euclaise/mathqa_programs huggingface dataset:
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m ?
Options: a ) 24000 , b ) 23000 , c ) 22000 , d ) 25000 , e ) 26000
Rationale: "25 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 25 = 1 / 100 * x = > x = 25000 answer : d"
Answer: d
Python program:
a = 25 * 100
b = 2 * 100
c = a * b
d = 0 * 75
e = c * d
f = e / 20
g = f / 10
h = g / 7
Problem: the ratio of the incomes of a and b is 5 : 4 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 1600 then the income of a is ?
Options: a ) $ 1500 , b ) $ 4000 , c ) $ 2000 , d ) $ 2500 , e ) $ 3200
Rationale: let the income of a and b be $ 5 x and $ 4 x let their expenditures be $ 3 y and $ 2 y 5 x - 3 y = 1600 - - - - - - - 1 ) 4 x - 2 y = 1600 - - - - - - - 2 ) from 1 ) and 2 ) x = 800 a ' s income = 5 x = 5 * 800 = $ 4000 answer is b
Answer: b
Python program:
a = 5 / 2
b = a * 1600
Problem: a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 8 cm x 7 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 8 * 7 * 6 = 1000000 answer : b
Answer: b
Python program:
a = 4 * 0
b = 7 * 100
c = a * b
d = 8 * 100
e = c * d
f = 8 * 7
g = f * 7
h = e / g
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 420 , e ) 663
Rationale: "1 h - - - - - 3 ? - - - - - - 60 12 h rs = 16 + 19 = 35 t = 12 d = 35 * 12 = 420 answer : d"
Answer: d
Python program:
a = 19 - 16
b = 60 / a
c = b * 16
d = 19 - 16
e = 60 / d
f = e * 19
g = c + f
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 60 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 15 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 60 / 3 = 20 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 20 / 2 = 4 km / hr so time taken in upstream = 60 / 4 = 15 hrs answer : d"
Answer: d
Python program:
a = 60 / 3
b = a - 12
c = 12 - b
d = 60 / c
Problem: if there are 200 questions in a 3 hr examination . among these questions are 25 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 40 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 175 x + 25 * 2 x = 180 x = 180 / 225 x = 0.8 time taken for type a problem = 25 * 2 * 0.8 = 40 min answer : a"
Answer: a
Python program:
a = 3 * const_60
b = 200 - 25
c = 2 * 25
d = b + c 
e = a / d
f = 2 * e
g = f * 25
Problem: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 20 - inch screen would be how many square inches greater than the area of a square 18 - inch screen ?
Options: a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 40
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 20 ^ 2 / 2 - 18 ^ 2 / 2 = 76 / 2 = 38 ans d ."
Answer: d
Python program:
a = 20 ** 2
b = 18 ** 2
c = a - b
d = c / 2
Problem: in a group of 8 engineers , 3 engineers have a phd degree ; the others have only an ms or bs degree . a team of 3 engineers is to be chosen which must have at least 1 engineer with a phd , how many different teams can be chosen ?
Options: a ) 56 , b ) 46 , c ) 64 , d ) 65 , e ) 10
Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 8 r = 3 so , total teams is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , and n = 8 - 3 = 5 r = 3 for teams without a phd is 5 c 3 = 5 ! / ( 3 ! ( 5 - 3 ) ! ) = 10 , so , teams with at least 1 phd = 56 - 10 = 46 answer : b
Answer: b
Python program:
a = 8 - 3
b = a * 3
c = b * 3
d = 1 + c
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 4 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 4 * 180 / 12 = 60 ounces of water d"
Answer: d
Python program:
a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 4
Problem: in an election between two candidates , the winner has a margin of 20 % of the votes polled . if 1000 people change their mind and vote for the loser , the loser would have won by a margin of 20 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 10000 , b ) 5000 , c ) 15000 , d ) 20000 , e ) 6000
Rationale: winner - looser 60 % - 40 % if 1000 people change their mind and vote for the loser : winner - looser 40 % - 60 % thus 1,000 people compose 20 % of all voters , which means that the total number of votes is 5,000 . answer : b
Answer: b
Python program:
a = 20 / 100
b = 1000 / a
Problem: there are 600 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 243 , b ) 265 , c ) 375 , d ) 390 , e ) 400
Rationale: in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 600 . hence 3 x + 5 x = 600 solve for x 8 x = 600 x = 75 number of boys 3 x = 3 × 75 = 225 number of girls 5 x = 5 × 75 = 375 c
Answer: c
Python program:
a = 600 / 5
b = a * 3
Problem: 8 is 2 % of a , and 2 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 16 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 8
Rationale: "2 a / 100 = 8 a = 400 8 b / 100 = 2 b = 25 c = b / a = 25 / 400 = 1 / 16 the answer is a ."
