply(3.2, 10)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "required run rate = 252 - ( 3.2 x 10 ) = 220 = 5.5 40 40 d" | gain |
math_qa__wRci7MB132XQtMnm | The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall? Select
A) 20.8 B) 30.4 C) 31.8 D) 32.5 E) 33.8 | <gadget id="calculator">69 - 48</gadget>
<output>21</output>
<gadget id="calculator">21 / 69</gadget>
<output>7/23 = around 0.304348</output>
<gadget id="calculator">(7/23) * 100</gadget>
<output>700/23 = around 30.434783</output>
<result>B</result> | B | 30.4 | The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall? | {
"A": "20.8",
"B": "30.4",
"C": "31.8",
"D": "32.5",
"E": "33.8"
} | multiply(divide(subtract(69.0, 48.0), 69.0), const_100) | subtract(n1,n0)|divide(#0,n1)|multiply(#1,const_100)| | "$ 69 - $ 48 = 21 $ ( 21 / 69 ) * 100 = 30.434 % answer : b" | gain |
math_qa__q1r9ULtyql445iq6 | What is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh? Choices:
A) 5 hours
B) 3 hours
C) 8 hours
D) 6 hours
E) 4 hours | <gadget id="calculator">450 / 90</gadget>
<output>5</output>
<result>A</result> | A | 5 | What is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh? | {
"A": "5 hours",
"B": "3 hours",
"C": "8 hours",
"D": "6 hours",
"E": "4 hours"
} | divide(450, 90) | divide(n0,n1) | time = distance / speed time = 450 / 90 = 5 answer : a | physics |
math_qa__KUkfDxe2RSvij6SS | How many even multiples of 25 are there between 249 and 501?
Choose the correct choice:
A) 5
B) 6
C) 9
D) 10
E) 11 | <gadget id="calculator">501 - 249</gadget>
<output>252</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">252 / 50</gadget>
<output>126/25 = around 5.04</output>
<gadget id="calculator">(126/25) + 1</gadget>
<output>151/25 = around 6.04</output>
<result>B</result> | B | 6 | How many even multiples of 25 are there between 249 and 501? | {
"A": "5",
"B": "6",
"C": "9",
"D": "10",
"E": "11"
} | add(divide(subtract(501, 249), multiply(25, const_2)), const_1) | multiply(n0,const_2)|subtract(n2,n1)|divide(#1,#0)|add(#2,const_1)| | "250 = 10 * 25 500 = 20 * 25 the even multiples are 25 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ." | general |
math_qa__VOV3jE0OBEZ2AFov | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 8 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? Select the correct option.
A) 64 %
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">8 / 8</gadget>
<output>1</output>
<gadget id="calculator">(16/25) * 1</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">(16/25) * 100</gadget>
<output>64</output>
<result>A</result> | A | 64 | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 8 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": "64 %",
"B": "80 %",
"C": "100 %",
"D": "120 %",
"E": "125 %"
} | multiply(multiply(power(divide(8, 10), const_2), divide(8, 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 * 8 = 128 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 128 pi / 200 pi = 0.64 a" | physics |
math_qa__gIOpy4JU8lWfSYkC | In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors C? Choose the correct option: A) 2 B) 3 C) 5 D) 6 E) 8 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<result>B</result> | B | 3 | In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors C? | {
"A": "2",
"B": "3",
"C": "5",
"D": "6",
"E": "8"
} | add(divide(add(const_1, const_4), divide(divide(divide(60, const_2), const_2), const_3)), const_2) | add(const_1,const_4)|divide(n2,const_2)|divide(#1,const_2)|divide(#2,const_3)|divide(#0,#3)|add(#4,const_2)| | "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have c = 2 * 3 * 5 * 7 = 840 thus , answer b" | general |
math_qa__ttcEiZ8i8t9GVRV4 | The average of marks obtained by 120 boys was 40. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is? Select
A) 100 B) 110 C) 125 D) 130 E) 145 | <gadget id="calculator">40 * 120</gadget>
<output>4_800</output>
<gadget id="calculator">120 * 15</gadget>
<output>1_800</output>
<gadget id="calculator">4_800 - 1_800</gadget>
<output>3_000</output>
<gadget id="calculator">39 - 15</gadget>
<output>24</output>
<gadget id="calculator">3_000 / 24</gadget>
<output>125</output>
<result>C</result> | C | 125 | The average of marks obtained by 120 boys was 40. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is? | {
"A": "100",
"B": "110",
"C": "125",
"D": "130",
"E": "145"
} | divide(subtract(multiply(40, 120), multiply(120, 15)), subtract(39, 15)) | multiply(n0,n1)|multiply(n0,n3)|subtract(n2,n3)|subtract(#0,#1)|divide(#3,#2)| | "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 40 24 x = 4800 - 1800 = > x = 3000 / 24 x = 125 hence , the number of boys passed = 125 . answer : c" | general |
math_qa__r4lrpojjDySHcP1A | On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters?
Answers: A) 515 B) 500 C) 525 D) 530 E) 535 | <gadget id="calculator">127 / 2.54</gadget>
<output>50</output>
<gadget id="calculator">35 / 3.5</gadget>
<output>10</output>
<gadget id="calculator">50 * 10</gadget>
<output>500</output>
<result>B</result> | B | 500 | On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters? | {
"A": "515",
"B": "500",
"C": "525",
"D": "530",
"E": "535"
} | multiply(divide(127, 2.54), divide(35, 3.5)) | divide(n2,n4)|divide(n1,n0)|multiply(#0,#1)| | "1 inch = 2.54 cm 3.5 inch = 2.54 * 3.5 cm 8.89 cm = 35 miles 127 cms = 35 / 8.89 * 127 = 500 miles answer : b" | physics |
math_qa__QW01z7eaQYrL9MRJ | How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length? Options: A) 16.5 B) 16.0 C) 15 D) 16.8 E) 16.1 | <gadget id="calculator">110 + 140</gadget>
<output>250</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">250 / (50/3)</gadget>
<output>15</output>
<result>C</result> | C | 15 | How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length? | {
"A": "16.5",
"B": "16.0",
"C": "15",
"D": "16.8",
"E": "16.1"
} | divide(add(110, 140), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | "d = 110 + 140 = 250 m s = 60 * 5 / 18 = 50 / 3 t = 250 * 3 / 50 = 15 sec answer : c" | physics |
math_qa__PTt14wbVDqXw7rWM | What is the number of integers from 1 to 500 (inclusive) that are divisible by neither 10 nor by 15? Pick.
