euclaise/mathqa_programs huggingface dataset:
Problem: the average weight of 12 person ' s increases by 4 kg when a new person comes in place of one of them weighing 58 kg . what is the weight of the new person ?
Options: a ) 85 , b ) 80 , c ) 95 , d ) 90 , e ) 106
Rationale: "total increase in weight = 12 × 4 = 48 if x is the weight of the new person , total increase in weight = x − 58 = > 48 = x - 58 = > x = 48 + 58 = 106 answer : e"
Answer: e
Python program:
a = 12 * 4
b = a + 58
Problem: a cube 125 mt is colored pink on two opposite surfaces and then cut in to 125 smaller cubes then find how many number of cubes have pink color ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: answer : b
Answer: b
Python program:
a = math.floor(cube_edge_by_volume)
Problem: 6 ) a marketing firm determined that , of 180 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 10 , e ) e ) 45
Rationale: 100 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 100 = > 4 x = 40 = > x = 10 answer - d
Answer: d
Python program:
a = 180 - 80
b = a - 60
c = b / 4
Problem: one machine takes 3 minutes to check fault in 100 km fiber optic cable . another machine does the same job in 3 seconds . what time will it take to do the same job when both machines are put to work ?
Options: a ) 2.00 seconds , b ) 2.20 seconds , c ) 2.50 seconds , d ) 2.95 seconds , e ) 3.00 seconds
Rationale: by guess it is clear that the time taken will be less than 3 seconds and very near to it . therefore , answer 2.95 seconds will be correct . answer - d
Answer: d
Python program:
a = 3 * const_60
b = 1/(a)
c = 1/(3)
d = b + c 
e = 1/(d)
Problem: a certain telescope increases the visual range at a particular location from 60 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 150 %
Rationale: "original visual range = 60 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 60 ) / 60 * 100 % = 3 / 2 * 100 % = 150 % answer e"
Answer: e
Python program:
a = 150 - 60
b = a / 60
c = b * 100
Problem: a small company reduced its faculty by approximately 13 percent to 181 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 302
Rationale: "if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 181 x = 208 so the original number of employees is 208 correct answer - b"
Answer: b
Python program:
a = 100 - 13
b = a / 100
c = 181 / b
Problem: 66 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 150 , c ) 152 , d ) 216 , e ) 256
Rationale: "66 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 66 = 150 hence , b is the answer ."
Answer: b
Python program:
a = cube_edge_by_volume + ( 
b = volume_cube - (
Problem: 0.9 * 0.007 = ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ _________
Options: a ) 0.063 , b ) 0.0063 , c ) 0.63 , d ) 0.00063 , e ) 63
Rationale: 9 * 7 = 63 sum of decimal places = 4 so , 0.9 * 0.007 = 0.0063 answer : b
Answer: b
Python program:
a = 0 * 9
Problem: a train passes a station platform in 31 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 165 , d ) 166 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 31 = 15 = > x = 165 m . answer : c"
Answer: c
Python program:
a = 54 * const_0_2778
b = 20 * a
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 768 square meters , then what is the width of the rectangular garden ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "let x be the width of the garden . 3 x ^ 2 = 768 x ^ 2 = 256 x = 16 the answer is a ."
Answer: a
Python program:
a = 768 / 3
b = math.sqrt(a)
Problem: mr . hernandez , who was a resident of state x for only 9 months last year , had a taxable income of $ 42,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 1275 , c ) $ 1200 , d ) $ 1300 , e ) $ 1060
Rationale: total tax for the year = 42,500 x 4 % = 1700 as stated annual tax is prorated as per the duration of stay . prorated tax = 1700 ( 9 / 12 ) = 1275 answer b
Answer: b
Python program:
a = 4 * 100
b = a * 100
c = 100 * const_0_25
d = c * 100
e = b + d 
f = e / 100
g = f * 4
h = g * 9
i = 3 * 4
j = h / i
Problem: if a man lost 10 % by selling oranges at the rate of 10 a rupee at how many a rupee must he sell them to gain 50 % ?
