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__RQ0RsXSgkUmJ9nfz | A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long?
Answers
A) 15.60 B) 16.0 C) 17.8 D) 18.7 E) 19.1 | <gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">0.4 * 4</gadget>
<output>1.6</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">0.4 * 7</gadget>
<output>2.8</output>
<gadget id="calculator">2.8 * 5</gadget>
<output>14</output>
<gadget id="calculator">1.6 + 14</gadget>
<output>15.6</output>
<gadget id="calculator">15.6 + 3.1</gadget>
<output>18.7</output>
<result>D</result> | D | 18.7 | A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long? | {
"A": "15.60",
"B": "16.0",
"C": "17.8",
"D": "18.7",
"E": "19.1"
} | add(add(multiply(0.4, subtract(5, 1)), multiply(multiply(0.4, subtract(8, 1)), 5)), 3.1) | subtract(n2,n1)|subtract(n6,n1)|multiply(n3,#0)|multiply(n3,#1)|multiply(n2,#3)|add(#2,#4)|add(n0,#5) | first 1 / 5 minute charge = 3.10 cents rest of the minute = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the minute = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 cents answer is d . | general |
math_qa__KsFymTOGkGHAo8VE | A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there?
Choose the correct choice from the following choices
A) 30
B) 32
C) 36
D) 40
E) 45 | <gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">8 * 50</gadget>
<output>400</output>
<gadget id="calculator">400 / 10</gadget>
<output>40</output>
<result>D</result> | D | 40 | A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. How many men were originally there? | {
"A": "30",
"B": "32",
"C": "36",
"D": "40",
"E": "45"
} | divide(multiply(8, subtract(60, 10)), 10) | subtract(n0,n2)|multiply(n1,#0)|divide(#1,n2) | originally 1 et there be x men . more men , less days ( x + 8 ) : x ∷ 60 : 50 so , x + 8 / x = 60 / 50 or x = 40 . answer : d | physics |
math_qa__ynCiR1oo9N12pQd6 | How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7.5 m x 6 m x 22.5 cm? Select the correct option:
A) 6000 B) 6410 C) 6440 D) 6500 E) 6800 | <gadget id="calculator">7.5 * 100</gadget>
<output>750</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">750 * 600</gadget>
<output>450_000</output>
<gadget id="calculator">450_000 * 22.5</gadget>
<output>10_125_000</output>
<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>
<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>
<gadget id="calculator">10_125_000 / 1_687.5</gadget>
<output>6_000</output>
<result>A</result> | A | 6,000 | How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7.5 m x 6 m x 22.5 cm? | {
"A": "6000",
"B": "6410",
"C": "6440",
"D": "6500",
"E": "6800"
} | divide(multiply(multiply(multiply(7.5, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6)) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)| | "number of bricks = volume of wall / volume of bricks = 750 x 600 x 22.5 / 25 x 11.25 x 6 = = 6000 answer : a" | physics |
math_qa__ehMgBklYpik56tMT | If the function Q is defined by the formula Q = 5w/(4vf(z^2)), by what factor will Q be multiplied if w is quadrupled, f is doubled, and z is tripled?
Choices:
A) 1 / 9 B) 2 / 9 C) 4 / 9 D) 3 / 9 E) 2 / 27 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">2 * 9</gadget>
<output>18</output>
<gadget id="calculator">4 / 18</gadget>
<output>2/9 = around 0.222222</output>
<result>B</result> | B | 0.222222 | If the function Q is defined by the formula Q = 5w/(4vf(z^2)), by what factor will Q be multiplied if w is quadrupled, f is doubled, and z is tripled? | {
"A": "1 / 9",
"B": "2 / 9",
"C": "4 / 9",
"D": "3 / 9",
"E": "2 / 27"
} | divide(4, multiply(2, power(const_3, 2))) | power(const_3,n2)|multiply(n2,#0)|divide(n1,#1)| | "we just need to find the factor thats all , w - > quadrupled - > 4 w f - > doubled - > 2 f z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and f * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b" | general |
math_qa__Fx1kQjIZwkskgv9N | 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are? Choose one
A) 6 rs
B) 2 rs
C) 4 rs
D) 9 rs
E) 3 rs | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">90 / 15</gadget>
<output>6</output>
<result>A</result> | A | 6 | 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are? | {
"A": "6 rs",
"B": "2 rs",
"C": "4 rs",
"D": "9 rs",
"E": "3 rs"
} | divide(90, multiply(const_3, 5)) | multiply(n0,const_3)|divide(n2,#0)| | "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : a" | general |
math_qa__gJHaBTW5cvArWSM1 | A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? Pick one
A) 0.9 B) 0.75 C) 0.6 D) 0.8 E) 0.5 | <gadget id="calculator">50 + 30</gadget>
<output>80</output>
<gadget id="calculator">80 + 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<result>A</result> | A | 0.9 | A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? | {
"A": "0.9",
"B": "0.75",
"C": "0.6",
"D": "0.8",
"E": "0.5"
} | divide(add(add(50, 30), 10), 100) | add(n1,n2)|add(n3,#0)|divide(#1,n0)| | "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 10 ) / 100 = 90 / 100 = 0.9 . answer is a" | other |
math_qa__lUFPCjfHOXmZREBW | A heap of coconuts is divided into groups of 2, 3 and 11 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
Choose the correct option
A) 31 B) 41 C) 51 D) 67 E) 71 | <gadget id="calculator">lcm(2, 3)</gadget>
<output>6</output>
<gadget id="calculator">lcm(6, 11)</gadget>
<output>66</output>
<gadget id="calculator">66 - 1</gadget>
<output>65</output>
<result>D</result> | D | 67 | A heap of coconuts is divided into groups of 2, 3 and 11 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61 | {
"A": "31",
"B": "41",
"C": "51",
"D": "67",
"E": "71"
} | subtract(lcm(lcm(2, 3), 11), const_1) | lcm(n0,n1)|lcm(n2,#0)|subtract(#1,const_1) | lcm = 66 = > 66 + 1 = 67 answer : d | general |
math_qa__WU1jevzfnMn8ErTW | Along a yard 441 metres long, 22 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees Choose the correct answer
A) 18 B) 19 C) 20 D) 21 E) 12 | <gadget id="calculator">22 - 1</gadget>
<output>21</output>
<gadget id="calculator">441 / 21</gadget>
<output>21</output>
<result>D</result> | D | 21 | Along a yard 441 metres long, 22 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees | {
"A": "18",
"B": "19",
"C": "20",
"D": "21",
"E": "12"
} | divide(441, subtract(22, const_1)) | subtract(n1,const_1)|divide(n0,#0)| | "explanation : 22 trees have 21 gaps between them , required distance ( 441 / 21 ) = 21 option d" | physics |
math_qa__HMCZrY3dLDWVrmIj | Calculate the area of a triangle, if the sides are 30 cm, 21 cm and 10 cm, what is its area? Options:
A) 145 cm 2
B) 105 cm 2
C) 125 cm 2
D) 115 cm 2
E) 135 cm 2 | <gadget id="calculator">21 / 2</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">(21/2) * 10</gadget>
<output>105</output>
<result>B</result> | B | 105 | Calculate the area of a triangle, if the sides are 30 cm, 21 cm and 10 cm, what is its area? | {
"A": "145 cm 2",
"B": "105 cm 2",
"C": "125 cm 2",
"D": "115 cm 2",
"E": "135 cm 2"
} | multiply(divide(21, const_2), 10) | divide(n1,const_2)|multiply(n2,#0)| | "the triangle with sides 30 cm , 21 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 21 * 10 = 105 cm 2 answer : b" | geometry |
math_qa__SDWLUTKPuNkCgYgf | the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long . what is the distance traveled by the cart , when the front wheel has done 5 more revolutions than the rear wheel ?
Pick:
A) 20 ft
B) 25 ft
C) 750 ft
D) 900 ft
E) 2400 ft | <gadget id="calculator">30 * 5</gadget>
<output>150</output>
<gadget id="calculator">32 - 30</gadget>
<output>2</output>
<gadget id="calculator">150 / 2</gadget>
<output>75</output>
<gadget id="calculator">75 + 5</gadget>
<output>80</output>
<gadget id="calculator">30 * 80</gadget>
<output>2_400</output>
<result>E</result> | E | 2,400 | the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long . what is the distance traveled by the cart , when the front wheel has done 5 more revolutions than the rear wheel ? | {
"A": "20 ft",
"B": "25 ft",
"C": "750 ft",
"D": "900 ft",
"E": "2400 ft"
} | multiply(30, add(divide(multiply(30, 5), subtract(32, 30)), 5)) | multiply(n0,n2)|subtract(n1,n0)|divide(#0,#1)|add(n2,#2)|multiply(n0,#3) | point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 32 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 75 . sub x = 75 either in ( x + 5 ) * 30 or in x * 32 to get the distance , which is 2400 . so the correct choice is e . | physics |
math_qa__ljHc3jQRj5xsdiVW | Find the annual income derived by investing $ 6800 in 50% stock at 136. Pick one.
A) 550 B) 2500 C) 250 D) 3000 E) 400 | <gadget id="calculator">6_800 * 50</gadget>
<output>340_000</output>
<gadget id="calculator">340_000 / 136</gadget>
<output>2_500</output>
<result>B</result> | B | 2,500 | Find the annual income derived by investing $ 6800 in 50% stock at 136. | {
"A": "550",
"B": "2500",
"C": "250",
"D": "3000",
"E": "400"
} | divide(multiply(6800, 50), 136) | multiply(n0,n1)|divide(#0,n2)| | "by investing $ 136 , income obtained = $ 50 . by investing $ 6800 , income obtained = $ [ ( 50 / 136 ) * 6800 ] = $ 2500 . answer b ." | gain |
math_qa__Lx8mX5xuqrIWoRT3 | A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes. Then the speed of the current is : Choose the correct choice from the following answers
A) 1 kmph B) 0.5 kmph C) 3 kmph D) 2.5 kmph E) 3.5 kmph | <gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) * 60</gadget>
<output>4</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 60</gadget>
<output>3</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<result>B</result> | B | 0.5 | A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes. Then the speed of the current is : | {
"A": "1 kmph",
"B": "0.5 kmph",
"C": "3 kmph",
"D": "2.5 kmph",
"E": "3.5 kmph"
} | divide(subtract(multiply(divide(1, 15), const_60), multiply(divide(1, 20), const_60)), const_2) | divide(n0,n3)|divide(n0,n1)|multiply(#0,const_60)|multiply(#1,const_60)|subtract(#2,#3)|divide(#4,const_2)| | "rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate down stream = 1 / 15 * 60 = 4 kmph rate of the current = ½ ( 4 - 3 ) = 0.5 kmph answer : b" | physics |
math_qa__1j8vWureOoRPHAgX | A motorcyclist X drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist Y at a rate of 4 rounds per hour. After how long they will cross each other for the first time? Options:
A) 10 min
B) 20 min
C) 30 min
D) 40 min
E) none of these | <gadget id="calculator">2 * 60</gadget>
<output>120</output>
<gadget id="calculator">120 / 4</gadget>
<output>30</output>
<result>C</result> | C | 30 | A motorcyclist X drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist Y at a rate of 4 rounds per hour. After how long they will cross each other for the first time? | {
"A": "10 min",
"B": "20 min",
"C": "30 min",
"D": "40 min",
"E": "none of these"
} | divide(multiply(const_2, const_60), 4) | multiply(const_2,const_60)|divide(#0,n1) | explanation : since x and y move in the same direction they cross each other when there is a difference of two round between the two . relative speed of x and y = 4 - 2 = 2 . time taken to complete one round at this speed = 1 / 2 hour = 30 minutes answer : c | gain |
math_qa__PYpAEToYlRithRuc | A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 30% lemonade syrup? Answers.
A) 1.5 B) 1.75 C) 2.14 D) 2.34 E) 2.64 | <gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(7/15) - (2/5)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) / (7/15)</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/7) * 15</gadget>
<output>15/7 = around 2.142857</output>
<result>C</result> | C | 2.14 | A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 30% lemonade syrup? | {
"A": "1.5",
"B": "1.75",
"C": "2.14",
"D": "2.34",
"E": "2.64"
} | multiply(divide(subtract(divide(7, add(8, 7)), divide(const_2, add(const_2, const_3))), divide(7, add(8, 7))), add(8, 7)) | add(n0,n1)|add(const_2,const_3)|divide(n1,#0)|divide(const_2,#1)|subtract(#2,#3)|divide(#4,#2)|multiply(#0,#5)| | "let the total solution is 150 l with 80 l water 70 l syrup . to make 30 % syrup solution , the result solution must have 105 l syrup and 45 l syrup . therefore we are taking 25 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 25 l syrup in 53.6 l solution we started by multiplying 10 now to get to the result we need to divide by 25 = > amount of solution to be replaced with water = ( 53.6 / 25 ) = 2.14 . correct option : c" | gain |
math_qa__f2MjzfRcKVtV13IE | How many times are the hands of a clock at right angle in 5 days?
Pick.
