euclaise/mathqa_programs huggingface dataset:
Problem: a certain league has two divisions . the respective divisions had 11 and 13 teams qualify for the playoffs . each division held its own double - elimination tournament - - where a team is eliminated from the tournament upon losing two games - - in order to determine its champion . the 4 division champions then played in a single - elimination tournament - - where a team is eliminated upon losing one game - - in order to determine the overall league champion . assuming that there were no ties and no forfeits , what is the maximum number of games that could have been played in order to determine the overall league champion ?
Options: a ) 41 , b ) 42 , c ) 45 , d ) 47 , e ) 49
Rationale: overall , there can be 47 minuses . tus , it is d .
Answer: d
Python program:
a = 13 * 2
b = a - 1
c = 11 * 2
d = c - 1
e = b + d
Problem: if the ratio of a to b is 5 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 5 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 4 : 15 answer b"
Answer: b
Python program:
a = 5 * 1
b = 3 * 5
c = a / b
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 100 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 100 / 50 = 30 minutes to print 100 pages ( answer e )"
Answer: e
Python program:
a = 4 * 2
b = a + 4 
c = 100 * b
d = c / 40
Problem: what does the hexa number e 78 in radix 7 .
Options: a ) 12455 , b ) 14153 , c ) 14256 , d ) 13541 , e ) 14541
Rationale: conversion of hexa decimal to decimal ( e 78 ) = ( 8 * 16 ^ 0 ) + ( 7 * 16 ^ 1 ) + ( 14 * 16 ^ 2 ) = 8 + 112 + 3584 = 3704 conversion of decimal to radix 7 3704 / 7 : reminder : 1 and dividend : 529 529 / 7 : reminder : 4 and dividend : 75 75 / 7 : reminder : 5 and dividend : 10 10 / 7 : reminder : 3 and dividend : 1 1 / 7 : reminder 1 then finally result is : 13541 answer : d
Answer: d
Python program:
a = 78 * 7
b = 10 + 3 
c = 100 * 10
d = b * c
e = a + d 
f = 4 + 1 
g = e - f
Problem: rs . 1170 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) rs . 720 , b ) rs . 920 , c ) rs . 537 , d ) rs . 540 , e ) rs . 637
Rationale: a + b + c = 1170 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1170 = rs . 540 answer : d
Answer: d
Python program:
a = 4 + 2 
b = a + 3 
c = 1170 / b
d = 4 * c
Problem: how much is 55 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 2 , d ) 12 , e ) 99
Rationale: "( 55 / 100 ) * 40 – ( 4 / 5 ) * 25 22 - 20 = 2 answer : c"
Answer: c
Python program:
a = 55 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: find large number from below question the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 16 as quotient and the 15 as remainder
Options: a ) 1209 , b ) 1615 , c ) 1245 , d ) 1300 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 16 x + 15 15 x = 1500 x = 100 large number = 100 + 1515 = 1615 answer : b"
Answer: b
Python program:
a = 1515 - 15
b = 16 - 1
c = a / b
d = c * 16
Problem: the price of a t . v . set worth rs . 60000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 22678 , b ) 59000 , c ) 26788 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 60000 - 1000 ) = rs . 59000 answer : b"
Answer: b
Python program:
a = 60000 - 1000
Problem: p and q can complete a work in 15 days and 10 days respectively . they started the work together and then q left after 2 days . p alone completed the remaining work . the work was finished in - - - days .
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "explanation : work done by p in 1 day = 1 / 15 work done by q in 1 day = 1 / 10 work done by p and q in 1 day = 1 / 15 + 1 / 10 = 1 / 6 work done by p and q in 2 days = 2 × ( 1 / 6 ) = 1 / 3 remaining work = 1 – 1 / 3 = 2 / 3 time taken by p to complete the remaining work 2 / 3 = ( 2 / 3 ) / ( 1 / 15 ) = 10 days total time taken = 2 + 10 = 12 days answer : option a"
Answer: a
Python program:
a = 2 / 15
b = 1 - a
c = 1/(15)
d = 1/(10)
e = c + d 
f = b / e
g = 2 + f
Problem: a rectangular grass field is 65 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1971 , c ) 9676 , d ) 1679 , e ) 1250
Rationale: "area = ( l + b + 2 d ) 2 d = ( 65 + 55 + 2.5 * 2 ) 2 * 2.5 = > 625 625 * 2 = rs . 1250 answer : e"
Answer: e
Python program:
a = 2 * 5
b = 65 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 10 , e ) 20
Rationale: "3 % sugar solution means that currently there are 1.5 liters of sugar and this amount must be 5 % of a reduced final amount ( 50 - x ) 1.5 = 0.05 * ( 50 - x ) 0.05 x = 1 x = 20 answer e"
Answer: e
Python program:
a = 50 / 100
b = a * 5
c = 50 - b
Problem: the mall charges 40 cents for the first hour of parking and $ 3 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 2 per hour . if mr . park parked his car in the mall for 7 hours and 30 minutes , how much is he going to pay ?