A) 170 B) 250 C) 300 D) 560 E) 420 | <gadget id="calculator">500 / 10</gadget>
<output>50</output>
<gadget id="calculator">500 / 15</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">50 + (100/3)</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">10 * 15</gadget>
<output>150</output>
<gadget id="calculator">500 / 150</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">(250/3) - (10/3)</gadget>
<output>80</output>
<gadget id="calculator">500 - 80</gadget>
<output>420</output>
<result>E</result> | E | 420 | What is the number of integers from 1 to 500 (inclusive) that are divisible by neither 10 nor by 15? | {
"A": "170",
"B": "250",
"C": "300",
"D": "560",
"E": "420"
} | subtract(500, subtract(add(divide(500, 10), divide(500, 15)), divide(500, multiply(10, 15)))) | divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5) | in 500 consecutive numbers , number of multiples of 10 = 500 / 10 = 50 ( ignore decimals ) in 500 consecutive numbers , number of multiples of 15 = 500 / 15 = 33 number of multiples of 10 * 15 i . e . 150 = 500 / 150 = 3 number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - ( 50 + 33 - 3 ) { using the concept of sets here ) = 420 answer is e | other |
math_qa__htK49lo1MpYtFkkm | What is the number of integers from 11 to 1010 (inclusive) that are divisible by neither 12 nor by 15? Choose the correct choice from the following answers:
A) 565
B) 856
C) 783
D) 590
E) 300 | <gadget id="calculator">1_010 / 12</gadget>
<output>505/6 = around 84.166667</output>
<gadget id="calculator">1_010 / 15</gadget>
<output>202/3 = around 67.333333</output>
<gadget id="calculator">(505/6) + (202/3)</gadget>
<output>303/2 = around 151.5</output>
<gadget id="calculator">12 * 15</gadget>
<output>180</output>
<gadget id="calculator">1_010 / 180</gadget>
<output>101/18 = around 5.611111</output>
<gadget id="calculator">(303/2) - (101/18)</gadget>
<output>1_313/9 = around 145.888889</output>
<gadget id="calculator">1_010 - (1_313/9)</gadget>
<output>7_777/9 = around 864.111111</output>
<result>B</result> | B | 856 | What is the number of integers from 11 to 1010 (inclusive) that are divisible by neither 12 nor by 15? | {
"A": "565",
"B": "856",
"C": "783",
"D": "590",
"E": "300"
} | subtract(1010, subtract(add(divide(1010, 12), divide(1010, 15)), divide(1010, multiply(12, 15)))) | divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5)| | "in 1000 consecutive numbers , number of multiples of 12 = 1000 / 12 = 83 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 15 = 1000 / 15 = 66 number of multiples of 12 * 15 i . e . 180 = 1000 / 180 = 5 number of integers from 11 to 1010 that are divisible by neither 12 nor by 15 = 1000 - ( 83 + 66 - 5 ) { using the concept of sets here ) = 856 answer is b" | other |
math_qa__qUWBaLKpuqdnXbzJ | A rectangular field has a length 10 meters more than it is width. If the area of the field is 171, what is the length (in meters) of the rectangular field? Choose the correct choice from the following answers: A) 17 B) 19 C) 21 D) 23 E) 25 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">171 / 10</gadget>
<output>171/10 = around 17.1</output>
<gadget id="calculator">(171/10) / 2</gadget>
<output>171/20 = around 8.55</output>
<gadget id="calculator">(1/3) + (171/20)</gadget>
<output>533/60 = around 8.883333</output>
<gadget id="calculator">(1/4) + (533/60)</gadget>
<output>137/15 = around 9.133333</output>
<gadget id="calculator">10 + (137/15)</gadget>
<output>287/15 = around 19.133333</output>
<result>B</result> | B | 19 | A rectangular field has a length 10 meters more than it is width. If the area of the field is 171, what is the length (in meters) of the rectangular field? | {
"A": "17",
"B": "19",
"C": "21",
"D": "23",
"E": "25"
} | add(10, add(const_0_25, add(const_0_33, divide(divide(171, 10), const_2)))) | divide(n1,n0)|divide(#0,const_2)|add(#1,const_0_33)|add(#2,const_0_25)|add(n0,#3) | area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 the length is 19 meters . the answer is b . | geometry |
math_qa__uQt0szgvRih5uQE2 | A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? Choose the correct choice
A) 16 B) 19 C) 15 D) 24 E) 10 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">24 / 1</gadget>
<output>24</output>
<result>D</result> | D | 24 | A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? | {
"A": "16",
"B": "19",
"C": "15",
"D": "24",
"E": "10"
} | divide(subtract(26, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "let the son ' s present age be x years . then , man ' s present age = ( x + 26 ) years . ( x + 26 ) + 2 = 2 ( x + 2 ) x + 28 = 2 x + 4 = > x = 24 . answer : d" | general |
math_qa__Nit9xUTUktzQGvEu | If a2 + b2 + c2 = 250 and ab + bc + ca = 3, then a + b + c is Select the correct option:
A) 4 B) 8 C) 16 D) 32 E) 64 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">250 + 6</gadget>
<output>256</output>
<gadget id="calculator">256 ** (1/2)</gadget>
<output>16</output>
<result>C</result> | C | 16 | If a2 + b2 + c2 = 250 and ab + bc + ca = 3, then a + b + c is | {
"A": "4",
"B": "8",
"C": "16",
"D": "32",
"E": "64"
} | sqrt(add(250, multiply(3, 2))) | multiply(n4,n0)|add(n3,#0)|sqrt(#1)| | "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 250 and ab + bc + ca = 3 , ( a + b + c ) ^ 2 = 250 + 2 ( 3 ) = 256 = 16 ^ 2 therefore : a + b + c = 16 answer : c" | general |
math_qa__ASTMqyqFCXgmJs39 | If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of
Rs. 1000
Choose the correct choice from the following answers
A) 10 B) 20 C) 30 D) 40 E) 50 | <gadget id="calculator">1_000 * 5</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>
<gadget id="calculator">1_000 * 4</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 100</gadget>
<output>40</output>
<gadget id="calculator">50 - 40</gadget>
<output>10</output>
<result>A</result> | A | 10 | If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of
Rs. 1000 | {
"A": "10",
"B": "20",
"C": "30",
"D": "40",
"E": "50"
} | subtract(divide(multiply(1000, 5), const_100), divide(multiply(1000, 4), const_100)) | multiply(n0,n2)|multiply(n1,n2)|divide(#0,const_100)|divide(#1,const_100)|subtract(#2,#3) | explanation : clue : answer will be 5 % of 1000 - 4 % of 1000 answer : option a | general |
math_qa__TwT6nWKlPVgIgCGe | Of all the homes on Gotham Street, 1/3 are termite-ridden, and 1/4 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Choose the correct choice from the following answers
A) 1 / 3 B) 2 / 5 C) 1 / 4 D) 1 / 6 E) 3 / 4 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">3 / 12</gadget>
<output>1/4 = around 0.25</output>
<result>C</result> | C | 0.25 | Of all the homes on Gotham Street, 1/3 are termite-ridden, and 1/4 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing? | {
"A": "1 / 3",
"B": "2 / 5",
"C": "1 / 4",
"D": "1 / 6",
"E": "3 / 4"
} | divide(add(1, const_2.0), multiply(3, 4)) | add(n0,const_2.0)|multiply(n1,n3)|divide(#0,#1)| | "the fraction of homes which are termite - infested but not collapsing is 3 / 4 * 1 / 3 = 1 / 4 the answer is c ." | general |
math_qa__tapgYhNK26WwFkz8 | Take number 1000 and then add 20 to it. Now add 1000 one more time. Now add 30. Now add 1000 one more time. Now add 40. Now add 1000 one more time. Now add 10. What is the total? Answers: A) 4100 B) 3590 C) 2800 D) 3700 E) 3600 | <gadget id="calculator">1_000 + 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 + 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 + 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">20 + 30</gadget>