A) 202
B) 220
C) 210
D) 212
E) 222 | <gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">24 * 5</gadget>
<output>120</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">48 - 4</gadget>
<output>44</output>
<gadget id="calculator">120 * 44</gadget>
<output>5_280</output>
<gadget id="calculator">5_280 / 24</gadget>
<output>220</output>
<result>B</result> | B | 220 | How many times are the hands of a clock at right angle in 5 days? | {
"A": "202",
"B": "220",
"C": "210",
"D": "212",
"E": "222"
} | divide(multiply(multiply(multiply(const_12, const_2), 5), subtract(multiply(const_12, const_4), const_4)), multiply(const_12, const_2)) | multiply(const_12,const_2)|multiply(const_12,const_4)|multiply(n0,#0)|subtract(#1,const_4)|multiply(#2,#3)|divide(#4,#0) | in 1 day , they are at right angles 44 times . in 5 days , they are at right angles 220 times . answer : option b | physics |
math_qa__rjIG6oBCqHXQJT5e | Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.57. How much did the meal cost without the tip? Select the correct option:
A) $ 31.80 B) $ 29.91 C) $ 30.15 D) $ 30.60 E) $ 30.85 | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">36.57 * (3/20)</gadget>
<output>5.4855</output>
<gadget id="calculator">36.57 - 5.4855</gadget>
<output>31.0845</output>
<result>A</result> | A | 31.8 | Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.57. How much did the meal cost without the tip? | {
"A": "$ 31.80",
"B": "$ 29.91",
"C": "$ 30.15",
"D": "$ 30.60",
"E": "$ 30.85"
} | subtract(36.57, multiply(36.57, divide(15, const_100))) | divide(n0,const_100)|multiply(n1,#0)|subtract(n1,#1) | the tip is a percent increase of 15 % , which is 115 % . let x equal the price before the tip . thus , 115 % of this price equals $ 36.57 : 1.15 x = 36.57 divide both sides by 1.15 : = > x = 36.57 / 1.15 = 31.80 correct answer a ) $ 31.80 | general |
math_qa__ZJytJWlGLfsGztI9 | What should be the least number to be added to the 4499 number to make it divisible by 9? Choose one.
A) 1 B) 17 C) 18 D) 77 E) 26 | <gadget id="calculator">4_499 % 9</gadget>
<output>8</output>
<gadget id="calculator">9 - 8</gadget>
<output>1</output>
<result>A</result> | A | 1 | What should be the least number to be added to the 4499 number to make it divisible by 9? | {
"A": "1",
"B": "17",
"C": "18",
"D": "77",
"E": "26"
} | subtract(9, reminder(4499, 9)) | reminder(n0,n1)|subtract(n1,#0)| | "answer : 1 option : a" | general |
math_qa__wqucCiyWhrWd7F1N | We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value E of the ratio A/B? Pick:
A) 1 / 2 B) 1 / 3 C) 2 / 3 D) 1 / 4 E) 1 / 5 | <gadget id="calculator">2_020 / 2_020</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value E of the ratio A/B? | {
"A": "1 / 2",
"B": "1 / 3",
"C": "2 / 3",
"D": "1 / 4",
"E": "1 / 5"
} | divide(divide(2020, 2020), add(divide(2020, 2020), divide(2020, 2020))) | divide(n6,n6)|add(#0,#0)|divide(#0,#1)| | "e - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ." | general |
math_qa__ryXatkSADyFWZ0OE | Jane started baby-sitting when she was 20 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? Choose the correct choice from the following choices.
A) 20 B) 21 C) 22 D) 23 E) 24 | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">32 - 20</gadget>
<output>12</output>
<gadget id="calculator">10 + 12</gadget>
<output>22</output>
<result>C</result> | C | 22 | Jane started baby-sitting when she was 20 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? | {
"A": "20",
"B": "21",
"C": "22",
"D": "23",
"E": "24"
} | add(divide(20, const_2), subtract(32, 20)) | divide(n0,const_2)|subtract(n1,n0)|add(#0,#1) | check two extreme cases : jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : c . | general |
math_qa__CxAmBxkU2T11kRCj | If integer k is equal to the sum of all even multiples of 25 between 295 and 615, what is the greatest prime factor of k?
Choose the correct choice from the following answers: A) 5 B) 7 C) 11 D) 13 E) 17 | <gadget id="calculator">615 / 25</gadget>
<output>123/5 = around 24.6</output>
<gadget id="calculator">floor(123/5)</gadget>
<output>24</output>
<gadget id="calculator">24 * 25</gadget>
<output>600</output>
<gadget id="calculator">295 / 25</gadget>
<output>59/5 = around 11.8</output>
<gadget id="calculator">floor(59/5)</gadget>
<output>11</output>
<gadget id="calculator">11 * 25</gadget>
<output>275</output>
<gadget id="calculator">600 - 275</gadget>
<output>325</output>
<gadget id="calculator">325 / 25</gadget>
<output>13</output>
<gadget id="calculator">13 + 1</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>B</result> | B | 7 | If integer k is equal to the sum of all even multiples of 25 between 295 and 615, what is the greatest prime factor of k? | {
"A": "5",
"B": "7",
"C": "11",
"D": "13",
"E": "17"
} | divide(add(divide(subtract(multiply(floor(divide(615, 25)), 25), multiply(floor(divide(295, 25)), 25)), 25), const_1), const_2) | divide(n2,n0)|divide(n1,n0)|floor(#0)|floor(#1)|multiply(n0,#2)|multiply(n0,#3)|subtract(#4,#5)|divide(#6,n0)|add(#7,const_1)|divide(#8,const_2) | if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600 . using arithmetic progression to find n : 600 = 300 + ( n - 1 ) 50 300 + 50 = 50 n 350 = 50 n = > n = 7 the sum would be : 11 * mean mean = [ 600 + 300 ] / 2 = 450 7 * 450 = 4950 b | general |
math_qa__CFqlzWXdJbOG0vDz | Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? Choose the correct option: A) 9680 B) 4280 C) 2789 D) 7892 E) 2792 | <gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">9_200 - 8_000</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 / 3</gadget>
<output>400</output>
<gadget id="calculator">400 / 8_000</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/50) + (1/20)</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">(7/100) * 8_000</gadget>
<output>560</output>
<gadget id="calculator">560 * 3</gadget>
<output>1_680</output>
<gadget id="calculator">1_680 + 8_000</gadget>
<output>9_680</output>
<result>A</result> | A | 9,680 | Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? | {
"A": "9680",
"B": "4280",
"C": "2789",
"D": "7892",
"E": "2792"
} | add(multiply(multiply(add(divide(2, const_100), divide(divide(subtract(9200, 8000), 3), 8000)), 8000), 3), 8000) | 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)| | "( 8000 * 3 * 2 ) / 100 = 480 9200 - - - - - - - - 9680 answer : a" | gain |
math_qa__3ezI3EPgMhosuP5A | How long does a train 150 m long traveling at 50 kmph takes to cross a bridge of 250m in length? Options: A) 28.8 sec B) 16.8 sec C) 15.2 sec D) 25.4 sec E) 16.2 sec | <gadget id="calculator">150 + 250</gadget>
<output>400</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">50 * (5/18)</gadget>
<output>125/9 = around 13.888889</output>
<gadget id="calculator">400 / (125/9)</gadget>
<output>144/5 = around 28.8</output>
<result>A</result> | A | 28.8 | How long does a train 150 m long traveling at 50 kmph takes to cross a bridge of 250m in length? | {
"A": "28.8 sec",
"B": "16.8 sec",
"C": "15.2 sec",
"D": "25.4 sec",
"E": "16.2 sec"
} | divide(add(150, 250), multiply(50, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | "d = 150 + 250 = 400 m s = 50 * 5 / 18 = 125 / 9 t = 400 * 125 / 9 = 28.8 sec answer : a" | physics |
math_qa__pRak0dLhx1LhuS0y | A train 50 m long passes a platform 100 m long in 10 seconds. The speed of the train in m/sec is ?
Choose the correct choice from the following answers:
A) 150 B) 50 C) 10 D) 15 E) 12 | <gadget id="calculator">50 + 100</gadget>
<output>150</output>
<gadget id="calculator">150 / 10</gadget>
<output>15</output>
<result>D</result> | D | 15 | A train 50 m long passes a platform 100 m long in 10 seconds. The speed of the train in m/sec is ? | {
"A": "150",
"B": "50",
"C": "10",
"D": "15",
"E": "12"
} | divide(add(50, 100), 10) | add(n0,n1)|divide(#0,n2) | speed of train = distance covered / time . = ( 50 + 100 ) / 10 = 15 m / sec . answer : d | physics |
math_qa__vUSw483gS5tjKhMb | The sale price sarees listed for Rs.550 after successive discount is 18% and 12% is?
Choose one: A) 298 B) 237 C) 342 D) 396 E) 291 | <gadget id="calculator">550 * 18</gadget>
<output>9_900</output>
<gadget id="calculator">9_900 / 100</gadget>
<output>99</output>
<gadget id="calculator">550 - 99</gadget>
<output>451</output>
<gadget id="calculator">451 * 12</gadget>
<output>5_412</output>
<gadget id="calculator">5_412 / 100</gadget>
<output>1_353/25 = around 54.12</output>
<gadget id="calculator">451 - (1_353/25)</gadget>
<output>9_922/25 = around 396.88</output>
<result>D</result> | D | 396 | The sale price sarees listed for Rs.550 after successive discount is 18% and 12% is? | {
"A": "298",
"B": "237",
"C": "342",
"D": "396",
"E": "291"
} | subtract(subtract(550, divide(multiply(550, 18), const_100)), divide(multiply(subtract(550, divide(multiply(550, 18), const_100)), 12), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | "550 * ( 88 / 100 ) * ( 82 / 100 ) = 396 answer : d" | gain |
math_qa__NGvKa4TRUdhj0ARg | An empty wooden vessel weighs 12% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled. Choose the correct choice from the following:
A) 3 / 5 B) 5 / 11 C) 1 / 24 D) 4 / 9 E) 2 / 5 | <gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">5 / 11</gadget>
<output>5/11 = around 0.454545</output>
<result>B</result> | B | 0.454545 | An empty wooden vessel weighs 12% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled. | {
"A": "3 / 5",
"B": "5 / 11",
"C": "1 / 24",
"D": "4 / 9",
"E": "2 / 5"
} | divide(subtract(divide(12, const_2), const_1), subtract(12, const_1)) | divide(n0,const_2)|subtract(n0,const_1)|subtract(#0,const_1)|divide(#2,#1)| | "an empty wooden vessel weighs 12 % of its total weight when filled with paint : vessel = 0.12 ( vessel + paint ) ; 12 v = v + p ( so the weight of completely filled vessel is 12 v ) p = 11 v ( so the weight of the paint when the vessels is completely filled is 11 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 12 v ; p ' = 5 v ( so the weight of the paint when the vessels is partially filled is 5 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 5 v / 11 v = 5 / 11 . answer : b ." | gain |
math_qa__9rZE7MstnvlF0AyL | A side of beef lost 50 percent of its weight in processing. If the side of beef weighed 750 pounds after processing, how many pounds did it weigh before processing? Choose the correct choice from the following choices.