Options: a ) 6 , b ) 8 , c ) 7 , d ) 4 , e ) 2
Rationale: "90 % - - - - 10 150 % - - - - ? 90 / 150 * 10 = 6 answer : a"
Answer: a
Python program:
a = 100 - 10
b = a * 10
c = 100 + 50 
d = b / c
Problem: a candidate appearing for an examination has to secure 42 % marks to pass paper i . but he secured only 42 marks and failed by 22 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 152 , e ) 150
Rationale: "he secured 42 marks nd fail by 22 marks so total marks for pass the examinatn = 64 let toal marks x x * 42 / 100 = 64 x = 152 answer : d"
Answer: d
Python program:
a = 42 + 22 
b = 42 / 100
c = a / b
Problem: if ( - 3 ) ^ ( 2 x ) = 3 ^ ( 12 - x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: since x is an integer , ( - 3 ) ^ ( 2 x ) is always positive . so , 3 ^ 2 x = 3 ^ ( 12 - x ) 2 x = 12 - x 3 x = 12 x = 4 answer : b
Answer: b
Python program:
a = 12 / 3
Problem: in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , what is the dividend ?
Options: a ) 5336 , b ) 5242 , c ) 6524 , d ) 3526 , e ) 4526
Rationale: "divisor = ( 5 * 46 ) = 230 10 * quotient = 230 quotient = 230 / 10 = 23 . dividend = ( divisor * quotient ) + remainder = ( 230 * 23 ) + 46 = ( 5290 + 46 ) = 5336 . answer is a"
Answer: a
Python program:
a = 5 * 46
b = 5 * 46
c = b / 10
d = a * c
Problem: a company plans to gradually replace its fleet of 20 cars with newer models . at the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models . how many years did it take before the number of older cars left in the company ' s fleet was less than 50 percent of the fleet ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: total fleet - - 20 end of year 2000 - - ( retires 5 and buys 6 ) total fleet - - 21 ( 15 old 6 new ) . end of year 2001 - - ( retires 5 and buys 6 ) total fleet - - 22 ( 10 old 12 new ) . answer is c - - after 2 years the company has a total of 22 cars ( 10 old 12 new ) , the old cars are already less than 50 % of its fleet .
Answer: c
Python program:
a = 10 + 1 
b = 20 / a
c = b + 1 
d = math.floor(c)
Problem: the ratio of radius of a circle and the side of a square is 2 : 3 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 9 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 3 â ‡ ’ area of circle / area of square = 4 / 9 answer : b"
Answer: b
Python program:
a = 2 / 3
b = a ** 2
Problem: find the compound interest on $ 500 in 5 years at 5 % per annum , the interest being compounded yearly ?
Options: a ) $ 138.14 , b ) $ 150.12 , c ) $ 142.65 , d ) $ 152 , e ) $ 164.12
Rationale: "principle = $ 500 rate = 5 % yearly amount = 500 * ( 1 + 5 / 100 ) ^ 5 = 500 * 21 / 20 * 21 / 20 * 21 / 20 * 21 / 20 * 21 / 20 = $ 638.14 c . i . = 638.14 - 500 = $ 138.14 answer is a"
Answer: a
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 5
d = 500 * c
e = d - 500
Problem: during 2003 , a company produced an average of 1,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 200 % over its 2003 average ?
Options: a ) 132,000 , b ) 235,000 , c ) 175,000 , d ) 200,000 , e ) 250,000
Rationale: "company produced 12 * 1000 = 12,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 12,000 . the gives the average of ( x + 12,000 ) / 4 . this average needs to be 200 % higher than that in 2003 . in math terms , 12,000 + 200 % ( 12,000 ) = 36,000 . so : ( x + 12,000 ) / 4 = 36,000 x + 12,000 = 144,000 x = 132,000 the answer is a ."
Answer: a
Python program:
a = 2007 - 2003
b = a / 2
c = 200 * b
Problem: the sum of two numbers is 45 . their difference is 5 . the bigger number is
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 45
Rationale: x + y = 45 x - y = 5 adding 2 x = 50 = = > x = 25 and y = 45 - 25 = 20 bigger number is x = 25 answer b .