<output>50</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">90 + 10</gadget>
<output>100</output>
<gadget id="calculator">4_000 + 100</gadget>
<output>4_100</output>
<result>A</result> | A | 4,100 | Take number 1000 and then add 20 to it. Now add 1000 one more time. Now add 30. Now add 1000 one more time. Now add 40. Now add 1000 one more time. Now add 10. What is the total? | {
"A": "4100",
"B": "3590",
"C": "2800",
"D": "3700",
"E": "3600"
} | add(add(add(add(1000, 1000), 1000), 1000), add(add(add(20, 30), 40), 10)) | add(n0,n0)|add(n1,n3)|add(n0,#0)|add(n5,#1)|add(n0,#2)|add(n7,#3)|add(#4,#5) | a 4100 | general |
math_qa__0LL19eIvC0gPvmkF | Elena’s bread recipe calls for 2 ounces of butter for each 5 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? Choose the correct choice from the following
A) 1 B) 4 C) 9 D) 13 E) 20 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<result>E</result> | E | 20 | Elena’s bread recipe calls for 2 ounces of butter for each 5 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": "20"
} | multiply(5, 4) | multiply(n1,n2)| | "solving through algebra route : 2 b + 5 f = x amount if we multiply this equation with 4 we get : 8 b + 20 f = 4 x therefore , we got 8 ounces of butter and 4 x amount of quantity when we use 20 ounces of floor . ans : e" | general |
math_qa__L32kYvUfCAQjIiD9 | Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 38 square meters. What is the area that is covered with three layers of wallpaper? Select the correct option
A) 5 square meters B) 36 square meters C) 42 square meters D) 83.3 square meters E) 41 square meters | <gadget id="calculator">300 - 180</gadget>
<output>120</output>
<gadget id="calculator">120 - 38</gadget>
<output>82</output>
<gadget id="calculator">82 / 2</gadget>
<output>41</output>
<result>E</result> | E | 41 | Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 38 square meters. What is the area that is covered with three layers of wallpaper? | {
"A": "5 square meters",
"B": "36 square meters",
"C": "42 square meters",
"D": "83.3 square meters",
"E": "41 square meters"
} | divide(subtract(subtract(300, 180), 38), const_2) | subtract(n0,n1)|subtract(#0,n2)|divide(#1,const_2) | 300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 38 = 82 sq m of the wallpaper overlaps in three layers . 82 sq m makes two extra layers hence the area over which it makes two extra layers is 41 sq m . answer ( e ) . | geometry |
math_qa__Lscais1venexI665 | 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 L in feet?
Choose the correct choice from the following answers:
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 L 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 . l = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d" | general |
math_qa__V6DxFK9czKIsEABs | All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have? Choose the correct answer.
A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">3 + 3</gadget>
<output>6</output>
<result>E</result> | E | 6 | All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have? | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | add(3, const_3) | add(n0,const_3) | the question can be done in seconds if you understand the properties of factors of a number . note that every distinct factor of a number which is not a perfect square has a complementary factor . for example , factors of 6 : 1 , 2 , 3 , 6 1 has a complementary factor 6 such that 1 * 6 = 6 ( the original number ) 2 has a complementary factor 3 such that 2 * 3 = 6 ( the original number ) so if you have a number , n , which is not a perfect square , and start multiplying its factors , you will get n to a certain power . the power will half of the number of factors . for example , 6 has 4 factors and when you multiply all 4 factors , you get 6 ^ 2 ( 2 is half of 4 ) . so if you know that the product of all factors is x ^ 3 , it means there must have been twice the number of factors i . e . 3 * 2 = 6 factors . e ) | general |
math_qa__TK2q2UFpakWaYyzp | Mike needs 30% to pass. If he scored 212 marks and falls short by 19 marks, what was the maximum marks he could have got?
Choose the correct answer: A) 543 B) 677 C) 770 D) 867 E) 832 | <gadget id="calculator">212 + 19</gadget>
<output>231</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">231 / (3/10)</gadget>
<output>770</output>
<result>C</result> | C | 770 | Mike needs 30% to pass. If he scored 212 marks and falls short by 19 marks, what was the maximum marks he could have got? | {
"A": "543",
"B": "677",
"C": "770",
"D": "867",
"E": "832"
} | divide(add(212, 19), divide(30, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | "if mike had scored 19 marks more , he could have scored 30 % therefore , mike required 212 + 19 = 231 marks let the maximum marks be m . then 30 % of m = 231 ( 30 / 100 ) × m = 231 m = ( 231 × 100 ) / 30 m = 23100 / 30 m = 770 answer : c" | gain |
math_qa__2HH0SSE0C4MAYhcF | Mary works in a restaurant a maximum of 40 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? Choose the correct choice from the following choices
A) 300 B) 420 C) 360 D) 320 E) 400 | <gadget id="calculator">40 * 8</gadget>
<output>320</output>
<gadget id="calculator">40 - 20</gadget>
<output>20</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">8 * (1/4)</gadget>
<output>2</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">320 + 40</gadget>
<output>360</output>
<result>C</result> | C | 360 | Mary works in a restaurant a maximum of 40 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? | {
"A": "300",
"B": "420",
"C": "360",
"D": "320",
"E": "400"
} | add(multiply(40, 8), multiply(subtract(40, 20), multiply(8, divide(25, const_100)))) | divide(n3,const_100)|multiply(n0,n2)|subtract(n0,n1)|multiply(n2,#0)|multiply(#3,#2)|add(#1,#4)| | "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 20 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 20 ) = $ 200 . the total amount is $ 160 + $ 200 = $ 360 answer c 360 ." | gain |
math_qa__mJmEffiH1il03tW2 | Sonika deposited Rs.13000 which amounted to Rs.10200 after 4 years at simple interest. Had the interest been 5% more. She would get how much? Choose the correct choice from the following answers
A) 18990
B) 13002
C) 12800
D) 12300
E) 14500 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">10_200 - 13_000</gadget>
<output>-2_800</output>
<gadget id="calculator">(-2_800) / 4</gadget>
<output>-700</output>
<gadget id="calculator">(-700) / 13_000</gadget>
<output>-7/130 = around -0.053846</output>
<gadget id="calculator">(1/20) + (-7/130)</gadget>
<output>-1/260 = around -0.003846</output>
<gadget id="calculator">(-1/260) * 13_000</gadget>
<output>-50</output>
<gadget id="calculator">(-50) * 4</gadget>
<output>-200</output>
<gadget id="calculator">(-200) + 13_000</gadget>
<output>12_800</output>
<result>C</result> | C | 12,800 | Sonika deposited Rs.13000 which amounted to Rs.10200 after 4 years at simple interest. Had the interest been 5% more. She would get how much? | {
"A": "18990",
"B": "13002",
"C": "12800",
"D": "12300",
"E": "14500"
} | add(multiply(multiply(add(divide(5, const_100), divide(divide(subtract(10200, 13000), 4), 13000)), 13000), 4), 13000) | divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)| | "( 13000 * 4 * 5 ) / 100 = 2600 10200 - - - - - - - - 12800 answer : c" | gain |
math_qa__oA5uB35vq6BxiODY | A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B? Choose the correct choice from the following options.