A) 191 B) 355 C) 737 D) 840 E) 1,500 | <gadget id="calculator">750 * 100</gadget>
<output>75_000</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">75_000 / 50</gadget>
<output>1_500</output>
<result>E</result> | E | 1,500 | A side of beef lost 50 percent of its weight in processing. If the side of beef weighed 750 pounds after processing, how many pounds did it weigh before processing? | {
"A": "191",
"B": "355",
"C": "737",
"D": "840",
"E": "1,500"
} | divide(multiply(750, const_100), subtract(const_100, 50)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | "let weight of side of beef before processing = x ( 50 / 100 ) * x = 750 = > x = ( 750 * 100 ) / 50 = 1500 answer e" | gain |
math_qa__Q1RjHmtv0cuTjfQP | 50% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
Select the correct option: A) 20 % B) 30 % C) 40 % D) 50 % E) 70 % | <gadget id="calculator">50 * 1</gadget>
<output>50</output>
<result>D</result> | D | 50 | 50% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks? | {
"A": "20 %",
"B": "30 %",
"C": "40 %",
"D": "50 %",
"E": "70 %"
} | multiply(50, const_1) | multiply(n0,const_1)| | "to maximize the percentage of companies offering both , let ' s assume that all 50 % of companies which offer wireless internet also offer snacks . the answer is d ." | general |
math_qa__Ikh4wsXNmwtRIEhQ | A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Choose the correct choice: A) 22 B) 20 C) 88 D) 71 E) 10 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<result>E</result> | E | 10 | A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was? | {
"A": "22",
"B": "20",
"C": "88",
"D": "71",
"E": "10"
} | divide(multiply(multiply(3, const_2), 10), subtract(12, multiply(3, const_2))) | multiply(n1,const_2)|multiply(n2,#0)|subtract(n0,#0)|divide(#1,#2) | x - - - - - - - 12 ( x + 10 ) - - - - 6 x * 12 = ( x + 10 ) 6 x = 10 \ answer : e | physics |
math_qa__YJVdIGm3lPY34tDI | A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 23 per kg, then his gain percent is
Options:
A) 12 %
B) 23 %
C) 14 %
D) 15 %
E) 16 % | <gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">23 * 8</gadget>
<output>184</output>
<gadget id="calculator">5 * 18</gadget>
<output>90</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
<gadget id="calculator">184 - 150</gadget>
<output>34</output>
<gadget id="calculator">34 * 100</gadget>
<output>3_400</output>
<gadget id="calculator">3_400 / 150</gadget>
<output>68/3 = around 22.666667</output>
<result>B</result> | B | 23 | A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 23 per kg, then his gain percent is | {
"A": "12 %",
"B": "23 %",
"C": "14 %",
"D": "15 %",
"E": "16 %"
} | divide(multiply(subtract(multiply(23, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20))) | add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|add(#1,#2)|multiply(n4,#0)|subtract(#4,#3)|multiply(#5,const_100)|divide(#6,#3) | explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 23 ) = rs . 184 . profit = 184 - 150 = 34 so , profit % = ( 34 / 150 ) * 100 = 23 % option b | gain |
math_qa__GHXTx4uiXdzmLBjd | A can run 4 times as fast as B and gives B a start of 69 m. How long should the race course be so that A and B might reach in the same time? Choose the correct choice from the following choices: A) 70 m B) 60 m C) 80 m D) 65 m E) 92 m | <gadget id="calculator">69 / 4</gadget>
<output>69/4 = around 17.25</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">(69/4) / 3</gadget>
<output>23/4 = around 5.75</output>
<gadget id="calculator">4 * (23/4)</gadget>
<output>23</output>
<gadget id="calculator">23 + 69</gadget>
<output>92</output>
<result>E</result> | E | 92 | A can run 4 times as fast as B and gives B a start of 69 m. How long should the race course be so that A and B might reach in the same time? | {
"A": "70 m",
"B": "60 m",
"C": "80 m",
"D": "65 m",
"E": "92 m"
} | add(multiply(4, divide(divide(69, 4), subtract(4, const_1))), 69) | divide(n1,n0)|subtract(n0,const_1)|divide(#0,#1)|multiply(n0,#2)|add(n1,#3)| | "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 69 m he gains 69 * ( 4 / 3 ) i . e 92 m answer : e" | physics |
math_qa__fsmlCOwzwS0HQwnU | A car travels uphill at 30 km/hr and downhill at 40 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
Select.
A) 32 kmph
B) 33 kmph
C) 34 kmph
D) 35 kmph
E) 36 kmph | <gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">100 / 30</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">50 / 40</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(10/3) + (5/4)</gadget>
<output>55/12 = around 4.583333</output>
<gadget id="calculator">150 / (55/12)</gadget>
<output>360/11 = around 32.727273</output>
<result>B</result> | B | 33 | A car travels uphill at 30 km/hr and downhill at 40 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? | {
"A": "32 kmph",
"B": "33 kmph",
"C": "34 kmph",
"D": "35 kmph",
"E": "36 kmph"
} | divide(add(100, 50), add(divide(100, 30), divide(50, 40))) | add(n2,n3)|divide(n2,n0)|divide(n3,n1)|add(#1,#2)|divide(#0,#3)| | "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 40 = 5 / 4 ; avg speed = 150 / ( 10 / 3 + 5 / 4 ) = 33 kmph answer : b" | general |
math_qa__athn42eKUQkd1CAw | The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $7.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? Choose the correct choice from the following answers
A) $ 4.50 B) $ 5.10 C) $ 5.30 D) $ 7.50 E) $ 5.60 | <gadget id="calculator">7.8 - 3.2</gadget>
<output>4.6</output>
<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">(sqrt(2)) - 1</gadget>
<output>-1 + sqrt(2) = around 0.414214</output>
<gadget id="calculator">5 + (-1 + sqrt(2))</gadget>
<output>sqrt(2) + 4 = around 5.414214</output>
<gadget id="calculator">4.6 / (sqrt(2) + 4)</gadget>
<output>4.6/(sqrt(2) + 4) = around 0.849616</output>
<gadget id="calculator">(4.6/(sqrt(2) + 4)) * 5</gadget>
<output>23.0/(sqrt(2) + 4) = around 4.248078</output>
<gadget id="calculator">3.2 + (23.0/(sqrt(2) + 4))</gadget>
<output>3.2 + 23.0/(sqrt(2) + 4) = around 7.448078</output>
<result>D</result> | D | 7.5 | The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $7.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? | {
"A": "$ 4.50",
"B": "$ 5.10",
"C": "$ 5.30",
"D": "$ 7.50",
"E": "$ 5.60"
} | add(3.20, multiply(divide(subtract(7.80, 3.20), add(5, subtract(sqrt(2), 1))), 5)) | sqrt(n3)|subtract(n1,n0)|subtract(#0,n4)|add(n2,#2)|divide(#1,#3)|multiply(n2,#4)|add(n0,#5)| | "i tried using time / rate approach : - initial price difference = 7.80 - 3.20 = 4.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 4.6 = t ( 5.4 x ) - > t = ( 4.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 4.6 / 5.4 = 7.5 answer d ." | general |
math_qa__FgPoUoohQvJOf045 | The diagonals of the two squares are in the ratio of 7:9 find the ratio of their area
Choose the correct answer
A) 78 : 89 B) 5 : 48 C) 49 : 81 D) 74 : 36 E) 25 : 49 | <gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">49 / 2</gadget>
<output>49/2 = around 24.5</output>
<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">81 / 2</gadget>
<output>81/2 = around 40.5</output>
<gadget id="calculator">(49/2) / (81/2)</gadget>
<output>49/81 = around 0.604938</output>
<result>C</result> | C | 0.604938 | The diagonals of the two squares are in the ratio of 7:9 find the ratio of their area | {
"A": "78 : 89",
"B": "5 : 48",
"C": "49 : 81",
"D": "74 : 36",
"E": "25 : 49"
} | divide(divide(power(7, const_2), const_2), divide(power(9, const_2), const_2)) | power(n0,const_2)|power(n1,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,#3) | let the diagonals of the square be 7 x and 9 x respectively . ratio of their areas = 1 / 2 ( 7 x ) ^ 2 : 1 / 2 ( 9 x ) = 49 x ^ 2 : 81 x ^ 2 = 49 : 81 answer ( c ) | geometry |
math_qa__sYt3ZizvCg80xIO1 | For what value of “k†will the equation (2kx2 + 7kx +2)=0 have equal roots? Select the correct option.
A) 2 / 7
B) 16 / 49
C) 16 / 25
D) 7 / 1
E) 7 / 2 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">16 / 49</gadget>
<output>16/49 = around 0.326531</output>
<result>B</result> | B | 0.326531 | For what value of “k†will the equation (2kx2 + 7kx +2)=0 have equal roots? | {
"A": "2 / 7",
"B": "16 / 49",
"C": "16 / 25",
"D": "7 / 1",
"E": "7 / 2"
} | divide(power(2, add(2, 2)), power(7, 2)) | add(n0,n0)|power(n2,n0)|power(n0,#0)|divide(#2,#1)| | "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 7 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 49 answer : b" | general |
math_qa__PbdNisjZ5dvYVGCB | in how many ways can 5 different rings be worn in 4 particular fingers ? ( some fingers may get more than one ring and some may get no rings . ) can somebody explain ? Choose the correct option:
A) 6720 B) 7720 C) 7820 D) 7950 E) 8120 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">20 * 6</gadget>
<output>120</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">120 * 7</gadget>
<output>840</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">840 * 8</gadget>
<output>6_720</output>
<result>A</result> | A | 6,720 | in how many ways can 5 different rings be worn in 4 particular fingers ? ( some fingers may get more than one ring and some may get no rings . ) can somebody explain ? | {
"A": "6720",
"B": "7720",
"C": "7820",
"D": "7950",
"E": "8120"
} | multiply(multiply(multiply(multiply(4, 5), add(const_4, const_2)), add(add(const_4, const_2), const_1)), add(add(add(const_4, const_2), const_1), const_1)) | add(const_2,const_4)|multiply(n0,n1)|add(#0,const_1)|multiply(#0,#1)|add(#2,const_1)|multiply(#2,#3)|multiply(#4,#5) | first ring can be worn in 4 ways ( on any of the four fingers ) ; second ring can be worn in 5 ways ( as it can go on any of four fingers - 4 ways ; plus it can go below the first one - 1 ) ; third ring can be worn in 6 ways ( the same logic as for the second ring ) ; fourth ring can be worn in 7 ways ; fifth ring can be worn in 8 ways ; total : 4 * 5 * 6 * 7 * 8 = 6720 . ans : a | general |
math_qa__qDMlBEMxFzJJl1OY | Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 50 white marbles. How many red marbles could be in bag A? Choose the correct choice from the following answers.
A) 1 B) 5 C) 4 D) 6 E) 8 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<result>B</result> | B | 5 | Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 50 white marbles. How many red marbles could be in bag A? | {
"A": "1",
"B": "5",
"C": "4",
"D": "6",
"E": "8"
} | divide(50, add(multiply(3, 2), 4)) | multiply(n1,n2)|add(n5,#0)|divide(n6,#1) | 6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 50 = 6 k + 4 k = > k = 5 total red ' s in bag a will be 2 k = 10 b | other |
math_qa__sL1I5ZkxUexR6N5V | A box contains 6 pairs of shoes (12 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? Choose the correct choice from the following choices:
A) 1 / 11 B) 1 / 20 C) 1 / 19 D) 1 / 10 E) 1 / 9 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>
<result>A</result> | A | 0.090909 | A box contains 6 pairs of shoes (12 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes? | {
"A": "1 / 11",
"B": "1 / 20",
"C": "1 / 19",
"D": "1 / 10",
"E": "1 / 9"
} | divide(const_1, subtract(12, const_1)) | subtract(n1,const_1)|divide(const_1,#0) | the problem with your solution is that we do n ' t choose 1 shoe from 12 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 11 as after taking one at random there are 11 shoes left and only one is the pair of the first one ) = 1 / 11 answer : a . | general |
math_qa__F39Yjcsem5mSm97s | The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 12 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 8:6. As a result of the gift, Kaye had how many more stamps than Alberto? Choose the most appropriate option:
A) 20
B) 30
C) 40
D) 32
E) 90 | <gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">lcm(8, 14)</gadget>
<output>56</output>
<gadget id="calculator">56 / 14</gadget>
<output>4</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<result>D</result> | D | 32 | The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 12 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 8:6. As a result of the gift, Kaye had how many more stamps than Alberto? | {
"A": "20",
"B": "30",
"C": "40",
"D": "32",
"E": "90"
} | multiply(8, divide(lcm(add(5, 3), add(8, 6)), add(8, 6))) | add(n0,n1)|add(n3,n4)|lcm(#0,#1)|divide(#2,#1)|multiply(n3,#3) | c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 12 a 2 = 3 x + 12 k 2 / a 2 = 8 / 6 ( 5 x - 12 ) / ( 3 x + 12 ) = 8 / 6 6 * ( 5 x - 12 ) = 8 * ( 3 x + 12 ) 30 x - 72 = 24 x + 96 6 x = 168 x = 28 k 2 = 5 * 28 - 12 = 128 a 2 = 3 * 28 + 12 = 96 k 2 - a 2 = 32 answer : d | other |
math_qa__eMGyOLDklnUEZVGd | A number x is 11 times another number y. The percentage that y is less than x is Choose the correct option
A) 12.5 %
B) 90.9
C) 91.7
D) 11 %
E) 1 % | <gadget id="calculator">11 - 1</gadget>
<output>10</output>
<gadget id="calculator">10 / 11</gadget>
<output>10/11 = around 0.909091</output>
<gadget id="calculator">(10/11) * 100</gadget>
<output>1_000/11 = around 90.909091</output>
<result>B</result> | B | 90.9 | A number x is 11 times another number y. The percentage that y is less than x is | {
"A": "12.5 %",
"B": "90.9",
"C": "91.7",
"D": "11 %",
"E": "1 %"
} | multiply(divide(subtract(11, const_1), 11), const_100) | subtract(n0,const_1)|divide(#0,n0)|multiply(#1,const_100)| | "say y = 1 and x = 11 . then y = 1 is less than x = 11 by ( 11 - 1 ) / 11 * 100 = 10 / 11 * 100 = 90.9 % . answer : b ." | general |
math_qa__SBkpUmLXF70HceE3 | Ravi's 4days average income is 1025.68. But in a form he should write his average income as the greatest positive even integer less than or equal to his 4days average income. what is the difference between his real average and form filling average?