Answer: b
Python program:
a = 45 + 5 
b = a / 2
Problem: the present worth of rs . 338 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 312.5 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 338 / ( 1 + 4 / 100 ) ² ] = rs . ( 338 x 25 / 26 x 25 / 26 ) = rs . 312.5 answer a"
Answer: a
Python program:
a = 4 / 100
b = a + 1 
c = b ** 2
d = 338 / c
Problem: the average of 6 observations is 11 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 66 + x ) / 7 = 10 = > x = 4 . hence , the seventh observation is 4 . answer : a"
Answer: a
Python program:
a = 11 - 1
b = 6 + 1 
c = a * b
d = 11 * 6
e = c - d
Problem: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 350 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "the smallest amount that the company can spend is the lcm of 350 and 200 , which is 1400 for each , which is total 2800 . the number of 1 st type of computers which costing $ 350 = 1400 / 350 = 4 . the number of 2 nd type of computers which costing $ 200 = 1400 / 200 = 7 . total = 4 + 7 = 11 answer is c ."
Answer: c
Python program:
a = math.lcm(350, 200)
b = a / 350
c = math.lcm(350, 200)
d = c / 200
e = b + d
Problem: after decreasing 40 % in the price of an article costs rs . 1050 . find the actual cost of an article ?
Options: a ) 1200 , b ) 1750 , c ) 1050 , d ) 1570 , e ) 1005
Rationale: "cp * ( 60 / 100 ) = 1050 cp = 17.5 * 100 = > cp = 1750 answer : b"
Answer: b
Python program:
a = 40 / 100
b = 1 - a
c = 1050 / b
Problem: a fair sided dice labeled 1 to 6 is tossed 2 times . what is the probability the sum of the 2 throws is 5 ?
Options: a ) 1 / 6 , b ) 7 / 216 , c ) 4 / 36 , d ) 9 / 216 , e ) 11 / 216
Rationale: the total possible number of combination if the dice is thrown 2 times is 36 . there are 4 possible outcomes that the sum of the number is 5 which is ( 2 + 3 ) ( 3 + 2 ) ( 1 + 4 ) and ( 4 + 1 ) answer : c
Answer: c
Python program:
a = 5 - 1
b = 6 ** 2
c = a / b
Problem: a merchant marks his goods up by 50 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 21 % , b ) 25 % , c ) 69 % , d ) 35 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 150 after a 50 % markup . now a discount of 10 % on 150 . profit = 135 - 100 35 % answer d"
Answer: d
Python program:
a = 50 + 100 
b = 50 + 100 
c = b * 10
d = c / 100
e = a - d
f = e - 100
Problem: i bought two books ; for rs . 460 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337.33 , b ) 280.33 , c ) 299.33 , d ) 268.33 , e ) 289.33
Rationale: "x * ( 85 / 100 ) = ( 460 - x ) 119 / 100 x = 280 answer : d"
Answer: d
Python program:
a = 100 + 19 
b = 460 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: what is the least number of squares tiles required to pave the floor of a room 6 m 75 cm long and 4 m 5 cm broad ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 44 , e ) 54
Rationale: "length of largest tile = h . c . f . of 675 cm and 405 cm = 135 cm . area of each tile = ( 135 x 135 ) cm 2 . required number of tiles = 675 x 405 / ( 135 ^ 2 ) = 15 answer : a"
Answer: a
Python program:
a = 6 * 100
b = 75 * 100
c = rectangle_area / (
Problem: in how many years will a sum of money doubles itself at 5 % per annum simple interest
Options: a ) 25 years , b ) 28 years , c ) 10 years , d ) 20 years , e ) 21 years
Rationale: "let the initial sum be x then , amount = 2 x ( because sum will be double ) amount = principal + s . i 2 x = x + s . i s . i = x s . i = ( p * r * t ) / 100 x = ( x * 5 * t ) / 100 therefore , t = 20 years answer : d"
Answer: d
Python program:
a = 100 / 5
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of odd all the integers between 1 and 50 ?