A) 10 years B) 12 years C) 14 years D) 18 years E) 16 years | <gadget id="calculator">47 - 2</gadget>
<output>45</output>
<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">90 / 5</gadget>
<output>18</output>
<result>D</result> | D | 18 | A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B? | {
"A": "10 years",
"B": "12 years",
"C": "14 years",
"D": "18 years",
"E": "16 years"
} | divide(multiply(subtract(47, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 x = 9 . hence , b ' s age = 2 x = 19 years . d )" | general |
math_qa__sRntLthtD8OD4z0j | A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? Choose the correct option.
A) rs . 59
B) rs . 58
C) rs . 09
D) rs . 50
E) rs . 13 | <gadget id="calculator">18_000 / 400</gadget>
<output>45</output>
<gadget id="calculator">45 + 5</gadget>
<output>50</output>
<result>D</result> | D | 50 | A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? | {
"A": "rs . 59",
"B": "rs . 58",
"C": "rs . 09",
"D": "rs . 50",
"E": "rs . 13"
} | add(divide(18000, 400), 5) | divide(n1,n0)|add(n2,#0)| | "sp per metre = 18000 / 400 = rs . 45 loss per metre = rs . 5 cp per metre = 45 + 5 = rs . 50 answer : d" | gain |
math_qa__aUEMyixnTvvrpo9n | The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6? Select.
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">2 - 3</gadget>
<output>-1</output>
<gadget id="calculator">6 + (-1)</gadget>
<output>5</output>
<result>E</result> | E | 5 | The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | add(6, subtract(2, 3)) | subtract(n0,n1)|add(n2,#0) | m is 2 more than a multiple of 6 ; n is 3 more than a multiple of 6 . m - n will be 1 less than a multiple of 6 ( 5 , 11 , 17 , . . . ) , therefore m - n will yield a remainder of 5 when divided by 6 . answer : e . | physics |
math_qa__BOxMaNdZlEBwXnEr | The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is Choose the correct choice
A) 35.22 B) 36.12 C) 36.22 D) 36.42 E) none | <gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>D</result> | D | 36.42 | The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is | {
"A": "35.22",
"B": "36.12",
"C": "36.22",
"D": "36.42",
"E": "none"
} | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)| | "solution correct sum = ( 36 x 50 + 44 - 23 ) = 1821 . â ˆ ´ correct mean = 1821 / 50 = 36.42 . answer d" | general |
math_qa__lS7sAKzqEnyakDSs | The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5292 sq cm. What is the ratio of the width and the area of the rectangle? Choose the most appropriate option:
A) 1 : 72
B) 1 : 76
C) 1 : 80
D) 1 : 84
E) 1 : 88 | <gadget id="calculator">3 * 5_292</gadget>
<output>15_876</output>
<gadget id="calculator">15_876 ** (1/2)</gadget>
<output>126</output>
<gadget id="calculator">126 / 2</gadget>
<output>63</output>
<gadget id="calculator">63 / 5_292</gadget>
<output>1/84 = around 0.011905</output>
<result>D</result> | D | 0.011905 | The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5292 sq cm. What is the ratio of the width and the area of the rectangle? | {
"A": "1 : 72",
"B": "1 : 76",
"C": "1 : 80",
"D": "1 : 84",
"E": "1 : 88"
} | divide(divide(sqrt(multiply(3, 5292)), const_2), 5292) | multiply(n2,n1)|sqrt(#0)|divide(#1,const_2)|divide(#2,n2)| | "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 5292 12 x ^ 2 = 5292 x ^ 2 = 441 x = 21 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 84 the answer is d ." | geometry |
math_qa__EWb4i4nKMjuTvq0W | is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B? Options
A) 7 B) 8 C) 9 D) 10 E) 11 | <gadget id="calculator">27 - 2</gadget>
<output>25</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">25 / 5</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<result>D</result> | D | 10 | is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | multiply(divide(subtract(27, const_2), add(const_3, const_2)), const_2) | add(const_2,const_3)|subtract(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)| | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 = > x = 5 hence , b ' s age = 2 x = 10 years . answer : d" | general |
math_qa__kdxG6d9cBznz4EI2 | If a * b = 2a – 3b + ab, then 5 * 7 + 7 * 5 is equal to:
Choose the correct choice from the following options:
A) 34 B) 18 C) 72 D) 78 E) 82 | <gadget id="calculator">5 * 7</gadget>
<output>35</output>
<result>A</result> | A | 34 | If a * b = 2a – 3b + ab, then 5 * 7 + 7 * 5 is equal to: | {
"A": "34",
"B": "18",
"C": "72",
"D": "78",
"E": "82"
} | multiply(5, 7) | multiply(n2,n3) | 5 * 7 + 7 * 5 = ( 2 * 5 – 5 * 7 + 5 * 7 ) + ( 2 * 7 – 5 * 5 + 7 * 5 ) = ( 10 + 14 – 25 + 35 ) = 34 . answer : a | general |
math_qa__SqPfLWmpSwCQyQLq | Two family reunions are happening at the Park Avenue hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 70 people attend the Hall reunion, how many people attend both reunions Choose the correct choice from the following answers:
A) 2
B) 5
C) 10
D) 16
E) 22 | <gadget id="calculator">40 + 70</gadget>
<output>110</output>
<gadget id="calculator">110 - 100</gadget>
<output>10</output>
<result>C</result> | C | 10 | Two family reunions are happening at the Park Avenue hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 70 people attend the Hall reunion, how many people attend both reunions | {
"A": "2",
"B": "5",
"C": "10",
"D": "16",
"E": "22"
} | subtract(add(40, 70), 100) | add(n1,n2)|subtract(#0,n0) | no of people in oates reunion = 40 no of people in hall reunion = 70 attending both = x all guests attend at least one . therefore , 100 = 40 + 70 - ( both ) both = 10 answer c | other |
math_qa__8X387LvTGdf2Tehc | A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 4 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour?
Answers
A) 38 B) 47 C) 50 D) 53 E) 54 | <gadget id="calculator">450 / 9</gadget>
<output>50</output>
<gadget id="calculator">50 + 4</gadget>
<output>54</output>
<result>E</result> | E | 54 | A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 4 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour? | {
"A": "38",
"B": "47",
"C": "50",
"D": "53",
"E": "54"
} | add(divide(450, 9), 4) | divide(n2,n0)|add(n1,#0) | if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 4 each hour . in any equally spaced list , the median equals the mean . here , the mean is 450 / 9 = 50 , so the median is also 50 , and that is the amount eaten in the 5 th hour . we need to add 4 to find the total eaten in the next hour , so the answer is 54 option e . | general |
math_qa__WBQROxBcwLcesKDU | A waiter's salary consists of his salary and tips. During one week his tips were 9/4 of his salary. What fraction of his income came from tips ?