Answer: a
Python program:
a = 2 / 8
b = a * 100
c = 8 / 2
d = c * 100
e = b / d
Problem: a certain psychologist charges $ 30 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 400 , what is the total charge to a patient who receives only 3 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 252
Rationale: "let the charge for first hour = x + 30 then charge for each additional hour = x x + 30 + 4 x = 400 = > 5 x = 370 = > x = 74 total charge for patient for 3 hours of therapy = x + 30 + 2 x = 3 x + 30 = 252 $ answer e"
Answer: e
Python program:
a = 400 - 30
b = a / 5
c = b * 3
d = c + 30
Problem: in a race , the speeds of a and b are in the ratio 3 : 4 . a takes 30 minutes more than b to reach the destination . the time taken by a to reach the destination is ?
Options: a ) 1 hr , b ) 2 hr , c ) 1.5 hr , d ) 2.5 hr , e ) 3 hr
Rationale: explanation : ratio of speeds = 3 : 4 distance remaining constant , the ratio of time taken = 4 : 3 a takes 0.5 hours more than bhence time taken by a = 4 × 0.5 = 2 hour answer : b
Answer: b
Python program:
a = 3 * 30
b = 30 + a 
c = b / const_60
Problem: by selling an article at rs . 800 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 640 , d ) s . 480 , e ) s . 489
Rationale: sp = 800 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / ( 100 + 25 ) ] = 800 * [ 100 / 125 ] = rs . 640 answer : c
Answer: c
Python program:
a = 800 * 100
b = 100 + 25 
c = a / b
Problem: kanul spent $ 500 in buying raw materials , $ 400 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 1010 , b ) $ 1025 , c ) $ 1125 , d ) $ 1100 , e ) $ 1000
Rationale: "let the total amount be x then , ( 100 - 10 ) % of x = 500 + 400 90 % of x = 900 90 x / 100 = 9000 / 9 x = $ 1000 answer is e"
Answer: e
Python program:
a = 500 + 400 
b = 10 / 100
c = 1 - b
d = a / c
Problem: the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 44 , what is the value of x ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the areas are ( x + 4 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 4 and 2 x - 5 . if we add the two perimeters : 4 ( x + 4 ) + 4 ( 2 x - 5 ) = 44 12 x = 48 x = 4 the answer is b ."
Answer: b
Python program:
a = 8 / 2
b = 4 * a
c = b - 8
d = 44 - c
e = d / 8
Problem: what is the probability of getting exactly three heads on five flips of a fair coin ?
Options: a ) 1 / 32 , b ) 3 / 32 , c ) 1 / 4 , d ) 5 / 16 , e ) 1 / 2
Rationale: "5 flips of a fair coin to get = hhhtt = no . of ways this can be achieved = 5 ! / 3 ! x 2 ! = 10 probability to get any of the above 10 arrangements ( hhhtt ) = ( 1 / 2 ) ^ 5 = 1 / 32 total probability = 1 / 32 x 10 = 5 / 16 answer : d"
Answer: d
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: simple interest on a certain sum of money for 4 years at 10 % per annum is half the compound interest on rs . 3000 for 3 years at 12 % per annum . the sum placed on simple interest is
Options: a ) rs . 3000 , b ) rs . 607.39 , c ) rs . 1214.78 , d ) rs . 1518.48 , e ) none
Rationale: "solution c . i . = rs [ 3000 x ( 1 + 12 / 100 ) 3 - 3000 ] rs . ( 3000 x 112 / 100 x 112 / 100 x 112 / 100 - 3000 ) = rs . 1214.78 . sum = rs . [ 607.39 x 100 / 4 x 10 ] = rs . 1518.48 . answer d"
Answer: d
Python program:
a = 3000 * 12
b = a / 100
c = 3000 * 12
d = c / 100
e = 3000 + d 
f = e * 12
g = f / 100
h = b + g 
i = h / 3
j = i / 4
k = j * 100
l = k / 10
Problem: in a certain lottery , the probability that a number between 14 and 20 , inclusive , is drawn is 1 / 6 . if the probability that a number 14 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 3 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 14 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 14 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 6 = 1 p ( set 2 ) = 1 / 2 answer ( c )"
Answer: c
Python program:
a = 14 / 3
b = 14 + a 
c = 2 / 6
d = b - c
Problem: x is the product of each integer from 1 to 50 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 0 , b ) 5 , c ) 6 , d ) 10 , e ) 12