Options: a ) 500 , b ) 625 , c ) 750 , d ) 550 , e ) 600
Rationale: "numbers are 1 , 3,5 - - - - - - - , 47,49 average of the set : ( largest + smallest ) / 2 = ( 49 + 1 ) / 2 = 25 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 49 - 1 ) / 2 + 1 = 25 the sum = 25 * 25 = 625 answer : b"
Answer: b
Python program:
a = 50 - 1
b = 1 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: on dividing a number by 357 , we get 41 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 41 = ( 17 * 21 * y ) + ( 17 * 2 ) + 7 = 17 * ( 21 y + 2 ) + 7 . required number = 7 . answer is d"
Answer: d
Python program:
a = 41 ** 2
b = a / 357
c = 41 ** 2
d = c / 357
e = math.floor(d)
f = b - e
g = f * 357
Problem: machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 6 hours and machine y produces k bottles in 12 hours . how many hours does it take machines x and y , working simultaneously , to produce 12 k bottles ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 48 , e ) 24
Rationale: "x rate = k / 6 y rate = k / 12 k / 6 + k / 12 = 12 k / t solving t = 48 answer d"
Answer: d
Python program:
a = 6 + 12 
b = a / 2
c = 12 * b
d = c / 12
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 80 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 1 / 600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 80 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 80 / 800 * 1 / 600 = 1 / 6,000 . answer : c ."
Answer: c
Python program:
a = 80 / 800
b = 1 / 600
c = a * b
Problem: in a race where 8 cars are running , the chance that car x will win is 1 / 2 , that y will win is 1 / 4 and that z will win is 1 / 3 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 11 / 12 , c ) 14 / 8 , d ) 13 / 12 , e ) 57 / 120
Rationale: required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 2 + 1 / 4 + 1 / 3 = 13 / 12 answer : d
Answer: d
Python program:
a = 1 / 2
b = 1 / 4
c = a + b 
d = 1 / 3
e = c + d
Problem: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 4 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1160 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 4 ) = $ 160 total revenue : 1000 + 160 = $ 1160 the answer is b ."
Answer: b
Python program:
a = 10 + 4 
b = a * 30
c = 100 - 30
d = c * 10
e = b + d
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day should 4 pumps work in order to empty the tank in 1 day ?
Options: a ) 10 , b ) 12 , c ) 8 , d ) 15 , e ) 18
Rationale: "explanation : let the required hours needed be x more pumps , less hours ( indirect proportion ) more days , less hours ( indirect proportion ) hence we can write as ( pumps ) 3 : 4 ( days ) 2 : 1 } : : x : 8 ⇒ 3 × 2 × 8 = 4 × 1 × x ⇒ 3 × 2 × 2 = x ⇒ x = 12 answer : option b"
Answer: b
Python program:
a = 3 * 8
b = a * 2
c = b / 4
Problem: in what ratio must rice of rs . 54 per kg be mixed with rice of rs . 35 per kg so that cost of mixture is rs . 42 per kg ?
Options: a ) 9 : 7 , b ) 7 : 12 , c ) 12 : 7 , d ) 5 : 6 , e ) 7 : 9
Rationale: ( 42 - 35 ) / ( 54 - 42 ) = 7 / 12 = 7 : 12 answer : b
Answer: b
Python program:
a = 42 - 35
b = 54 - 35
c = a / b
d = 42 - 35
e = 54 - 35
f = d / e
g = 1 - f
h = c / g
Problem: the sum of the numbers is 264 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 27
Rationale: let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 264 11 x / 3 = 264 x = 72 answer : c
Answer: c
Python program:
a = 264 * 3
b = 10 + 1 
c = a / b
Problem: if rs . 64 amount to rs . 83.20 in 2 years , what will rs . 86 amount to in 4 years at the same rate percent per annum ?
Options: a ) rs . 114.80 , b ) rs . 86.70 , c ) rs . 55.40 , d ) rs . 51.60 , e ) none
Rationale: "solution p = rs . 64 , s . i . = rs . ( 83.20 - 64 ) = rs . 19.20 , t = 2 years . so , rate = ( 100 x 19.20 / 64 x 2 ) = 15 % . now , p = rs . 86 , r = 15 % , t = 4 years . ∴ s . i . = rs . ( 86 x 15 x 4 / 100 ) rs . 51.60 . answer d"
Answer: d
Python program:
a = 83 - 20
b = a * 86
c = 83 - 20
d = b - c
Problem: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm ?
Options: a ) 243 cm 2 , b ) 239 cm 2 , c ) 267 cm 2 , d ) 230 cm 2 , e ) 228 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : e"
Answer: e
Python program:
a = 20 + 18 
b = 12 * a
c = b / 2
Problem: if x = 6 ^ 36 and x ^ x = 6 ^ k , what is k ?