Pick one:
A) 4 / 9
B) 5 / 4
C) 9 / 13
D) 5 / 9
E) 6 / 9 | <gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) + 1</gadget>
<output>13/4 = around 3.25</output>
<gadget id="calculator">(9/4) / (13/4)</gadget>
<output>9/13 = around 0.692308</output>
<result>C</result> | C | 0.692308 | A waiter's salary consists of his salary and tips. During one week his tips were 9/4 of his salary. What fraction of his income came from tips ? | {
"A": "4 / 9",
"B": "5 / 4",
"C": "9 / 13",
"D": "5 / 9",
"E": "6 / 9"
} | divide(divide(9, 4), add(divide(9, 4), const_1)) | divide(n0,n1)|add(#0,const_1)|divide(#0,#1)| | "income = salary ( s ) + tips = s + s * 9 / 4 = s * 13 / 4 tips = s * 9 / 4 fraction of his income came from tips = ( s * 9 / 4 ) / ( s * 13 / 4 ) = 9 / 13 answer : c" | general |
math_qa__m0F884GJU1bBitRF | the average age of a husband and his wife was 23 years at the time of their marriage . after 5 years they have a one - year old child . the average age of the family now is :
Select.
A) 25 B) 23 C) 19 D) 18 E) 17 | <gadget id="calculator">23 * 2</gadget>
<output>46</output>
<gadget id="calculator">46 + 5</gadget>
<output>51</output>
<gadget id="calculator">51 + 5</gadget>
<output>56</output>
<gadget id="calculator">56 + 1</gadget>
<output>57</output>
<gadget id="calculator">57 / 3</gadget>
<output>19</output>
<result>C</result> | C | 19 | the average age of a husband and his wife was 23 years at the time of their marriage . after 5 years they have a one - year old child . the average age of the family now is : | {
"A": "25",
"B": "23",
"C": "19",
"D": "18",
"E": "17"
} | divide(add(add(add(multiply(23, const_2), 5), 5), const_1), const_3) | multiply(n0,const_2)|add(n1,#0)|add(n1,#1)|add(#2,const_1)|divide(#3,const_3) | explanation : sum of the present ages of husband , wife and child = ( 23 * 2 + 5 * 2 ) + 1 = 57 years . required average = ( 57 / 3 ) = 19 years . answer : c | general |
math_qa__1vw4rNdqsM1yQlOG | What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261? Choose the correct choice from the following answers.
A) rs . 8000 B) rs . 8400 C) rs . 7500 D) rs . 7800 E) none of these | <gadget id="calculator">9_261 / 8_820</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) - 1</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">8_820 / (441/400)</gadget>
<output>8_000</output>
<result>A</result> | A | 8,000 | What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261? | {
"A": "rs . 8000",
"B": "rs . 8400",
"C": "rs . 7500",
"D": "rs . 7800",
"E": "none of these"
} | divide(8820, power(add(subtract(divide(9261, 8820), const_1), const_1), 2)) | divide(n3,n1)|subtract(#0,const_1)|add(#1,const_1)|power(#2,n0)|divide(n1,#3)| | "explanation : 8820 - - - - 441 100 - - - - ? = > 5 % x * 105 / 100 * 105 / 100 = 8820 x * 1.1025 = 8820 x = 8820 / 1.1025 = > 8000 answer is a" | general |
math_qa__rvHLJZtjUN87D9CM | If the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres, what is the area of the field in square metres? Choose the correct choice.
A) 18000 B) 40000 C) 31000 D) 19000 E) 16000 | <gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">540 - 60</gadget>
<output>480</output>
<gadget id="calculator">480 / 4</gadget>
<output>120</output>
<gadget id="calculator">120 + 30</gadget>
<output>150</output>
<gadget id="calculator">120 * 150</gadget>
<output>18_000</output>
<result>A</result> | A | 18,000 | If the length of a rectangular field is 30 metres more than its breadth and the perimeter of the field is 540 metres, what is the area of the field in square metres? | {
"A": "18000",
"B": "40000",
"C": "31000",
"D": "19000",
"E": "16000"
} | rectangle_area(square_edge_by_perimeter(subtract(540, multiply(30, const_2))), add(square_edge_by_perimeter(subtract(540, multiply(30, const_2))), 30)) | multiply(n0,const_2)|subtract(n1,#0)|square_edge_by_perimeter(#1)|add(n0,#2)|rectangle_area(#3,#2) | let breadth is x then length is 30 + x now the perimeter = 2 ( x + 30 + x ) = 540 solving this we get x = 120 now the area is 120 * 150 = 18000 answer : a | geometry |
math_qa__ivBwcyLlEMSkqaPX | The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? Options:
A) 15 % B) 32 % C) 40 % D) 62 % E) 80 % | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(11/10) * (4/5)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">(3/2) * (22/25)</gadget>
<output>33/25 = around 1.32</output>
<gadget id="calculator">(33/25) - 1</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">100 * (8/25)</gadget>
<output>32</output>
<result>B</result> | B | 32 | The profits of QRS company rose 10% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? | {
"A": "15 %",
"B": "32 %",
"C": "40 %",
"D": "62 %",
"E": "80 %"
} | multiply(const_100, subtract(multiply(add(const_1, divide(50, const_100)), multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(20, const_100)))), const_1)) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(const_1,#2)|multiply(#4,#5)|multiply(#3,#6)|subtract(#7,const_1)|multiply(#8,const_100)| | "we need multipliers . multiplier for a 10 % increases = 1 + 0.10 = 1.1 multiplier for a 20 % decreases = 1 – 0.20 = 0.8 multiplier for a 50 % increases = 1 + 0.50 = 1.5 now , multiply these . first , multiply ( 0.8 ) and ( 1.5 ) , using the doubling & halving trick . half of 0.80 is 0.40 , and twice 1.5 is 3 ( 0.8 ) * ( 1.5 ) = ( 0.4 ) * ( 3 ) = 1.2 now , multiply this by 1.1 1.2 * 1.1 = 1.32 thus , the three percent changes combined produce a 32 % increase . answer = ( b ) ." | gain |
math_qa__hLIjQy8fWwN2bI7l | What will be the cost of building a fence around a circular plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? Pick one
A) rs . 3944
B) rs . 3495.28
C) rs . 3988
D) rs . 3949
E) rs . 3923 | <gadget id="calculator">289 / pi</gadget>
<output>289/pi = around 91.991557</output>
<gadget id="calculator">(289/pi) ** (1/2)</gadget>
<output>17/sqrt(pi) = around 9.591223</output>
<gadget id="calculator">2 * pi * (17/sqrt(pi))</gadget>
<output>34*sqrt(pi) = around 60.263431</output>
<gadget id="calculator">(34*sqrt(pi)) * 58</gadget>
<output>1972*sqrt(pi) = around 3_495.278994</output>
<result>B</result> | B | 3,495.28 | What will be the cost of building a fence around a circular plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? | {
"A": "rs . 3944",
"B": "rs . 3495.28",
"C": "rs . 3988",
"D": "rs . 3949",
"E": "rs . 3923"
} | multiply(circumface(sqrt(divide(289, const_pi))), 58) | divide(n0,const_pi)|sqrt(#0)|circumface(#1)|multiply(n1,#2) | let the side of the circular plot be a ft . pi * ( r ) ^ 2 = 289 = > r = 9.59 length of the fence = perimeter of the plot = 2 * pi * r = 60.26 ft . cost of building the fence = 60.26 * 58 = rs . 3495.28 answer : b | geometry |