Rationale: x = 1 * 2 * 3 * 4 * 5 * . . . . . . * 49 * 50 = 50 ! y = 100 ^ k 100 = 10 ^ 2 = 2 ^ 2 * 5 ^ 2 on prime factorization of x , power of 5 will always be greater than power of 2 concept : in every factorial value ( x ! ) , on prime factorization , the power of bigger prime number > the power of smaller prime number also , power of any prime number in any factorial can be calculated by following understanding power of prime x in n ! = [ n / x ] + [ n / x ^ 2 ] + [ n / x ^ 3 ] + [ n / x ^ 4 ] + . . . and so on where , [ x ] = greatest integer less than or equal to x and the explanation of terms is as follows [ n / x ] = no . of integers that are multiple of x from 1 to n [ n / x ^ 2 ] = no . of integers that are multiple of x ^ 2 from 1 to n whose first power has been counted in previous step and second is being counted at this step [ n / x ^ 3 ] = no . of integers that are multiple of x ^ 3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step and so on . . . . . where [ n / x ] is greatest integer value of ( n / x ) less than or equal to ( n / x ) i . e . [ 100 / 3 ] = [ 33.33 ] = 33 i . e . [ 100 / 9 ] = [ 11.11 ] = 11 etc . power of 5 in x = [ 50 / 5 ] + [ 50 / 5 ^ 2 ] + [ 50 / 5 ^ 3 ] . . . = 10 + 2 + 0 = 12 power of 2 in x = [ 50 / 2 ] + [ 50 / 2 ^ 2 ] + [ 50 / 2 ^ 3 ] . . . = 25 + 12 + 6 + 3 + 1 = 47 i . e . x = 50 ! = 2 ^ 47 * 5 ^ 12 * . . . = 10 ^ 12 * . . . = 100 ^ 6 * . . . i . e . x is divisible by a 6 th power of 100 at the most i . e . y = 100 ^ k = 100 ^ 6 i . e . k = 6 answer : option c
Answer: c
Python program:
a = 50 / 10
b = a + 1
Problem: in a can , there is a mixture of milk and water in the ratio 3 : 7 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 7 . find the capacity of the can ?
Options: a ) 16.6 , b ) 44 , c ) 27 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 3 / 10 ( t - 8 ) after adding milk , quantity of milk in the mixture = 4 / 11 t . 4 t / 11 - 8 = 3 / 10 ( t - 8 ) 37 t = 880 - 264 = > t = 16.6 . answer : a"
Answer: a
Python program:
a = 4 / 7
b = a * 7
c = b - 3
d = 8 / c
e = 7 * d
f = 4 / 7
g = f * 7
h = g - 3
i = 8 / h
j = e + i 
k = j + 8
Problem: dawson and henry are in a relay race . dawson runs the first leg of the course in 38 seconds . henry runs the second leg of the course in 7 seconds . what was the average time they took to run a leg of the course ?
Options: a ) 20.5 , b ) 21.5 , c ) 22.5 , d ) 23.5 , e ) 24.5
Rationale: ( 38 seconds + 7 seconds ) / 2 = 22.5 seconds correct option is : c
Answer: c
Python program:
a = 38 + 7 
b = a / 2
Problem: if 1500 is increased by 20 % , and then reduced by y % , yielding 1080 , what is y ?
Options: a ) 20 % , b ) 40 % , c ) 60 % , d ) 80 % , e ) 100 %
Rationale: soln : - 1,500 * 1.2 = 1,800 . 1,800 ( 1 - y / 100 ) = 1,080 - - > ( 1 - y / 100 ) = 0.6 - - > y = 40 % . answer : b
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = 1500 * b
d = 1080 / c
e = 1 - d
f = e * 100
Problem: if a is thrice as fast as b and together can do a work in 24 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 32 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 24 = 3 + 1 / 3 x = 4 / 3 x = 1 / 24 x = 24 * 4 / 3 = 32 answer : d"
Answer: d
Python program:
a = 24 * 4
b = 3 / a
c = 1/(b)
Problem: the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit u on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft
Rationale: "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer u is 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b"
Answer: b
Python program:
a = 12 / 2
b = 1 / 2
c = a - b
Problem: find the product of the local value and absolute value of 4 in 20468 ?
Options: a ) 1000 , b ) 1200 , c ) 1340 , d ) 1450 , e ) 1600
Rationale: "local value of 4 = 4 x 100 = 400 place value of 4 = 4 there fore = 4 x 400 = 1600 e"
Answer: e
Python program:
a = 4 * 1000
b = a * 4
Problem: a train 500 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 28 , c ) 49 , d ) 64 , e ) 21
Rationale: "s = ( 500 + 300 ) / 45 = 800 / 45 * 18 / 5 = 64 answer : d"
Answer: d
Python program:
a = 500 + 300 
b = a / 1000
c = 45 / 3600
d = b / c
Problem: a and b invests rs . 3000 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 0 , d ) 9 : 2 , e ) 9 : 1
Rationale: "( 3 * 6 + 6 * 6 ) : ( 4 * 12 ) 54 : 48 = > 9 : 8 answer : b"
Answer: b
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 4000 * e
g = d / f
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 30 , and the difference between the total number of strawberries and the total number of blueberries would increase by 100 . each blue box contains how many blueberries ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "let x be the number of blueberries in each blue box . then there are x + 30 strawberries in each red box . x + ( x + 30 ) = 100 x = 35 the answer is a ."