Choose the most appropriate option:
A) 2 B) 4.3 C) 1.68 D) 1.5 E) 3.2 | <gadget id="calculator">floor(1_025.68)</gadget>
<output>1_025</output>
<gadget id="calculator">1_025 - 1</gadget>
<output>1_024</output>
<gadget id="calculator">1_025.68 - 1_024</gadget>
<output>1.68</output>
<result>C</result> | C | 1.68 | Ravi's 4days average income is 1025.68. But in a form he should write his average income as the greatest positive even integer less than or equal to his 4days average income. what is the difference between his real average and form filling average? | {
"A": "2",
"B": "4.3",
"C": "1.68",
"D": "1.5",
"E": "3.2"
} | subtract(1025.68, subtract(floor(1025.68), const_1)) | floor(n1)|subtract(#0,const_1)|subtract(n1,#1) | since ravi ' s 4 days average income for form filling is defined as the greatest positive even integer less than or equal to his avg income , then avg income for form filling = 1024 ( the greatest positive even integer less than or equal to 1025.68 is 1024 ) . hence the difference = 1025.68 - 1024 = 1.68 answer : c . | general |
math_qa__tb7l3F9A8slP2jNZ | roy was suffering from severe headaches . he went to see his doctor and the doctor gave him 5 tablets asking him to take one tablet every 15 minutes . how much time will it take roy to consume all the 5 tablets ? Choose the correct choice from the following options.
A) 60 min B) 50 min C) 70 min D) 65 min E) 80 min | <gadget id="calculator">5 * 15</gadget>
<output>75</output>
<gadget id="calculator">75 - 15</gadget>
<output>60</output>
<result>A</result> | A | 60 | roy was suffering from severe headaches . he went to see his doctor and the doctor gave him 5 tablets asking him to take one tablet every 15 minutes . how much time will it take roy to consume all the 5 tablets ? | {
"A": "60 min",
"B": "50 min",
"C": "70 min",
"D": "65 min",
"E": "80 min"
} | subtract(multiply(5, 15), 15) | multiply(n0,n1)|subtract(#0,n1) | a 60 min roy will be able to consume all the five tablets in an hour . tablet 1 will be taken in 0 min . tablet 2 will be taken in 15 min . tablet 3 will be taken in 30 min . tablet 4 will be taken in 45 min . tablet 5 will be taken in 60 min . | general |
math_qa__TXanzMptpzbPCwg6 | If one root of the equation 2x^2 + 3x – k = 0 is 7, what is the value of k?
Answers
A) 100 B) 110 C) 119 D) 120 E) 112 | <gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">2 * 49</gadget>
<output>98</output>
<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">98 + 21</gadget>
<output>119</output>
<result>C</result> | C | 119 | If one root of the equation 2x^2 + 3x – k = 0 is 7, what is the value of k? | {
"A": "100",
"B": "110",
"C": "119",
"D": "120",
"E": "112"
} | add(multiply(2, power(7, const_2)), multiply(3, 7)) | multiply(n2,n4)|power(n4,const_2)|multiply(n0,#1)|add(#2,#0) | we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 7 ^ 2 + 3 * 7 - k = 0 k = 98 + 21 = 119 the answer is c | general |
math_qa__DG7KeVS5Is2KdkQf | At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 14th highest price and the 21st lowest price among the prices of the items sold, how many items were sold at the garage sale? Pick.
A) 33 B) 34 C) 35 D) 36 E) 37 | <gadget id="calculator">21 + 14</gadget>
<output>35</output>
<gadget id="calculator">35 - 1</gadget>
<output>34</output>
<result>B</result> | B | 34 | At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 14th highest price and the 21st lowest price among the prices of the items sold, how many items were sold at the garage sale? | {
"A": "33",
"B": "34",
"C": "35",
"D": "36",
"E": "37"
} | subtract(add(21, 14), const_1) | add(n0,n1)|subtract(#0,const_1) | there were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio . including the radio , there were 13 + 20 + 1 = 34 items sold . the answer is b . | other |
math_qa__LPSWU0mwDnwxQcbE | What distance will be covered by a city bus moving at 72 kmph in 30 seconds? Pick one
A) 200 m B) 300 m C) 600 m D) 500 m E) 400 m | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
<result>C</result> | C | 600 | What distance will be covered by a city bus moving at 72 kmph in 30 seconds? | {
"A": "200 m",
"B": "300 m",
"C": "600 m",
"D": "500 m",
"E": "400 m"
} | multiply(multiply(72, const_0_2778), 30) | multiply(n0,const_0_2778)|multiply(n1,#0) | 72 kmph = 72 * 5 / 18 = 20 mps dist = speed * time = 20 * 30 = 600 m . answer c | physics |
math_qa__BwsqrpsDjrwH5nLN | The cost of 3 pens and 5 pencils is Rs.260. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
Choose the correct choice from the following answers: A) rs . 200 B) rs . 250 C) rs . 300 D) rs . 780 E) none of these | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">260 / 4</gadget>
<output>65</output>
<gadget id="calculator">12 * 65</gadget>
<output>780</output>
<result>D</result> | D | 780 | The cost of 3 pens and 5 pencils is Rs.260. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens? | {
"A": "rs . 200",
"B": "rs . 250",
"C": "rs . 300",
"D": "rs . 780",
"E": "none of these"
} | multiply(multiply(const_3, const_4), divide(260, add(3, 1))) | add(n0,n4)|multiply(const_3,const_4)|divide(n2,#0)|multiply(#2,#1) | explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 260 15 x + 5 x = rs . 260 x = 260 / 20 = 13 : . cost of 1 pen = 5 x = 5 x 13 = 65 : . cost of 12 pens , i . e . ( one dozen ) = 65 x 12 = rs . 780 answer : option d | other |
math_qa__DJnjSK7DnoODrYyy | According to a recent student poll, 4/5 out of 25 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
Choose the correct choice from the following options.
A) 29 / 30 B) 4 / 49 C) 2 / 7 D) 45 / 49 E) 13 / 14 | <gadget id="calculator">binomial(25, 2)</gadget>
<output>300</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">25 * (4/5)</gadget>
<output>20</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">binomial(5, 2)</gadget>
<output>10</output>
<gadget id="calculator">300 - 10</gadget>
<output>290</output>
<gadget id="calculator">290 / 300</gadget>
<output>29/30 = around 0.966667</output>
<result>A</result> | A | 0.966667 | According to a recent student poll, 4/5 out of 25 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking? | {
"A": "29 / 30",
"B": "4 / 49",
"C": "2 / 7",
"D": "45 / 49",
"E": "13 / 14"
} | divide(subtract(choose(25, const_2), choose(subtract(25, multiply(25, divide(4, 5))), const_2)), choose(25, const_2)) | choose(n2,const_2)|divide(n0,n1)|multiply(n2,#1)|subtract(n2,#2)|choose(#3,const_2)|subtract(#0,#4)|divide(#5,#0)| | "20 students are interested , 5 are not interested prob = 1 - 5 c 2 / 25 c 2 = 1 - ( 5 * 4 / ( 25 * 24 ) ) = 1 - 1 / 30 = 29 / 30 answer : a" | gain |
math_qa__bi4iwDJdVPLbtDl1 | One side of a rectangular field is 16 m and one of its diagonal is 17 m. Find the area of the field. Select:
A) 100
B) 120
C) 91.2
D) 180
E) none | <gadget id="calculator">17 ** 2</gadget>
<output>289</output>
<gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<gadget id="calculator">289 - 256</gadget>
<output>33</output>
<gadget id="calculator">33 ** (1/2)</gadget>
<output>sqrt(33) = around 5.744563</output>
<gadget id="calculator">16 * (sqrt(33))</gadget>
<output>16*sqrt(33) = around 91.913002</output>
<result>C</result> | C | 91.2 | One side of a rectangular field is 16 m and one of its diagonal is 17 m. Find the area of the field. | {
"A": "100",
"B": "120",
"C": "91.2",
"D": "180",
"E": "none"
} | rectangle_area(16, sqrt(subtract(power(17, const_2), power(16, const_2)))) | power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)| | "solution other side = √ ( 17 ) 2 - ( 16 ) 2 = √ 289 - 256 = √ 33 = 5.7 m . ∴ area = ( 16 x 5.7 ) m 2 = 91.2 m 2 . answer c" | geometry |
math_qa__sVmZBKzpAMyeJy9t | A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
Pick one:
A) a . 72
B) b . 50
C) c . 48
D) d . 46
E) e . 23 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">11 / 11</gadget>
<output>1</output>
<gadget id="calculator">12 + 11</gadget>
<output>23</output>
<gadget id="calculator">1 * 23</gadget>
<output>23</output>
<result>E</result> | E | 23 | A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke? | {
"A": "a . 72",
"B": "b . 50",
"C": "c . 48",
"D": "d . 46",
"E": "e . 23"
} | multiply(divide(11, add(6, add(const_1, const_4))), add(12, add(6, add(const_1, const_4)))) | add(const_1,const_4)|add(n0,#0)|add(n3,#1)|divide(n2,#1)|multiply(#2,#3)| | "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 11 seconds . thus x = 1 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 23 seconds . answer e" | general |
math_qa__ZZ96ykiNCG6X9IlZ | -24x29+36=? Options: A) 2436 B) 2801 C) - 2801 D) - 660 E) none of them | <gadget id="calculator">1 - 2</gadget>
<output>-1</output>
<gadget id="calculator">24 * 29</gadget>
<output>696</output>
<gadget id="calculator">696 - 36</gadget>
<output>660</output>
<gadget id="calculator">(-1) * 660</gadget>
<output>-660</output>
<result>D</result> | D | -660 | -24x29+36=? | {
"A": "2436",
"B": "2801",
"C": "- 2801",
"D": "- 660",
"E": "none of them"
} | multiply(subtract(const_1, const_2), subtract(multiply(24, 29), 36)) | multiply(n0,n1)|subtract(const_1,const_2)|subtract(#0,n2)|multiply(#1,#2)| | "given exp . = - 24 x ( 30 - 1 ) + 36 = - ( 24 x 30 ) + 24 + 36 = - 720 + 60 = - 660 answer is d" | general |
math_qa__PY7S2XmQVA1Zqvpc | A person travels equal distances with speeds of 2km/hr, 6km/hr, 6km/hr. and takes a total time of 11minutes. Find the total distance ? Choose one.
A) 1 km B) 500 mts C) 660 mts D) 2 km E) 250 mts | <gadget id="calculator">11 / 60</gadget>
<output>11/60 = around 0.183333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/2) + (1/6)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + (1/6)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(11/60) / (5/6)</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">(11/50) * 3</gadget>
<output>33/50 = around 0.66</output>
<gadget id="calculator">(33/50) * 1_000</gadget>
<output>660</output>
<result>C</result> | C | 660 | A person travels equal distances with speeds of 2km/hr, 6km/hr, 6km/hr. and takes a total time of 11minutes. Find the total distance ? | {
"A": "1 km",
"B": "500 mts",
"C": "660 mts",
"D": "2 km",
"E": "250 mts"
} | multiply(multiply(divide(divide(11, const_60), add(add(divide(const_1, 2), divide(const_1, 6)), divide(const_1, 6))), const_3), const_1000) | divide(n3,const_60)|divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#1,#2)|add(#4,#3)|divide(#0,#5)|multiply(#6,const_3)|multiply(#7,const_1000)| | "let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 6 ) + ( x / 6 ) = 11 / 60 x = 0.22 total distance = 3 * 0.22 = 0.66 km = 660 meters correct option is c" | physics |
math_qa__Md1tjZ01RGWspoWq | Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? Select: A) 1.75 B) 2.25 C) 2.5 D) 2.75 E) 3.25 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>
<result>B</result> | B | 2.25 | Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? | {
"A": "1.75",
"B": "2.25",
"C": "2.5",
"D": "2.75",
"E": "3.25"
} | divide(divide(multiply(add(4, 2), 3), 2), 4) | add(n0,n1)|multiply(n2,#0)|divide(#1,n1)|divide(#2,n0) | let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3 km / hour x / 3 = 3 x = 9 km the average speed while climbing = distance / time = 9 / 4 = 2.25 km / h the answer is b . | physics |
math_qa__CpQeOxjQx9wcSv70 | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate P in miles per hour for the entire trip? Options.
A) p = 26.7 B) p = 30.0 C) p = 40.0 D) p = 53.3 E) p = 60.0 | <gadget id="calculator">640 / 2</gadget>
<output>320</output>
<gadget id="calculator">320 / 80</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">640 / 16</gadget>
<output>40</output>
<result>C</result> | C | 40 | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate P in miles per hour for the entire trip? | {
"A": "p = 26.7",
"B": "p = 30.0",
"C": "p = 40.0",
"D": "p = 53.3",
"E": "p = 60.0"
} | divide(640, add(add(multiply(divide(divide(640, const_2), 80), const_2), divide(divide(640, const_2), 80)), divide(divide(640, const_2), 80))) | divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_2)|add(#1,#2)|add(#3,#1)|divide(n0,#4)| | "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ." | physics |
math_qa__fpr1Qek1mqYdytCX | The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12 percent, what was the annual interest rate last year?