math_qa__Da2HCyPuQawjvICo | The amount of principal Rs.4000 at compound interest at the ratio of 10% p.a. for 3 years is
Pick one: A) rs . 5342 B) rs . 4325 C) rs . 5324 D) rs . 3425 E) rs . 3525 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 3</gadget>
<output>1_331/1_000 = around 1.331</output>
<gadget id="calculator">4_000 * (1_331/1_000)</gadget>
<output>5_324</output>
<result>C</result> | C | 5,324 | The amount of principal Rs.4000 at compound interest at the ratio of 10% p.a. for 3 years is | {
"A": "rs . 5342",
"B": "rs . 4325",
"C": "rs . 5324",
"D": "rs . 3425",
"E": "rs . 3525"
} | multiply(4000, power(add(const_1, divide(10, const_100)), const_3)) | divide(n1,const_100)|add(#0,const_1)|power(#1,const_3)|multiply(n0,#2) | 5324 answer : c | gain |
math_qa__X2s7yP18GWPYbIyt | Twenty eight meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
Pick:
A) 2 √ 2 B) 2 √ 5 C) 5 D) 7 E) none of these | <gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">14 * 2</gadget>
<output>28</output>
<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>D</result> | D | 7 | Twenty eight meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area? | {
"A": "2 √ 2",
"B": "2 √ 5",
"C": "5",
"D": "7",
"E": "none of these"
} | divide(divide(multiply(add(const_10, const_4), const_2), const_2), const_2) | add(const_10,const_4)|multiply(#0,const_2)|divide(#1,const_2)|divide(#2,const_2) | area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 28 = > x / 360 * 2 * pi * r + 2 r = 28 = > 2 a / r + 2 r = 28 = > a = r 14 - r ^ 2 = r 14 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 14 - 2 r = 0 r = 7 d | geometry |
math_qa__dOcF8vwLTrAtnNoZ | When a number is divided by 6 &then multiply by 12 the answer is 12 what is the no.? Choose the correct choice from the following options
A) 4.5 B) 5 C) 5.5 D) 5.8 E) 6 | <gadget id="calculator">12 / 12</gadget>
<output>1</output>
<gadget id="calculator">1 * 6</gadget>
<output>6</output>
<result>E</result> | E | 6 | When a number is divided by 6 &then multiply by 12 the answer is 12 what is the no.? | {
"A": "4.5",
"B": "5",
"C": "5.5",
"D": "5.8",
"E": "6"
} | multiply(divide(12, 12), 6) | divide(n2,n1)|multiply(n0,#0)| | "if $ x $ is the number , x / 6 * 12 = 12 = > 2 x = 12 = > x = 6 e" | general |
math_qa__7lFReB0P1dlx9uEd | Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. Pick
A) 4 B) 6 C) 8 D) 10 E) 12 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>E</result> | E | 12 | Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. | {
"A": "4",
"B": "6",
"C": "8",
"D": "10",
"E": "12"
} | multiply(multiply(2, 2), 3) | multiply(n0,n4)|multiply(n3,#0)| | "rx * ( t + 2 ) = w ry * ( t ) = w . also , w / ( t + 2 ) + w / t = ( 5 w / 4 ) * ( 1 / 3 ) or 1 / t + 1 / ( t + 2 ) = 5 / 12 - - > ( 3 + 2 ) / 12 = 1 / 4 + 1 / 6 thus , t = 4 . replacing , rx = w / 6 , w / 6 * t = 2 w or t = 12 days . answer : e" | general |
math_qa__pr5alKaEKiCpD8HL | How long will a boy take to run round a square field of side 60 meters, if he runs at the rate of 9km/hr? Choose the correct choice from the following answers.
A) 96 sec B) 45 sec C) 1 min D) 32 sec E) 25 sec | <gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">1_000 / 3_600</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">9 * (5/18)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">240 / (5/2)</gadget>
<output>96</output>
<result>A</result> | A | 96 | How long will a boy take to run round a square field of side 60 meters, if he runs at the rate of 9km/hr? | {
"A": "96 sec",
"B": "45 sec",
"C": "1 min",
"D": "32 sec",
"E": "25 sec"
} | divide(multiply(60, const_4), multiply(9, divide(const_1000, const_3600))) | divide(const_1000,const_3600)|multiply(n0,const_4)|multiply(n1,#0)|divide(#1,#2)| | "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 60 * 4 = 240 m time taken = 240 * 2 / 5 = 96 sec answer is a" | gain |
math_qa__umFNLRtsrjlEoMHZ | A 60 cm long wire is to be cut into two pieces so that one piece will be 2/4th of the other, how many centimeters will the shorter piece be? Options.
A) 73
B) 20
C) 83
D) 21
E) 52 | <gadget id="calculator">2 / 4</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">60 / (3/2)</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<result>B</result> | B | 20 | A 60 cm long wire is to be cut into two pieces so that one piece will be 2/4th of the other, how many centimeters will the shorter piece be? | {
"A": "73",
"B": "20",
"C": "83",
"D": "21",
"E": "52"
} | subtract(60, divide(60, add(divide(2, 4), const_1))) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | "explanation : 1 : 2 / 4 = 4 : 2 2 / 6 * 60 = 20 answer : option b" | physics |
math_qa__B1YYf3hk5tRQSiHX | If a book is sold at 9% profit instead of 9% loss, it would have brought Rs 9 more. Find out the cost price of the book Choices:
A) 75 B) 72 C) 50 D) 70 E) 80 | <gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">100 * (9/2)</gadget>
<output>450</output>
<gadget id="calculator">450 / 9</gadget>
<output>50</output>
<result>C</result> | C | 50 | If a book is sold at 9% profit instead of 9% loss, it would have brought Rs 9 more. Find out the cost price of the book | {
"A": "75",
"B": "72",
"C": "50",
"D": "70",
"E": "80"
} | divide(multiply(const_100, divide(9, const_2)), 9) | divide(n0,const_2)|multiply(#0,const_100)|divide(#1,n0) | let c . p . of the book be rs . ’ x ’ given , 1.09 x - 0.91 x = 9 = > 0.18 x = 9 = 9 / 0.18 = rs 50 answer : c | gain |
math_qa__M69s6Byx7MAqrwzo | A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is: Choose the correct choice.
A) 4120 m cube B) 4140 m cube C) 5140 m cube D) 5120 m cube E) none of these | <gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">48 - 16</gadget>
<output>32</output>
<gadget id="calculator">36 - 16</gadget>
<output>20</output>
<gadget id="calculator">32 * 20 * 8</gadget>
<output>5_120</output>
<result>D</result> | D | 5,120 | A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is: | {
"A": "4120 m cube",
"B": "4140 m cube",
"C": "5140 m cube",
"D": "5120 m cube",
"E": "none of these"
} | volume_rectangular_prism(subtract(48, multiply(8, const_2)), subtract(36, multiply(8, const_2)), 8) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2)| | "explanation : l = ( 48 - 16 ) m = 32 m , [ because 8 + 8 = 16 ] b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m cube = 5120 m cube . option d" | geometry |
math_qa__fsLT1Ms2HRBpBMll | Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?