Answer: a
Python program:
a = 100 - 30
b = a / 2
Problem: there are an average of 117 jellybeans in each of 34 bags of various sizes . after adding another bag , the average number of jellybeans per bag increases by 7 . how many jellybeans are in the new bag ?
Options: a ) 124 , b ) 97 , c ) 117 , d ) 229 , e ) 362
Rationale: total jellybeans in 34 bags = 34 * 117 = 3978 total jellybeans in 35 bags = 35 * 124 = 4340 number of jellybeans in new bag = 3978 - 4340 = 362 jellybeans answer is e
Answer: e
Python program:
a = 34 + 1 
b = 7 * a
c = 117 + b
Problem: a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 89 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 800 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 175 + 89 33 x / 100 = 264 x = 800 answer is c"
Answer: c
Python program:
a = 175 + 89 
b = 33 / 100
c = a / b
Problem: a solution of 90 litres contains milk and water in the ratio 7 : x . if 10 litres of water is added to the solution , the ratio becomes 3 : 2 , find the value of x ?
Options: a ) 2 , b ) 1.5 , c ) 3.5 , d ) 2.5 , e ) 3
Rationale: exp . total new quantity = original sol + water = 90 + 10 = 100 new ratio = 3 : 2 , new quantity of milk = 3 / 5 * 100 = 60 lit , new quantity of water = 2 / 5 * 100 = 40 lit water present initially = ( 40 - 10 ) = 30 lit ratio = 60 / 30 = 7 / x there for x = 3.5 answer : c
Answer: c
Python program:
a = 90 * 7
b = a / 10
c = 3 / 2
d = b / c
e = d - 10
f = 90 / 10
g = e / f
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 240 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 6 = 240 ) 100 % - - - - - > 600 ( 100 * 6 = 600 ) answer : option a"
Answer: a
Python program:
a = 100 * 240
b = 100 - 70
c = 70 - b
d = a / c
Problem: in covering a distance of 42 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7 kmph , e ) 7.8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 42 / x - 42 / 2 x = 3 6 x = 42 x = 7 km / hr . answer : option d"
Answer: d
Python program:
a = 42 / 2
b = 42 - a
c = 1 + 2 
d = b / c
Problem: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 96 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 81 , b ) 84 , c ) 85 , d ) 88 , e ) 90
Rationale: let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 96 or 1 / 7 t + 1 t = 96 therefore t = 96 * 7 / 8 = 84 b
Answer: b
Python program:
a = 96 * 2
b = 60 / 100
c = 96 * b
d = a - c
e = 60 / 100
f = e + 1 
g = d / f
Problem: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability t , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , t = 9 provide the desired outcome , making the answer e ."
Answer: e
Python program:
a = 2 + 4 
b = 2 + a 
c = b + 12 
d = 2 / c
e = 2 + 4 
f = 2 + e 
g = 2 + 4 
h = 2 + g 
i = h + 12 
j = f / i
k = d + j 
l = 2 + 4 
m = 2 + l 
n = m + 12 
o = 2 / n
p = 2 + 4 
q = 2 + p 
r = 2 + 4 
s = 2 + r 
t = s + 12 
u = q / t
v = o * u
w = k - v
Problem: evaluate : 86 x 863 - 86 x 237
Options: a ) 45823 , b ) 53836 , c ) 44824 , d ) 66524 , e ) none of them
Rationale: "86 x 863 + 986 x 237 = 986 x ( 863 - 237 ) = 86 x 626 = 53836 . answer is b"
Answer: b
Python program:
a = 863 * 86
b = a * 237
c = 86 - b
Problem: a man complete a journey in 40 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 30 km / hr . find the total journey in km .
Options: a ) 960 km , b ) 224 km , c ) 230 km , d ) 232 km , e ) 234 km
Rationale: "0.5 x / 20 + 0.5 x / 30 = 40 - - > x / 20 + x / 30 = 80 - - > 5 x = 60 x 80 - - > x = ( 60 x 80 ) / 5 = 960 km . answer : a"
Answer: a
Python program:
a = 20 * 30
b = a * 40
c = 20 + 30 
d = b / c
e = 2 * d