Answers:
A) 1 %
B) 1.1 %
C) 9.1 %
D) 10 %
E) 10.9 % | <gadget id="calculator">12 * 100</gadget>
<output>1_200</output>
<gadget id="calculator">12 + 100</gadget>
<output>112</output>
<gadget id="calculator">1_200 / 112</gadget>
<output>75/7 = around 10.714286</output>
<result>E</result> | E | 10.9 | The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12 percent, what was the annual interest rate last year? | {
"A": "1 %",
"B": "1.1 %",
"C": "9.1 %",
"D": "10 %",
"E": "10.9 %"
} | divide(multiply(12, const_100), add(12, const_100)) | add(n1,const_100)|multiply(n1,const_100)|divide(#1,#0)| | "12 = 1.1 * x x = 10.90 % answer e )" | gain |
math_qa__8kixsHmCwkZA9I24 | If a-b= 6 and a^2+b^2=100, find the value of ab Options.
A) 10 B) 32 C) 15 D) 18 E) 19 | <gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">16 * 2</gadget>
<output>32</output>
<result>B</result> | B | 32 | If a-b= 6 and a^2+b^2=100, find the value of ab | {
"A": "10",
"B": "32",
"C": "15",
"D": "18",
"E": "19"
} | multiply(multiply(add(6, divide(subtract(sqrt(100), 6), 2)), divide(subtract(sqrt(100), 6), 2)), 2) | sqrt(n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)|multiply(#3,#2)|multiply(n1,#4)| | "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 100 - 36 = 64 = > ab = 32 answer : b" | general |
math_qa__HUuFULgaYzoAAyx7 | the average amount with a group of 7 numbers is rs . 20 . if the newly joined member has rs . 56 with him , what was the average amount with the group before his joining the group ? Options
A) s . 13 B) s . 12 C) s . 15 D) s . 22 E) s . 14 | <gadget id="calculator">20 * 7</gadget>
<output>140</output>
<gadget id="calculator">140 - 56</gadget>
<output>84</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">84 / 6</gadget>
<output>14</output>
<result>E</result> | E | 14 | the average amount with a group of 7 numbers is rs . 20 . if the newly joined member has rs . 56 with him , what was the average amount with the group before his joining the group ? | {
"A": "s . 13",
"B": "s . 12",
"C": "s . 15",
"D": "s . 22",
"E": "s . 14"
} | divide(subtract(multiply(20, 7), 56), subtract(7, const_1)) | multiply(n0,n1)|subtract(n0,const_1)|subtract(#0,n2)|divide(#2,#1) | total members in the group = 7 average amount = rs . 20 total amount with them = 7 * 20 = rs . 140 one number has rs . 56 . so , the amount with remaining 6 people = 140 - 56 = rs . 84 the average amount with them = 84 / 6 = rs . 14 . answer : e | general |
math_qa__Ruja21dqIhLLopu3 | Find the missing figures :
?% of 50 = 2.125 Choose the correct choice from the following answers
A) 8.55 B) 6.55 C) 8.75 D) 7.75 E) 4.25 | <gadget id="calculator">2.125 * 100</gadget>
<output>212.5</output>
<gadget id="calculator">212.5 / 50</gadget>
<output>4.25</output>
<result>E</result> | E | 4.25 | Find the missing figures :
?% of 50 = 2.125 | {
"A": "8.55",
"B": "6.55",
"C": "8.75",
"D": "7.75",
"E": "4.25"
} | divide(multiply(2.125, const_100), 50) | multiply(n1,const_100)|divide(#0,n0) | ( i ) let x % of 50 = 2.125 . then , ( x / 100 ) * 50 = 2.125 x = ( 2.125 * 2 ) = 4.25 answer is e . | gain |
math_qa__qAN4xGeO7cfASsqb | A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 8% p.a for 2 years. Find his gain in the transaction per year.
Pick:
A) 167.5 B) 150 C) 200 D) 112.5 E) 212.5 | <gadget id="calculator">5_000 * 8</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 * 2</gadget>
<output>80_000</output>
<gadget id="calculator">80_000 / 100</gadget>
<output>800</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 * 2</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">800 - 400</gadget>
<output>400</output>
<gadget id="calculator">400 / 2</gadget>
<output>200</output>
<result>C</result> | C | 200 | A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 8% p.a for 2 years. Find his gain in the transaction per year. | {
"A": "167.5",
"B": "150",
"C": "200",
"D": "112.5",
"E": "212.5"
} | divide(subtract(divide(multiply(multiply(5000, 8), 2), const_100), divide(multiply(multiply(5000, 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) | explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 8 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 8 × 2 / 100 = 800 his overall gain in 2 years = rs . 800 - rs . 400 = rs . 400 his overall gain in 1 year = 400 / 2 = rs . 200 answer : option c | gain |
math_qa__kKrzbcr64jKZskH5 | The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 114 ounces, what is the volume, in cubic inches, of 63 ounces of this substance? Choose the correct choice.
A) 27 B) 26 C) 42 D) 64 E) 147 | <gadget id="calculator">48 / 114</gadget>
<output>8/19 = around 0.421053</output>
<gadget id="calculator">(8/19) * 63</gadget>
<output>504/19 = around 26.526316</output>
<result>B</result> | B | 26 | The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 114 ounces, what is the volume, in cubic inches, of 63 ounces of this substance? | {
"A": "27",
"B": "26",
"C": "42",
"D": "64",
"E": "147"
} | multiply(divide(48, 114), 63) | divide(n0,n1)|multiply(n2,#0)| | "112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 114 ) * 63 = 26 cubic inches answer b" | geometry |
math_qa__Wzm168r8EX0fhcox | The side of a square is increased by 5% then how much % does its area increases?
Choose the most appropriate option
A) 15.00 %
B) 10.25 %
C) 10.00 %
D) 12.25 %
E) 12.50 % | <gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">105 ** 2</gadget>
<output>11_025</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">11_025 - 10_000</gadget>
<output>1_025</output>
<gadget id="calculator">1_025 * 100</gadget>
<output>102_500</output>
<gadget id="calculator">102_500 / 10_000</gadget>
<output>41/4 = around 10.25</output>
<result>B</result> | B | 10.25 | The side of a square is increased by 5% then how much % does its area increases? | {
"A": "15.00 %",
"B": "10.25 %",
"C": "10.00 %",
"D": "12.25 %",
"E": "12.50 %"
} | divide(multiply(subtract(square_area(add(const_100, 5)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | "a = 100 a 2 = 10000 a = 105 a 2 = 11025 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 1025 100 - - - - - - - ? = > 10.25 % answer : b" | geometry |
math_qa__w4IzJgcc9aflrtfx | A circular mat with radius 10 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat? Pick:
A) 5 / 12 B) 2 / 5 C) 0.5451 D) 3 / 4 E) 5 / 6 | <gadget id="calculator">pi * (10 ** 2)</gadget>
<output>100*pi = around 314.159265</output>
<gadget id="calculator">24 ** 2</gadget>
<output>576</output>
<gadget id="calculator">(100*pi) / 576</gadget>
<output>25*pi/144 = around 0.545415</output>
<result>C</result> | C | 0.5451 | A circular mat with radius 10 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat? | {
"A": "5 / 12",
"B": "2 / 5",
"C": "0.5451",
"D": "3 / 4",
"E": "5 / 6"
} | divide(circle_area(10), square_area(24)) | circle_area(n0)|square_area(n1)|divide(#0,#1) | c . it is a circle inscribed in a square . square side = 24 - - - > square ( table ) area = 24 ^ 2 circle diameter = 20 - - - > circle area = pir ^ 2 = 100 pi ( where pi = ~ 3.14 ) covered fraction = 100 * 3.14 / 24 * 24 = ~ 314 / 24 * 24 = 0.5451 c | geometry |
math_qa__aLs2Z30xj35ljjhI | Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
Select the correct option
A) $ 3,750 B) $ 5,600 C) $ 13,500 D) $ 15,000 E) $ 22,500 | <gadget id="calculator">112 / 8</gadget>
<output>14</output>
<gadget id="calculator">28 / 14</gadget>
<output>2</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">1_500 * 9</gadget>
<output>13_500</output>
<result>C</result> | C | 13,500 | Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years? | {
"A": "$ 3,750",
"B": "$ 5,600",
"C": "$ 13,500",
"D": "$ 15,000",
"E": "$ 22,500"
} | multiply(1500, power(const_3, divide(28, divide(112, 8)))) | divide(n0,n2)|divide(n3,#0)|power(const_3,#1)|multiply(n1,#2)| | "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1500 triples to $ 4500 , in 28 years , it will again triple to $ 4500 * 3 = $ 13,500 answer c" | gain |
math_qa__n2Q2vFQihZWkuFf1 | In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? Choose the correct choice from the following choices.
A) 88
B) 90
C) 96
D) 98
E) 102 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">6 * 16</gadget>
<output>96</output>
<result>C</result> | C | 96 | In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? | {
"A": "88",
"B": "90",
"C": "96",
"D": "98",
"E": "102"
} | multiply(subtract(multiply(const_2, multiply(2, 2)), 2), multiply(const_4, const_4)) | multiply(const_4,const_4)|multiply(n1,n1)|multiply(#1,const_2)|subtract(#2,n1)|multiply(#0,#3) | 2 multiples - choice questions can be answered in = 4 x 4 = 16 ways 3 true - false questions can be answered in = 2 x 2 x 2 = 8 ways but out of the 8 ways , 2 ways [ ( true - true - true ) ( false - false - false ) ] will contain same answers thus 3 true - false questions can be answered in = 2 x 2 x 2 = 6 ways total ways to answer the quiz = 16 x 6 = 96 answer c | general |
math_qa__FPuKmqiwVHl8CUwS | A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol? Select the correct option:
A) 5.5 %
B) 6 %
C) 6 1 / 3 %
D) 6 2 / 3 %
E) 7 % | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">50 * (1/20)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) + 1.5</gadget>
<output>4</output>
<gadget id="calculator">1.5 + 8.5</gadget>
<output>10</output>
<gadget id="calculator">50 + 10</gadget>
<output>60</output>
<gadget id="calculator">4 / 60</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) * 100</gadget>
<output>20/3 = around 6.666667</output>
<result>E</result> | E | 7 | A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol? | {
"A": "5.5 %",
"B": "6 %",
"C": "6 1 / 3 %",
"D": "6 2 / 3 %",
"E": "7 %"
} | multiply(divide(add(multiply(50, divide(5, const_100)), 1.5), add(50, add(1.5, 8.5))), const_100) | add(n2,n3)|divide(n1,const_100)|add(n0,#0)|multiply(n0,#1)|add(n2,#3)|divide(#4,#2)|multiply(#5,const_100)| | "50 l * . 05 = 2.5 l of alc , 50 l - 2.5 l = 47.5 l of water 2.5 + 1.5 = 4 l of alcohol in new solution 47.5 l + 8.5 l = 56 l of water 4 l / 56 l = 1 / 14 this is ~ 7 % answer : e" | general |
math_qa__PX43o2xFqRXsZLPj | there are 3 departments having students 72 , 5824 . in an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only ( no mixing of departments ) . find the minimum number of rooms required ? Pick: A) 73 B) 74 C) 75 D) 76 E) 77 | <gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">36 + 12</gadget>
<output>48</output>
<gadget id="calculator">48 + 10</gadget>
<output>58</output>
<gadget id="calculator">58 / 2</gadget>
<output>29</output>
<gadget id="calculator">48 + 29</gadget>
<output>77</output>
<result>E</result> | E | 77 | there are 3 departments having students 72 , 5824 . in an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only ( no mixing of departments ) . find the minimum number of rooms required ? | {
"A": "73",
"B": "74",
"C": "75",
"D": "76",
"E": "77"
} | add(add(divide(72, const_2), const_12), divide(add(add(divide(72, const_2), const_12), const_10), const_2)) | divide(n1,const_2)|add(#0,const_12)|add(#1,const_10)|divide(#2,const_2)|add(#1,#3) | we need to take gcd which is 2 thus all the rooms will have 2 students of the same dept 1 ) 72 / 2 = 36 2 ) 58 / 2 = 29 3 ) 24 / 2 = 12 total no . of min rooms reqd = 36 + 12 + 29 = 77 answer : e | general |
math_qa__psLbE94mIQ4Yqi7x | A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 120 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? Select: A) 121.5 B) 122 C) 122.5 D) 113 E) 112.5 | <gadget id="calculator">1 / 120</gadget>
<output>1/120 = around 0.008333</output>
<gadget id="calculator">3_600 * (1/120)</gadget>
<output>30</output>
<gadget id="calculator">30 + 2</gadget>
<output>32</output>
<gadget id="calculator">32 / 3_600</gadget>
<output>2/225 = around 0.008889</output>
<gadget id="calculator">1 / (2/225)</gadget>
<output>225/2 = around 112.5</output>
<result>E</result> | E | 112.5 | A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 120 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? | {
"A": "121.5",
"B": "122",
"C": "122.5",
"D": "113",
"E": "112.5"
} | divide(1, divide(add(multiply(const_3600, divide(1, 120)), 2), const_3600)) | divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3)| | "e 120 * t = 1 km = > t = 1 / 120 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 120 + 2 / 3600 ) = 1 = > v = 112.5 km / h" | physics |
math_qa__3X46oVChwVTXwF0B | The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 70 per cent. The two reductions together are equal to a single reduction of Choose one
A) 45 % B) 40 % C) 35 % D) 77.5 % E) 30 % | <gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">(3/10) * 75</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">100 - (45/2)</gadget>
<output>155/2 = around 77.5</output>
<result>D</result> | D | 77.5 | The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 70 per cent. The two reductions together are equal to a single reduction of | {
"A": "45 %",
"B": "40 %",
"C": "35 %",
"D": "77.5 %",
"E": "30 %"
} | subtract(const_100, multiply(divide(subtract(const_100, 70), const_100), subtract(const_100, 25))) | subtract(const_100,n1)|subtract(const_100,n0)|divide(#0,const_100)|multiply(#2,#1)|subtract(const_100,#3)| | "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 70 percent is reduced which means the new price is merely 30 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 10 ) p = 9 / 40 p is the new price after both deduction which is 22.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 77.5 % of p . so answer is d = 77.5 %" | general |
math_qa__ggwKbYw4PnMh7U6j | The percentage profit earned by selling an article for Rs. 1920 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 35% profit? Select the correct option
A) 2080 B) 2778 C) 2299 D) 2778 E) 2771 | <gadget id="calculator">100 + 35</gadget>
<output>135</output>
<gadget id="calculator">135 / 100</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>
<gadget id="calculator">(27/20) * 1_600</gadget>
<output>2_160</output>
<result>A</result> | A | 2,080 | The percentage profit earned by selling an article for Rs. 1920 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 35% profit? | {
"A": "2080",
"B": "2778",
"C": "2299",
"D": "2778",
"E": "2771"
} | multiply(divide(add(const_100, 35), const_100), divide(add(1920, 1280), const_2)) | add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(#1,const_2)|multiply(#2,#3) | let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 130 % of rs . 1600 = 130 / 100 * 1600 = rs . 2080 . answer : a | gain |
math_qa__TvQbhBAavVpeV81h | Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Answers
A) 648 B) 1800 C) 2700 D) 10800 E) none | <gadget id="calculator">270 / 6</gadget>
<output>45</output>
<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">180 * 10</gadget>
<output>1_800</output>
<result>B</result> | B | 1,800 | Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? | {
"A": "648",
"B": "1800",
"C": "2700",
"D": "10800",
"E": "none"
} | multiply(multiply(divide(270, 6), 4), 10) | divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)| | "let the number of required bottles be x machine 6 : 10 time 1 : 4 = : : 270 : x therefore 6 x 1 x x = 10 x 4 x 270 = > x = ( 10 x 4 x 270 ) / ( 6 ) = > x = 1800 answer : option b" | gain |
math_qa__nm8F1Pp4L0SZUCpa | Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 40 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
Choose one: A) 60 B) 80 C) 100 D) 120 E) 140 | <gadget id="calculator">40 + 30</gadget>
<output>70</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">70 / (7/10)</gadget>
<output>100</output>
<result>C</result> | C | 100 | Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 40 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? | {
"A": "60",
"B": "80",
"C": "100",
"D": "120",
"E": "140"
} | divide(add(40, 30), divide(subtract(const_100, 30), const_100)) | add(n0,n1)|subtract(const_100,n1)|divide(#1,const_100)|divide(#0,#2)| | "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 40 = 70 members have not passed the test , thus 0.7 * total = 70 - - > total = 100 . answer : c ." | gain |
math_qa__G3bpVloCa6beqQI9 | What is the smallest number which when diminished by 8, is divisible by 9, 6, 12 and 18?