Select.
A) 6 days B) 18 days C) 21 days D) 3 days E) 13 days | <gadget id="calculator">3 * 6</gadget>
<output>18</output>
<result>B</result> | B | 18 | Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type? | {
"A": "6 days",
"B": "18 days",
"C": "21 days",
"D": "3 days",
"E": "13 days"
} | multiply(const_3, 6) | multiply(n0,const_3)| | "we have the important relation , more work , more time ( days ) a piece of work can be done in 6 days . three times of work of same type can be done in 6 x 3 = 18 days answer b" | physics |
math_qa__ER91OzWcvV72Vkme | A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 3 less, he would have made a profit of 10%. The C.P. of the article was
Choose the correct option.
A) 344 B) 218 C) 200 D) 600 E) 211 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">200 * 3</gadget>
<output>600</output>
<result>D</result> | D | 600 | A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 3 less, he would have made a profit of 10%. The C.P. of the article was | {
"A": "344",
"B": "218",
"C": "200",
"D": "600",
"E": "211"
} | multiply(multiply(multiply(5, const_4.0), 10), 3) | multiply(n0,const_4.0)|multiply(n3,#0)|multiply(n2,#1)| | "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 3 = > x = 600 answer : d ) rs 600" | gain |
math_qa__Wif1cBGdyrf8kMfj | The average (arithmetic mean) of 4 positive integers is 45. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?
Options: A) 55 B) 65 C) 100 D) 89 E) 115 | <gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">180 - 90</gadget>
<output>90</output>
<result>D</result> | D | 89 | The average (arithmetic mean) of 4 positive integers is 45. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have? | {
"A": "55",
"B": "65",
"C": "100",
"D": "89",
"E": "115"
} | subtract(multiply(45, 4), multiply(45, 2)) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)| | "a + b + c + d = 180 a + b = 90 c + d = 90 greatest possible = 89 ( just less than 1 ) answer = d" | general |
math_qa__iDcfZuFCUwiPErAZ | If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20, what is the value of r-p? Choose the correct answer.
A) 20 B) 10 C) 30 D) 40 E) 5 | <gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">40 - 20</gadget>
<output>20</output>
<result>A</result> | A | 20 | If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20, what is the value of r-p? | {
"A": "20",
"B": "10",
"C": "30",
"D": "40",
"E": "5"
} | subtract(multiply(20, const_2), multiply(10, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1) | arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 40 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 20 hence , the correct answer is a | general |
math_qa__k1cr1vpZNk8KGFwT | One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 260cm when it touches the floor on third time. What is the value of the original height? Pick:
A) 80 cm B) 90 cm C) 104 cm D) 120 cm E) 130 cm | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">260 / (5/2)</gadget>
<output>104</output>
<result>C</result> | C | 104 | One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 260cm when it touches the floor on third time. What is the value of the original height? | {
"A": "80 cm",
"B": "90 cm",
"C": "104 cm",
"D": "120 cm",
"E": "130 cm"
} | divide(260, add(const_2, divide(50, const_100))) | divide(n0,const_100)|add(#0,const_2)|divide(n1,#1) | when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 260 2.5 h = 260 h = 104 . c is the answer . | gain |
math_qa__6T0tjHIP2xaQgIjX | A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $17 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
Pick one:
A) $ 22.50 B) $ 23.50 C) $ 24.50 D) $ 25.50 E) $ 26.50 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 17</gadget>
<output>17/5 = around 3.4</output>
<gadget id="calculator">(17/5) + 17</gadget>
<output>102/5 = around 20.4</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">(102/5) / (4/5)</gadget>
<output>51/2 = around 25.5</output>
<result>D</result> | D | 25.5 | A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $17 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item? | {
"A": "$ 22.50",
"B": "$ 23.50",
"C": "$ 24.50",
"D": "$ 25.50",
"E": "$ 26.50"
} | divide(add(multiply(divide(20, const_100), 17), 17), divide(subtract(const_100, 20), const_100)) | divide(n0,const_100)|subtract(const_100,n0)|divide(#1,const_100)|multiply(n1,#0)|add(n1,#3)|divide(#4,#2)| | "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 17 ) = 0.8 x x = 1.2 ( 17 ) / 0.8 = 1.5 ( 17 ) = $ 25.50 the answer is d ." | gain |
math_qa__KR6zFDkdon6vYivn | The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A?
Select the correct option.
A) 12 B) 10 C) c is elder than a D) data inadequate E) none | <gadget id="calculator">10 * 1</gadget>
<output>10</output>
<result>B</result> | B | 10 | The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A? | {
"A": "12",
"B": "10",
"C": "c is elder than a",
"D": "data inadequate",
"E": "none"
} | multiply(10, const_1) | multiply(n0,const_1)| | "solution [ ( a + b ) - ( b + c ) ] = 10 â € ¹ = â € º a - c = 10 . answer b" | general |
math_qa__CyvdAT82aYgZTks6 | how many halves are there in 9 - fourth ?
Answers.