Options: a ) 6 ^ 36 , b ) 6 ^ 38 , c ) 6 ^ 72 , d ) 6 ^ 216 , e ) 6 ^ 432
Rationale: "solution : we know that x = 6 ^ 36 which implies x ^ x = ( 6 ^ 36 ) ^ ( 6 ^ 36 ) = 6 ^ ( 36 * 6 ^ 36 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 6 ^ ( 6 ^ 2 * 6 ^ 36 ) = 6 ^ ( 6 ^ ( 2 + 36 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 6 ^ ( 6 ^ 38 ) given that x ^ x = 6 ^ k so 6 ^ ( 6 ^ 38 ) = 6 ^ k since the base is same the exponent will also be same therefore k = 6 ^ 38 answer : b"
Answer: b
Python program:
a = 6 ** 36
b = a * 36
Problem: a cylindrical can has a radius of 6 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 144 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 6 * 12 = 144 pi answer is d ."
Answer: d
Python program:
a = 6 * 12
b = 2 * math.pi
c = a * b
Problem: a digital wristwatch was set accurately at 8.30 a . m and then lost 2 seconds every 5 minutes . what time was indicated on the watch at 6.30 p . m of the same day if the watch operated continuously that time ?
Options: a ) 5.56 , b ) 5.58 , c ) 6.0 , d ) 6.23 , e ) 6.26
Rationale: for every 5 min watch looses 2 secs , so for 60 ms it looses 24 sec , i . e . , for 1 hr it looses 24 secs 8.30 amto 6.30 pm = 10 hr it looses 240 secs i . e . , 4 mins , hence d watch will show 6.26 answer : e
Answer: e
Python program:
a = 3 * 4
b = a + 6 
c = b - 8
d = c * const_60
e = d / 5
f = e * 2
g = f / const_60
h = g / 100
i = 6 - 3
Problem: if each edge of cube increased by 10 % , the percentage increase in surface area is :
Options: a ) 33.1
b ) 33.5
c ) 33.7
d ) 33.2
e ) 33.9
Rationale: 100 × ( 110 ) / 100 × ( 110 ) / 100 × ( 110 ) / 100 = > 1331 / 100 = 33.1 % answer is a .
Answer: a
Python program:
a = 100 + 10 
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
Problem: a train 110 m long is running with a speed of 56 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6.4 , c ) 7 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 56 + 6 = 62 km / hr . = 62 * 5 / 18 = 155 / 9 m / sec . time taken to pass the men = 110 * 9 / 155 = 6.4 sec . answer : option b"
Answer: b
Python program:
a = 56 + 6 
b = a * const_0_2778
c = 110 / b
Problem: if a and b are integers and ( a * b ) ^ 5 = 48 y , y could be :
Options: a ) 8 , b ) 16 , c ) 162 , d ) 144 , e ) 100
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 48 y find the prime factorization of 48 . this is 2 ^ 4 * 3 ^ 1 . we need 2 ^ 1 * 3 ^ 4 ( or some other power of 3 that will give us a multiple of 3 ^ 5 as our second term ) . 3 ^ 4 * 2 = 81 * 2 = 162 the answer is c ."
Answer: c
Python program:
a = 2 ** 5
b = 48 / a
c = b * 2
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 105 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 4 rs , e ) 1 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 105 rs . 5 m + 5 m + 5 m - - - - - 105 rs . 15 m - - - - - - 105 rs . = > 1 m = 7 rs . answer : b"
Answer: b
Python program:
a = 3 * 5
b = 105 / a
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 520 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 5 , b ) 4 , c ) 12 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 520 / 40 = 13 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 5 miles / gallon is required to match the actual mileage . imo option a ."
Answer: a
Python program:
a = 520 / 40
b = a - 8
Problem: jerry travels 8 miles at an average speed of 40 miles per hour , stops for 11 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 37 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 11 minutes + ( 20 / 60 ) * 60 minutes = 45 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 45 / 60 ) hours = 28 * 60 / 45 = 37 miles per hour answer : option a"
Answer: a
Python program:
a = 8 + 20 
b = 8 / 40
c = 11 / 60
d = b + c 
e = 20 / 60
f = d + e 
g = a / f