Pick one
A) 50
B) 45
C) 44
D) 60
E) 65 | <gadget id="calculator">lcm(9, 6)</gadget>
<output>18</output>
<gadget id="calculator">lcm(12, 18)</gadget>
<output>36</output>
<gadget id="calculator">lcm(18, 36)</gadget>
<output>36</output>
<gadget id="calculator">36 + 8</gadget>
<output>44</output>
<result>C</result> | C | 44 | What is the smallest number which when diminished by 8, is divisible by 9, 6, 12 and 18? | {
"A": "50",
"B": "45",
"C": "44",
"D": "60",
"E": "65"
} | add(lcm(lcm(9, 6), lcm(12, 18)), 8) | lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)| | "explanation : required number = lcm of ( 9 , 6 , 12 and 18 ) + 8 = 36 + 8 = 44 answer : option c" | general |
math_qa__v9VEwMzLYoLu4gUw | On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets rain cloud, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him? Choose the correct choice from the following
A) 1 / 8 B) 1 / 6 C) 1 / 7 D) 1 / 5 E) 1 / 4 | <gadget id="calculator">lcm(2, 3)</gadget>
<output>6</output>
<gadget id="calculator">6 / 2.8</gadget>
<output>2.142857</output>
<gadget id="calculator">2.142857 - 2</gadget>
<output>0.142857</output>
<result>C</result> | C | 0.142857 | On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets rain cloud, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him? | {
"A": "1 / 8",
"B": "1 / 6",
"C": "1 / 7",
"D": "1 / 5",
"E": "1 / 4"
} | subtract(divide(lcm(const_2, const_3), 2.8), const_2) | lcm(const_2,const_3)|divide(#0,n1)|subtract(#1,const_2) | if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : c | general |
math_qa__XJKE9Hs3OF1rMEIO | Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?
Answers:
A) 120 B) 150 C) 200 D) 270 E) 420 | <gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">3_628_800 / 40_320</gadget>
<output>90</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">720 / 120</gadget>
<output>6</output>
<gadget id="calculator">45 * 6</gadget>
<output>270</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">3_628_800 / 362_880</gadget>
<output>10</output>
<gadget id="calculator">720 / 2</gadget>
<output>360</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">360 / 24</gadget>
<output>15</output>
<gadget id="calculator">10 * 15</gadget>
<output>150</output>
<gadget id="calculator">270 + 150</gadget>
<output>420</output>
<result>E</result> | E | 420 | Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle? | {
"A": "120",
"B": "150",
"C": "200",
"D": "270",
"E": "420"
} | add(multiply(divide(divide(factorial(10), factorial(subtract(10, const_2))), factorial(const_2)), divide(factorial(6), factorial(subtract(6, const_1)))), multiply(divide(factorial(10), factorial(subtract(const_10, const_1))), divide(divide(factorial(6), const_2), factorial(subtract(6, const_2))))) | factorial(n1)|factorial(const_2)|factorial(n0)|subtract(n1,const_2)|subtract(n0,const_1)|subtract(const_10,const_1)|subtract(n0,const_2)|divide(#2,const_2)|factorial(#3)|factorial(#4)|factorial(#5)|factorial(#6)|divide(#0,#8)|divide(#2,#9)|divide(#0,#10)|divide(#7,#11)|divide(#12,#1)|multiply(#14,#15)|multiply(#16,#13)|add(#18,#17) | to make a triangle , you need 2 checkpoints from one track and 1 from the other . you can not have all 3 from the same track since then the points will be in a line ( assuming straight line of track ) you select 2 checkpoints from the first track and one from the second or two from the second track and one from the first . 6 c 2 * 10 c 1 + 10 c 2 * 6 c 1 = 150 + 270 = 420 answer ( e ) | geometry |
math_qa__8kFu3bqsmpw5tH9w | An engineer undertakes a project to build a road 15 km long in 300 days and employs 55 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
Choose one:
A) a . 43
B) b . 45
C) c . 55
D) d . 68
E) e . 83 | <gadget id="calculator">15 - 2.5</gadget>
<output>12.5</output>
<gadget id="calculator">55 * 12.5</gadget>
<output>687.5</output>
<gadget id="calculator">687.5 * 100</gadget>
<output>68_750</output>
<gadget id="calculator">300 - 100</gadget>
<output>200</output>
<gadget id="calculator">2.5 * 200</gadget>
<output>500</output>
<gadget id="calculator">68_750 / 500</gadget>
<output>275/2 = around 137.5</output>
<gadget id="calculator">(275/2) - 55</gadget>
<output>165/2 = around 82.5</output>
<result>E</result> | E | 83 | An engineer undertakes a project to build a road 15 km long in 300 days and employs 55 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time. | {
"A": "a . 43",
"B": "b . 45",
"C": "c . 55",
"D": "d . 68",
"E": "e . 83"
} | subtract(divide(multiply(multiply(55, subtract(15, 2.5)), 100), multiply(2.5, subtract(300, 100))), 55) | subtract(n0,n4)|subtract(n1,n3)|multiply(n2,#0)|multiply(n4,#1)|multiply(n3,#2)|divide(#4,#3)|subtract(#5,n2)| | "55 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 55 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 137.5 that is approximately 138 thus , more men needed to finish the task = 138 - 55 = 83 hence answer is e" | physics |
math_qa__I2aEqXm2SeSIkw27 | Bob invested $2000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth how much more than his investment in fund B? Choose the correct choice from the following:
A) $ 500 B) $ 550 C) $ 600 D) $ 650 E) $ 700 | <gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">1 + (3/25)</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">2_000 * (28/25)</gadget>
<output>2_240</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">(13/10) ** 2</gadget>
<output>169/100 = around 1.69</output>
<gadget id="calculator">1_000 * (169/100)</gadget>
<output>1_690</output>
<gadget id="calculator">2_240 - 1_690</gadget>
<output>550</output>
<result>B</result> | B | 550 | Bob invested $2000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth how much more than his investment in fund B? | {
"A": "$ 500",
"B": "$ 550",
"C": "$ 600",
"D": "$ 650",
"E": "$ 700"
} | subtract(multiply(2000, add(const_1, divide(12, const_100))), multiply(1000, power(add(const_1, divide(30, const_100)), const_2))) | divide(n2,const_100)|divide(n3,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(n0,#2)|power(#3,const_2)|multiply(n1,#5)|subtract(#4,#6) | bob earned 2000 * ( 1 + 0.12 ) in total by fund a and earned 1000 * ( 1 + 0.3 ) ^ 2 in total by fund b . so 2000 * ( 1.12 ) - 1000 * ( 1.69 ) = 550 . the answer is , therefore , ( b ) . | general |
math_qa__vnerfYqerb1DtCLg | The ratio between the sale price and the cost price of an article is 6:5. What is the ratio between the profit and the cost price of that article? Choose the correct answer:
A) 2 : 9
B) 1 : 5
C) 3 : 6
D) 2 : 0
E) 2 : 1 | <gadget id="calculator">6 - 5</gadget>
<output>1</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<result>B</result> | B | 0.2 | The ratio between the sale price and the cost price of an article is 6:5. What is the ratio between the profit and the cost price of that article? | {
"A": "2 : 9",
"B": "1 : 5",
"C": "3 : 6",
"D": "2 : 0",
"E": "2 : 1"
} | divide(subtract(6, 5), 5) | subtract(n0,n1)|divide(#0,n1) | let c . p . = rs . 5 x and s . p . = rs . 6 x . then , gain = rs . x required ratio = x : 5 x = 1 : 5 answer : b | other |
math_qa__qxL5XhP6zjXBBlmi | How many digits 2^1000 has? Choose the correct choice from the following answers
A) 31 B) 35 C) 50 D) 99 E) 310 | <gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>
<gadget id="calculator">log(2) / log(10)</gadget>
<output>log(2)/log(10) = around 0.30103</output>
<gadget id="calculator">(log(2)/log(10)) * 1_000</gadget>
<output>1000*log(2)/log(10) = around 301.029996</output>
<gadget id="calculator">1 + (1000*log(2)/log(10))</gadget>
<output>1 + 1000*log(2)/log(10) = around 302.029996</output>
<gadget id="calculator">floor(1 + 1000*log(2)/log(10))</gadget>
<output>302</output>
<result>E</result> | E | 310 | How many digits 2^1000 has? | {
"A": "31",
"B": "35",
"C": "50",
"D": "99",
"E": "310"
} | floor(add(const_1, multiply(divide(log(2), log(const_10)), 1000))) | log(n0)|log(const_10)|divide(#0,#1)|multiply(n1,#2)|add(#3,const_1)|floor(#4)| | "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 1000 = ( 1.024 ) ^ 100 * 10 ^ 300 therefore 310 digits would be my best guess e" | general |
math_qa__0qob53XQMWBRLh7O | A salt manufacturing company produced a total of 2500 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year? Pick one
A) 100 B) 105 C) 109 D) 120 E) 90 | <gadget id="calculator">2_500 * 2</gadget>
<output>5_000</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 100</gadget>
<output>1_100</output>
<gadget id="calculator">5_000 + 1_100</gadget>
<output>6_100</output>
<gadget id="calculator">6_100 * 12</gadget>
<output>73_200</output>
<gadget id="calculator">73_200 / 2</gadget>
<output>36_600</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">300 + 60</gadget>
<output>360</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">360 + 5</gadget>
<output>365</output>
<gadget id="calculator">36_600 / 365</gadget>
<output>7_320/73 = around 100.273973</output>
<result>A</result> | A | 100 | A salt manufacturing company produced a total of 2500 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year? | {
"A": "100",
"B": "105",
"C": "109",
"D": "120",
"E": "90"
} | divide(divide(multiply(add(multiply(2500, const_2), multiply(subtract(const_12, const_1), 100)), const_12), const_2), add(add(multiply(const_3, 100), multiply(multiply(const_2, const_3), const_10)), add(const_2, const_3))) | add(const_2,const_3)|multiply(n0,const_2)|multiply(n1,const_3)|multiply(const_2,const_3)|subtract(const_12,const_1)|multiply(n1,#4)|multiply(#3,const_10)|add(#1,#5)|add(#2,#6)|add(#8,#0)|multiply(#7,const_12)|divide(#10,const_2)|divide(#11,#9)| | "total production of salt by the company in that year = 2500 + 2600 + 2700 + . . . . + 3600 = 36600 . average monthly production of salt for that year = 36600 / 365 â ‰ ˆ 100 answer : a" | general |
math_qa__ruXl1xOFQszTNOCG | 1200 men have provisions for 18 days. If 450 more men join them, for how many days will the provisions last now? Choices
A) 12.9
B) 12.0
C) 12.5
D) 12.2
E) 13.1 | <gadget id="calculator">18 * 1_200</gadget>
<output>21_600</output>
<gadget id="calculator">1_200 + 450</gadget>
<output>1_650</output>
<gadget id="calculator">21_600 / 1_650</gadget>
<output>144/11 = around 13.090909</output>
<result>E</result> | E | 13.1 | 1200 men have provisions for 18 days. If 450 more men join them, for how many days will the provisions last now? | {
"A": "12.9",
"B": "12.0",
"C": "12.5",
"D": "12.2",
"E": "13.1"
} | divide(multiply(18, 1200), add(1200, 450)) | add(n0,n2)|multiply(n0,n1)|divide(#1,#0)| | "1200 * 18 = 1650 * x x = 13.1 answer : e" | physics |