A) 8
B) 4.5
C) 3.2
D) 7
E) 3 | <gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(9/4) / (1/2)</gadget>
<output>9/2 = around 4.5</output>
<result>B</result> | B | 4.5 | how many halves are there in 9 - fourth ? | {
"A": "8",
"B": "4.5",
"C": "3.2",
"D": "7",
"E": "3"
} | divide(divide(9, const_4), divide(const_1, const_2)) | divide(n0,const_4)|divide(const_1,const_2)|divide(#0,#1) | divide 9 / 4 by 1 / 2 = 9 / 4 ÷ 1 / 2 = 9 / 4 * 2 / 1 = 18 / 4 = 4.5 . answer is b . | general |
math_qa__O1vGv7MiX3VIXswh | What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125? Pick one
A) 18.2 B) 20 C) 25 D) 26 E) 28 | <gadget id="calculator">121 + 125</gadget>
<output>246</output>
<gadget id="calculator">246 - 100</gadget>
<output>146</output>
<gadget id="calculator">146 - 96</gadget>
<output>50</output>
<gadget id="calculator">83 / 3</gadget>
<output>83/3 = around 27.666667</output>
<gadget id="calculator">50 - (83/3)</gadget>
<output>67/3 = around 22.333333</output>
<gadget id="calculator">(67/3) - 4</gadget>
<output>55/3 = around 18.333333</output>
<result>A</result> | A | 18.2 | What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125? | {
"A": "18.2",
"B": "20",
"C": "25",
"D": "26",
"E": "28"
} | subtract(subtract(subtract(subtract(add(121, 125), 100), 96), divide(83, const_3)), const_4) | add(n4,n5)|divide(n1,const_3)|subtract(#0,n3)|subtract(#2,n2)|subtract(#3,#1)|subtract(#4,const_4) | 1 . firstly find the mean : mean = ( 75 + 83 + 96 + 100 + 121 + 125 ) ÷ 6 = 600 ÷ 6 = 100 2 . next find the variance . to calculate the variance , take each difference , square it , and then average the result : ( 75 - 100 ) 2 + ( 83 - 100 ) 2 + ( 96 - 100 ) 2 + ( 100 - 100 ) 2 + ( 121 - 100 ) 2 + ( 125 - 100 ) 2 = ( - 25 ) 2 + ( - 17 ) 2 + ( - 4 ) 2 + ( 0 ) 2 + ( 21 ) 2 + ( 25 ) 2 = 625 + 289 + 16 + 0 + 441 + 625 = 1996 so the variance = 1996 ÷ 6 = 332.66 . . . 3 . the standard deviation is just the square root of the variance = √ ( 332.66 . . . ) = 18.2 correct to 1 decimal places answer is a | general |
math_qa__PJBW7nI1EBklQ55L | 63 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Choose the correct choice from the following:
A) 64
B) 128
C) 152
D) 216
E) 153 | <gadget id="calculator">63 ** (1/3)</gadget>
<output>63**(1/3) = around 3.979057</output>
<gadget id="calculator">(63**(1/3)) + 2</gadget>
<output>2 + 63**(1/3) = around 5.979057</output>
<gadget id="calculator">(2 + 63**(1/3)) ** 3</gadget>
<output>(2 + 63**(1/3))**3 = around 213.746064</output>
<gadget id="calculator">((2 + 63**(1/3))**3) - 63</gadget>
<output>-63 + (2 + 63**(1/3))**3 = around 150.746064</output>
<result>E</result> | E | 153 | 63 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? | {
"A": "64",
"B": "128",
"C": "152",
"D": "216",
"E": "153"
} | subtract(volume_cube(add(cube_edge_by_volume(63), const_2)), 63) | cube_edge_by_volume(n0)|add(#0,const_2)|volume_cube(#1)|subtract(#2,n0)| | "63 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 63 = 153 hence , e is the answer ." | geometry |
math_qa__g5qDSonJAT2DI6cf | There are two tanks A & B with same capacity of 20 litres. If the water inflow rate (speed) in Tank A is 2 litres per hour & in Tank B is 4 litres per hour. How much longer tank A takes to fill than Tank B? Select: A) 4 hours B) 5 hours C) 3 hours D) 2 hours E) 1 hour | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<result>B</result> | B | 5 | There are two tanks A & B with same capacity of 20 litres. If the water inflow rate (speed) in Tank A is 2 litres per hour & in Tank B is 4 litres per hour. How much longer tank A takes to fill than Tank B? | {
"A": "4 hours",
"B": "5 hours",
"C": "3 hours",
"D": "2 hours",
"E": "1 hour"
} | subtract(divide(20, 2), divide(20, 4)) | divide(n0,n1)|divide(n0,n2)|subtract(#0,#1) | time taken for tank a to fill = 20 / 2 = 10 hours time taken for tank b to fill = 20 / 4 = 5 hours so tank a takes 5 more hours to fill answer : b | physics |
math_qa__c9wNaZrRJVdSbGqT | While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%)
Choose the correct choice from the following options
A) 4.09 B) 4.0 C) 4.04 D) 4.02 E) 4.01 | <gadget id="calculator">100 + 2</gadget>
<output>102</output>
<gadget id="calculator">102 ** 2</gadget>
<output>10_404</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_404 - 10_000</gadget>
<output>404</output>
<gadget id="calculator">404 / 100</gadget>
<output>101/25 = around 4.04</output>
<result>C</result> | C | 4.04 | While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%) | {
"A": "4.09",
"B": "4.0",
"C": "4.04",
"D": "4.02",
"E": "4.01"
} | divide(subtract(square_area(add(const_100, 2)), square_area(const_100)), const_100) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|divide(#3,const_100) | explanation : given error = 2 % while measuring the side of a square . if the correct value of the side of square is 100 , the measured value : = > 100 + 2 % * 100 = 100 + 2 = 102 the area of square with edge 100 = side * side = > 100 * 100 = > 10000 the area of square with side 102 = 102 * 102 = 10404 error in area calculation = 10404 - 1000 = 404 % error = ( 404 / 10000 ) * 100 = 4.04 % answer : c | geometry |
math_qa__TEEGbaSvfsI2eNbD | A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $40,000 commission, how many machines did she sell?
Choose the correct choice from the following options:
A) 90 B) 103 C) 105 D) 115 E) 125 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">7 * 6</gadget>
<output>42</output>
<gadget id="calculator">42 * 100</gadget>
<output>4_200</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">4_200 * 10</gadget>
<output>42_000</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">10_000 * (3/100)</gadget>
<output>300</output>
<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">42_000 - 30_000</gadget>
<output>12_000</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">10_000 * (1/25)</gadget>
<output>400</output>
<gadget id="calculator">12_000 / 400</gadget>
<output>30</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<result>E</result> | E | 125 | A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $40,000 commission, how many machines did she sell? | {
"A": "90",
"B": "103",
"C": "105",
"D": "115",
"E": "125"
} | add(100, divide(subtract(multiply(multiply(multiply(add(4, 3), multiply(3, const_2)), 100), multiply(add(4, const_1), const_2)), multiply(multiply(multiply(100, 100), divide(3, 100)), 100)), multiply(multiply(100, 100), divide(4, 100)))) | add(n0,n2)|add(const_1,n2)|divide(n0,n1)|divide(n2,n1)|multiply(const_2,n0)|multiply(n1,n1)|multiply(#0,#4)|multiply(#1,const_2)|multiply(#2,#5)|multiply(#3,#5)|multiply(#6,n1)|multiply(n1,#8)|multiply(#10,#7)|subtract(#12,#11)|divide(#13,#9)|add(n1,#14)| | "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 40000 - 30000 = 10000 so 25 more machines . . total = 125 machines imo e . . ." | gain |
math_qa__zZ0hjB8FdEKKInoG | Find the average of all the numbers between 6 and 30 which are divisible by 4.
Choose the correct choice from the following choices
A) 15 B) 18 C) 20 D) 22 E) none | <gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">30 - 4</gadget>
<output>26</output>
<gadget id="calculator">10 + 26</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<result>B</result> | B | 18 | Find the average of all the numbers between 6 and 30 which are divisible by 4. | {
"A": "15",
"B": "18",
"C": "20",
"D": "22",
"E": "none"
} | divide(add(add(6, const_4), subtract(30, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | "sol . average = ( 8 + 12 + 16 + 20 + 24 + 28 / 6 ) = 108 / 6 = 18 answer b" | general |
math_qa__iraCOjJ4oa7Pkmf6 | In a renowned city, the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds. Estimate the size of the population net increase that occurs in one day. Pick:
A) 32,300 B) 172,800 C) 468,830 D) 86,400 E) 259,200 | <gadget id="calculator">8 - 6</gadget>
<output>2</output>
<gadget id="calculator">2 * 3_600</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 * 12</gadget>
<output>86_400</output>
<result>D</result> | D | 86,400 | In a renowned city, the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds. Estimate the size of the population net increase that occurs in one day. | {
"A": "32,300",
"B": "172,800",
"C": "468,830",
"D": "86,400",
"E": "259,200"
} | multiply(multiply(subtract(8, 6), const_3600), const_12) | subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)| | "every 2 seconds , 2 persons are added ( 8 - 6 ) . every second 1 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option d" | general |
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