math_qa__MFMFEfS87b4UhHiL | A student needs 60% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 40 marks, find the maximum marks set for the test. Choose the most appropriate option
A) 180
B) 200
C) 220
D) 240
E) 260 | <gadget id="calculator">80 + 40</gadget>
<output>120</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">120 / (3/5)</gadget>
<output>200</output>
<result>B</result> | B | 200 | A student needs 60% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 40 marks, find the maximum marks set for the test. | {
"A": "180",
"B": "200",
"C": "220",
"D": "240",
"E": "260"
} | divide(add(80, 40), divide(60, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | "60 % = 120 marks 1 % = 2 marks 100 % = 200 marks the answer is b ." | gain |
math_qa__m1VvD9sIkBe7di6t | The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 21-inch flat-screen television than a square 19 -inch flat-screen television? Options: A) 42 B) 40 C) 38 D) 36 E) 48 | <gadget id="calculator">21 ** 2</gadget>
<output>441</output>
<gadget id="calculator">441 / 2</gadget>
<output>441/2 = around 220.5</output>
<gadget id="calculator">19 ** 2</gadget>
<output>361</output>
<gadget id="calculator">361 / 2</gadget>
<output>361/2 = around 180.5</output>
<gadget id="calculator">(441/2) - (361/2)</gadget>
<output>40</output>
<result>B</result> | B | 40 | The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 21-inch flat-screen television than a square 19 -inch flat-screen television? | {
"A": "42",
"B": "40",
"C": "38",
"D": "36",
"E": "48"
} | subtract(divide(power(21, const_2), const_2), divide(power(19, const_2), const_2)) | power(n0,const_2)|power(n1,const_2)|divide(#0,const_2)|divide(#1,const_2)|subtract(#2,#3)| | "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 21 - inch flat - screen television the diagonal ( hypotenuse ) = 21 so , we can apply the pythagorean theorem to get x ² + x ² = 21 ² simplify : 2 x ² = 21 ² divide both sides by 2 to get : x ² = 21 ² / 2 since the area of the square = x ² , we can see that the area of this square is 21 ² / 2 square 19 - inch flat - screen television the diagonal ( hypotenuse ) = 19 so , we can apply the pythagorean theorem to get x ² + x ² = 19 ² simplify : 2 x ² = 19 ² divide both sides by 2 to get : x ² = 19 ² / 2 since the area of the square = x ² , we can see that the area of this square is 19 ² / 2 difference in areas = 21 ² / 2 - 19 ² / 2 = ( 21 + 19 ) ( 21 - 19 ) / 2 = 40 b" | geometry |
math_qa__Ap0G7uJEVSAOkawc | The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass? Choose the correct choice:
A) 37 kg B) 35 kg C) 85 kg D) 45 kg E) 25 kg | <gadget id="calculator">7 + 13</gadget>
<output>20</output>
<gadget id="calculator">7 / 20</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>B</result> | B | 35 | The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass? | {
"A": "37 kg",
"B": "35 kg",
"C": "85 kg",
"D": "45 kg",
"E": "25 kg"
} | multiply(divide(7, add(7, 13)), 100) | add(n0,n1)|divide(n1,#0)|multiply(n2,#1) | 7 / 20 * 100 = 35 answer : b | general |
math_qa__8V7h86lyIyoIGfSI | If a man lost 8% by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 45%? Choose the correct option
A) 33.56 B) 23.68 C) 11.42 D) 9.56 E) 23.55 | <gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">92 * 18</gadget>
<output>1_656</output>
<gadget id="calculator">100 + 45</gadget>
<output>145</output>
<gadget id="calculator">1_656 / 145</gadget>
<output>1_656/145 = around 11.42069</output>
<result>C</result> | C | 11.42 | If a man lost 8% by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 45%? | {
"A": "33.56",
"B": "23.68",
"C": "11.42",
"D": "9.56",
"E": "23.55"
} | divide(multiply(subtract(const_100, 8), 18), add(const_100, 45)) | add(n2,const_100)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,#0)| | "92 % - - - - 18 145 % - - - - ? 92 / 145 * 18 = 11.42 answer : c" | gain |
math_qa__fTn7l1m3iW6g2TvJ | The time it took car P to travel 150 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
Pick one: A) 23 B) 50 C) 60 D) 70 E) 80 | <gadget id="calculator">-10</gadget>
<output>-10</output>
<gadget id="calculator">(-10) ** 2</gadget>
<output>100</output>
<gadget id="calculator">150 * 10</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 2</gadget>
<output>750</output>
<gadget id="calculator">-750</gadget>
<output>-750</output>
<gadget id="calculator">4 * (-750)</gadget>
<output>-3_000</output>
<gadget id="calculator">100 - (-3_000)</gadget>
<output>3_100</output>
<gadget id="calculator">3_100 ** (1/2)</gadget>
<output>10*sqrt(31) = around 55.677644</output>
<gadget id="calculator">(-10) + (10*sqrt(31))</gadget>
<output>-10 + 10*sqrt(31) = around 45.677644</output>
<gadget id="calculator">(-10 + 10*sqrt(31)) / 2</gadget>
<output>-5 + 5*sqrt(31) = around 22.838822</output>
<result>A</result> | A | 23 | The time it took car P to travel 150 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour? | {
"A": "23",
"B": "50",
"C": "60",
"D": "70",
"E": "80"
} | divide(add(negate(10), sqrt(subtract(power(negate(10), 2), multiply(const_4, negate(divide(multiply(150, 10), 2)))))), 2) | multiply(n0,n2)|negate(n2)|divide(#0,n1)|power(#1,n1)|negate(#2)|multiply(#4,const_4)|subtract(#3,#5)|sqrt(#6)|add(#1,#7)|divide(#8,n1)| | "let speed of car r be = x then speed of car p = x + 10 a / q , ( 150 / x ) - ( 150 / ( x + 10 ) ) = 2 solving for x = 23 miles \ hr . a" | physics |
math_qa__N4ZFjjnYMiEyDcAq | Subtracting 2% of A from A is equivalent to multiplying A by how much ?
Options:
A) 0.98 B) 9.4 C) 0.094 D) 94 E) none | <gadget id="calculator">100 - 2</gadget>
<output>98</output>
<gadget id="calculator">98 / 100</gadget>
<output>49/50 = around 0.98</output>
<result>A</result> | A | 0.98 | Subtracting 2% of A from A is equivalent to multiplying A by how much ? | {
"A": "0.98",
"B": "9.4",
"C": "0.094",
"D": "94",
"E": "none"
} | divide(subtract(const_100, 2), const_100) | subtract(const_100,n0)|divide(#0,const_100) | answer let a - 2 % of a = ab . ⇒ ( 98 x a ) / 100 = ab ∴ b = 0.98 correct option : a | general |
math_qa__POgfU44B5DrO14dD | A cistern 5 m long and 2 m wide contains water up to a breadth of 1 m 10 cm. Find the total area of the wet surface. Choose the correct answer: A) 42 m sqaure B) 49 m sqaure C) 25 m sqaure D) 28 m sqaure E) none of these | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) * 2</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">(11/10) * 5</gadget>
<output>11/2 = around 5.5</output>
<gadget id="calculator">(11/5) + (11/2)</gadget>
<output>77/10 = around 7.7</output>
<gadget id="calculator">2 * (77/10)</gadget>
<output>77/5 = around 15.4</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">(77/5) + 10</gadget>
<output>127/5 = around 25.4</output>
<result>C</result> | C | 25 | A cistern 5 m long and 2 m wide contains water up to a breadth of 1 m 10 cm. Find the total area of the wet surface. | {
"A": "42 m sqaure",
"B": "49 m sqaure",
"C": "25 m sqaure",
"D": "28 m sqaure",
"E": "none of these"
} | add(multiply(const_2, add(multiply(add(divide(10, const_100), 1), 2), multiply(add(divide(10, const_100), 1), 5))), multiply(2, 5)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 2 * 1.1 + 5 * 1.1 ) ] + 5 * 2 = 25 m square option c" | physics |
math_qa__tsyE2ecorSDt1xw9 | Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 42 years. What is Molly's age right now? Pick one:
A) 24 B) 27 C) 30 D) 33 E) 36 | <gadget id="calculator">42 - 6</gadget>
<output>36</output>
<gadget id="calculator">36 / 4</gadget>
<output>9</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<result>B</result> | B | 27 | Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 42 years. What is Molly's age right now? | {
"A": "24",
"B": "27",
"C": "30",
"D": "33",
"E": "36"
} | multiply(divide(subtract(42, 6), 4), 3) | subtract(n3,n2)|divide(#0,n0)|multiply(n1,#1)| | "now , sandy is 42 - 6 = 36 molly ' s age is ( 3 / 4 ) * 36 = 27 the answer is b ." | other |
math_qa__vaWDTNZB4Er9IDbc | How many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles? Select the correct option.
A) 40 B) 35 C) 20 D) 25 E) 30 | <gadget id="calculator">240 / 12</gadget>
<output>20</output>
<result>C</result> | C | 20 | How many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles? | {
"A": "40",
"B": "35",
"C": "20",
"D": "25",
"E": "30"
} | divide(240, const_12) | divide(n0,const_12)| | "c 20 240 pairs of bangles = 480 bangles = 40 dozens . 40 ÷ 2 = 20 boxes ." | geometry |
math_qa__cyliLxlpUJT0N2o6 | In an election, candidate A got 85% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate? Choices
A) 355600
B) 355800
C) 404600
D) 356800
E) 357000 | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">560_000 * (17/20)</gadget>
<output>476_000</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">476_000 * (17/20)</gadget>
<output>404_600</output>
<result>C</result> | C | 404,600 | In an election, candidate A got 85% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate? | {
"A": "355600",
"B": "355800",
"C": "404600",
"D": "356800",
"E": "357000"
} | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(85, const_100)) | divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3)| | "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 85 % therefore , the number of valid votes polled in favour of candidate a = 85 % of 476000 = 85 / 100 × 476000 = 40460000 / 100 = 404600 c )" | gain |
math_qa__ZdstkBHsrm176MRa | Jerry bought a bottle of perfume for a gift for his wife.
The perfume cost $92 before tax.
If the total price including tax was $98.90, find the tax rate
Choose the correct choice from the following choices.
A) 7.5 % B) 5 % C) 12 % D) 8 % E) 10 % | <gadget id="calculator">98.9 / 92</gadget>
<output>1.075</output>
<gadget id="calculator">1.075 - 1</gadget>
<output>0.075</output>
<gadget id="calculator">0.075 * 100</gadget>
<output>7.5</output>
<result>A</result> | A | 7.5 | Jerry bought a bottle of perfume for a gift for his wife.
The perfume cost $92 before tax.
If the total price including tax was $98.90, find the tax rate | {
"A": "7.5 %",
"B": "5 %",
"C": "12 %",
"D": "8 %",
"E": "10 %"
} | multiply(subtract(divide(98.9, 92), const_1), const_100) | divide(n1,n0)|subtract(#0,const_1)|multiply(#1,const_100) | total price including tax is $ 98.90 perfume cost before tax is = 92 ie 92 * 7.5 % + 98.90 answer is 7.5 % | general |
math_qa__oaVaBtHJH2CTgBhb | Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ? Choose the correct choice from the following choices.
A) 175.5 B) 182.5 C) 170.0 D) 180.0 E) 190.0 | <gadget id="calculator">153 + 10</gadget>
<output>163</output>
<gadget id="calculator">163 + 10</gadget>
<output>173</output>
<gadget id="calculator">173 + 2</gadget>
<output>175</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">175 + (1/2)</gadget>
<output>351/2 = around 175.5</output>
<result>A</result> | A | 175.5 | Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ? | {
"A": "175.5",
"B": "182.5",
"C": "170.0",
"D": "180.0",
"E": "190.0"
} | add(add(add(add(153, const_10), const_10), 2), add(const_0_25, const_0_25)) | add(n5,const_10)|add(const_0_25,const_0_25)|add(#0,const_10)|add(n4,#2)|add(#3,#1)| | "tea worth rs . 126 ratio 1 : 1 average price = ( 126 + 135 ) / 2 = 130.5 mean price = ( x - 153 ) : 22.50 = > x - 153 = 22.50 x = 175.5 answer a" | other |
math_qa__gyEHJXQ0zUu97pXn | a 7 - digit number comprises of only 2 ' s and 3 ' s . how many of these are multiples of 12 ? Choose the correct choice from the following options.
A) 11 B) 12 C) 10 D) 22 E) 44 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">120 / 12</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>A</result> | A | 11 | a 7 - digit number comprises of only 2 ' s and 3 ' s . how many of these are multiples of 12 ? | {
"A": "11",
"B": "12",
"C": "10",
"D": "22",
"E": "44"
} | add(divide(factorial(add(3, 2)), multiply(factorial(3), factorial(2))), const_1) | add(n1,n2)|factorial(n2)|factorial(n1)|factorial(#0)|multiply(#1,#2)|divide(#3,#4)|add(#5,const_1) | detailed solution number should be a multiple of 3 and 4 . so , the sum of the digits should be a multiple of 3 . we can either have all seven digits as 3 , or have three 2 ' s and four 3 ' s , or six 2 ' s and a 3 . ( the number of 2 ' s should be a multiple of 3 ) . for the number to be a multiple of 4 , the last 2 digits should be 32 . now , let us combine these two . all seven 3 ' s - no possibility . three 2 ' s and four 3 ' s - the first 5 digits should have two 2 ' s and three 3 ' s in some order . no of possibilities = 5 ! 3 ! 2 ! = 10 six 2 ' s and one 3 - the first 5 digits should all be 2 ' s . so , there is only one number 2222232 . so , there are a total of 10 + 1 = 11 solutions . correct answer : a . | general |
math_qa__LQcIZRmny1WqE3ao | Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8110/-. Find out the amount that he borrowed.
Answers
A) rs . 4,900 B) rs . 5,000 C) rs . 5,100 D) rs . 5266 E) none of these | <gadget id="calculator">6 * 9</gadget>
<output>54</output>
<gadget id="calculator">54 / 100</gadget>
<output>27/50 = around 0.54</output>
<gadget id="calculator">1 + (27/50)</gadget>
<output>77/50 = around 1.54</output>
<gadget id="calculator">8_110 / (77/50)</gadget>
<output>405_500/77 = around 5_266.233766</output>
<result>D</result> | D | 5,266 | Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8110/-. Find out the amount that he borrowed. | {
"A": "rs . 4,900",
"B": "rs . 5,000",
"C": "rs . 5,100",
"D": "rs . 5266",
"E": "none of these"
} | divide(8110, add(const_1, divide(multiply(6, 9), const_100))) | multiply(n0,n1)|divide(#0,const_100)|add(#1,const_1)|divide(n3,#2)| | "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8110 = p + ( 54 p / 100 ) 8110 = ( 100 p + 54 p ) / 100 8110 = 154 p / 100 p = ( 8110 * 100 ) / 154 = rs . 5266.233 answer d" | gain |
math_qa__8mVi0oNro8SQeh4i | A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed? Select the correct option:
A) 5 % B) 10 % C) 25 % D) 40 % E) 55 % | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">10 * 50</gadget>
<output>500</output>
<gadget id="calculator">500 / 100</gadget>
<output>5</output>
<gadget id="calculator">50 + 5</gadget>
<output>55</output>
<result>E</result> | E | 55 | A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed? | {
"A": "5 %",
"B": "10 %",
"C": "25 %",
"D": "40 %",
"E": "55 %"
} | add(divide(const_100, const_2), divide(multiply(10, divide(const_100, const_2)), const_100)) | divide(const_100,const_2)|multiply(n0,#0)|divide(#1,const_100)|add(#0,#2)| | "assuming that the technician makes a round - trip of 40 miles ( each way is 20 miles ) , then the technician would have completed 20 miles + 2 miles ( 10 % of the remaining 20 miles ) . therefore , the total is 22 miles . 22 miles / 40 miles is 55 % of the entire trip . answer : e" | gain |
math_qa__oEolbsIXTfdHbVUE | A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? Choose one.
A) 15
B) 30
C) 28
D) 24
E) 32 | <gadget id="calculator">25 - 10</gadget>
<output>15</output>
<gadget id="calculator">15 * 10</gadget>
<output>150</output>
<gadget id="calculator">25 - 15</gadget>
<output>10</output>
<gadget id="calculator">150 / 10</gadget>
<output>15</output>
<result>A</result> | A | 15 | A certain number of workers can do a work in 25 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there? | {
"A": "15",
"B": "30",
"C": "28",
"D": "24",
"E": "32"
} | divide(multiply(subtract(25, 10), 10), subtract(25, subtract(25, 10))) | subtract(n0,n1)|multiply(n1,#0)|subtract(n0,#0)|divide(#1,#2) | number of workers = 10 * ( 25 - 10 ) / 10 = 15 answer is a | physics |
math_qa__LYq7rKk63zbJ2UwF | A big container is 30% full with water. If 9 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container? Choices
A) 20 liters B) 40 liters C) 45 liters D) 54 liters E) 60 liters | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/4) - (3/10)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">9 / (9/20)</gadget>
<output>20</output>
<result>A</result> | A | 20 | A big container is 30% full with water. If 9 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container? | {
"A": "20 liters",
"B": "40 liters",
"C": "45 liters",
"D": "54 liters",
"E": "60 liters"
} | divide(9, subtract(divide(3, 4), divide(30, const_100))) | divide(n2,n3)|divide(n0,const_100)|subtract(#0,#1)|divide(n1,#2)| | "a big container is 30 % full with water and after 9 liters of water is added , the container becomes 75 % full . hence these 9 liters account for 45 % of the container , which means that the capacity of it is 9 / 0.45 = 20 liters . or : if the capacity of the container is x liters then : 0.3 x + 9 = 0.75 x - - > x = 20 liters . answer : a ." | general |
math_qa__jmWcA6X6Wf3UTua4 | A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. Choose the correct answer:
A) 19.81 %
B) 20 %
C) 37.5 %
D) 25 %
E) 42.86 % | <gadget id="calculator">100 + 11</gadget>
<output>111</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">9.09 + 80</gadget>
<output>89.09</output>
<gadget id="calculator">111 - 89.09</gadget>
<output>21.91</output>
<gadget id="calculator">21.91 * 2</gadget>
<output>43.82</output>
<result>E</result> | E | 42.86 | A man cheats while buying as well as while selling. While buying he takes 11% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. | {
"A": "19.81 %",
"B": "20 %",
"C": "37.5 %",
"D": "25 %",
"E": "42.86 %"
} | multiply(subtract(add(const_100, 11), add(9.09, subtract(const_100, 20))), const_2) | add(n0,const_100)|subtract(const_100,n1)|add(n2,#1)|subtract(#0,#2)|multiply(#3,const_2) | there is a one step calculation method too . it requires more thought but is faster . the man takes 11 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 111 pounds for which he will take from the customer $ 111 . hence , in effect , there is a 11 % mark up . while selling , he sells 30 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 70 pounds and should have got only $ 70 for it . so this is again a mark up of $ 30 on $ 70 . but he also sells at 9.09 % less i . e . gives a discount of 1 / 11 . ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 10 / 7 * 10 / 11 = ( 1 + p % ) profit % = 42.86 % e | gain |
math_qa__0VS4QYrBIkFoWd2z | A number is doubled and 15 is added. If resultant is trebled, it becomes 75. What is that number Choices
A) 8 B) 10 C) 5 D) 14 E) 7 | <gadget id="calculator">3 * 15</gadget>
<output>45</output>
<gadget id="calculator">75 - 45</gadget>
<output>30</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">30 / 6</gadget>
<output>5</output>
<result>C</result> | C | 5 | A number is doubled and 15 is added. If resultant is trebled, it becomes 75. What is that number | {
"A": "8",
"B": "10",
"C": "5",
"D": "14",
"E": "7"
} | divide(subtract(75, multiply(const_3, 15)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "explanation : = > 3 ( 2 x + 15 ) = 75 = > 2 x + 15 = 25 = > x = 5 option c" | general |
math_qa__xu67Z81EJMKJEYim | If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+69)=? Choose one:
A) 3675 B) 3575 C) 3475 D) 3375 E) 3275 | <gadget id="calculator">69 + 1</gadget>
<output>70</output>
<gadget id="calculator">69 * 70</gadget>
<output>4_830</output>
<gadget id="calculator">4_830 / 2</gadget>
<output>2_415</output>
<gadget id="calculator">69 - 1</gadget>
<output>68</output>
<gadget id="calculator">68 / 2</gadget>
<output>34</output>
<gadget id="calculator">34 + 1</gadget>
<output>35</output>
<gadget id="calculator">34 * 35</gadget>
<output>1_190</output>
<gadget id="calculator">2_415 - 1_190</gadget>
<output>1_225</output>
<gadget id="calculator">1_225 * 3</gadget>
<output>3_675</output>
<result>A</result> | A | 3,675 | If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+69)=? | {
"A": "3675",
"B": "3575",
"C": "3475",
"D": "3375",
"E": "3275"
} | multiply(subtract(divide(multiply(69, add(69, const_1)), const_2), multiply(divide(subtract(69, const_1), const_2), add(divide(subtract(69, const_1), const_2), const_1))), const_3) | add(n8,const_1)|subtract(n8,const_1)|divide(#1,const_2)|multiply(n8,#0)|add(#2,const_1)|divide(#3,const_2)|multiply(#4,#2)|subtract(#5,#6)|multiply(#7,const_3) | explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 69 = 1 + ( n - 1 ) 2 = > n = 35 use value of n in ( 1 ) then , sn = ( 35 / 2 ) ( 1 + 69 ) = 1225 ans : - 3 ( sn ) = 3675 answer : a | general |
math_qa__9BDboKDwpMUrUei3 | If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is Choose the correct choice from the following answers
A) 407 B) 518 C) 519 D) 521 E) 525 | <gadget id="calculator">414 - 8</gadget>
<output>406</output>
<gadget id="calculator">406 + 1</gadget>
<output>407</output>
<result>A</result> | A | 407 | If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is | {
"A": "407",
"B": "518",
"C": "519",
"D": "521",
"E": "525"
} | add(subtract(414, 8), const_1) | subtract(n1,n0)|add(#0,const_1) | a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 8 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 4 th and 5 th numbers in the set ) . this means that numbers 4 and 5 in this set are 413 and 415 . because we know that number 4 is 413 , we know that the smallest number is 3 odd numbers below this , which means that it is 3 * 2 = 6 below this ( every odd number is every other number ) . therefore 413 - 6 = 407 , answer choice a | general |
math_qa__uagKaup4ivyxMazg | A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
A.
B.
C.
D.
E.
Answers
A) 1 / 250 B) 1 / 84 C) 1 / 11 D) 1 / 9 E) 1 / 3 | <gadget id="calculator">84 / 250</gadget>
<output>42/125 = around 0.336</output>
<gadget id="calculator">84 - 1</gadget>
<output>83</output>
<gadget id="calculator">250 + 1</gadget>
<output>251</output>
<gadget id="calculator">83 / 251</gadget>
<output>83/251 = around 0.330677</output>
<gadget id="calculator">(42/125) * (83/251)</gadget>
<output>3_486/31_375 = around 0.111108</output>
<result>D</result> | D | 0.111111 | A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
A.
B.
C.
D.
E. | {
"A": "1 / 250",
"B": "1 / 84",
"C": "1 / 11",
"D": "1 / 9",
"E": "1 / 3"
} | multiply(divide(84, 250), divide(subtract(84, const_1), add(250, const_1))) | add(n0,const_1)|divide(n1,n0)|subtract(n1,const_1)|divide(#2,#0)|multiply(#1,#3) | probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = ( 84 / 250 ) probability of choosing one defective phone from a lot of 249 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 249 ) combined probability of series of events = product of the probabilities = ( 84 / 250 ) * ( 83 / 249 ) 84 / 250 is close to ( 1 / 3 ) and ( 83 / 249 ) = ( 1 / 3 ) so answer is ( 1 / 3 ) * ( 1 / 3 ) = ( 1 / 9 ) answer : d | other |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.