Options: a ) $ 6.8 , b ) $ 12 . , c ) $ 13 . , d ) $ 14.5 . , e ) $ 15 .
Rationale: "0.40 + 2 * 2 + 1 * 2 + 0.40 = $ 6.8 answer : $ 6.8"
Answer: a
Python program:
a = 3 * 3
b = 7 - 4
c = 40 / 100
d = b + c 
e = d * 2
f = a + e 
g = 40 / 100
h = f + g
Problem: david spends $ 350 buying his favorite dolls . if he buys only small lemonhead dolls , which are $ 2 cheaper than the large lemonhead dolls , he could buy 20 more dolls than if he were to buy only large lemonhead dolls . how much does a large lemonhead doll cost ?
Options: a ) $ 5 , b ) $ 7 , c ) $ 6 , d ) $ 8 , e ) $ 9
Rationale: if large doll costs $ 5 , then he can buy 350 / 5 = 70 large dolls and 350 / 3 = 116 small dolls . difference is more than 20 . discard . if large doll costs $ 7 , then he can buy 350 / 7 = 50 large dolls and 350 / 5 = 70 small dolls . difference is 20 , which is we wanted . answer b .
Answer: b
Python program:
a = 350 / 10
b = 20 - 2
c = b + 10 
d = a - c
Problem: ratio of ages of 3 persons is 4 : 7 : 9 , 8 years ago , the sum of their ages was 56 . find their present ages
Options: a ) 16 , 35,36 , b ) 12 , 28,36 , c ) 16 , 28,27 , d ) 16 , 28,36 , e ) none of these
Rationale: explanation : let the present ages are 4 x , 7 x , 9 x . = > ( 4 x - 8 ) + ( 7 x - 8 ) + ( 9 x - 8 ) = 56 = > 20 x = 80 = > x = 4 so their present ages are : 16 , 28,36 answer : option d
Answer: d
Python program:
a = 56 + 8 
b = a + 8 
c = b + 8 
d = 4 + 7 
e = d + 9 
f = c / e
g = f * 3
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 12,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 100,000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Python program:
a = 2 + 3 
b = a * 1000
c = b * 12
d = c / 2
Problem: if 12 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "this question is asking how many power of 3 exists in 12 ! easiest way is to identify factor of three 12 - > 4 * 3 = > 1 power of 3 9 - > 3 * 3 = > 2 power of 3 6 - > 2 * 3 = > 1 power of 3 3 - > 1 * 3 = > 1 power of 3 total equal 5 answer : c"
Answer: c
Python program:
a = 12 / 3
b = 12 / 3
c = 3 / b
d = a + c
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 13 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 6 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: ad = ( a + 1 ) ( d + 1 ) - 13 0 = a + d - 12 a + d = 12 a = d ( as they are twin brothers ) a = d = 6 b is the answer
Answer: b
Python program:
a = 13 - 1
b = a / 2
Problem: a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 350 bolts ?
Options: a ) 84 , b ) 72 , c ) 120 , d ) 144 , e ) 180
Rationale: old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 350 bolts 350 * 6 / 25 = 84 mins ans a
Answer: a
Python program:
a = 100 / const_60
b = 150 / const_60
c = a + b 
d = 350 / c
Problem: what is the minimum possible range in scores of the 3 test - takers ? 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 18 , 26 and 32 .
Options: a ) 26 , b ) 32 , c ) 18 , d ) 20 , e ) 30
Rationale: i simply looked at the 3 different possible scores for each individual test : 18 , 32,26 we have to find the minimum range : 32 - 18 = 14 32 - 26 = 6 26 - 18 = 8 the find the minimum range , you have to make the set of the 5 scores as small as possible . which means that 4 of the 5 scores of each individual person is zero . 6 * 5 = 30 answer : e
Answer: e
Python program:
a = 32 - 26
b = a * 5
Problem: a leak in the bottom of a tank can empty the full tank in 8 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 8640 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 8 - 1 / 12 ) = 1 / 24 . work done by the inlet in 1 min . = ( 1 / 24 × 1 / 60 ) = 1 / 1440 . volume of 1 / 1440 part = 6 litres . therefore , volume of whole = ( 1440 × 6 ) ‹ = › 8640 litres . answer d"
Answer: d
Python program:
a = 12 * const_60
b = 6 * a
c = 12 * const_60
d = 8 * const_60
e = c / d
f = e - 1
g = b / f
Problem: how many hours in one year ?
Options: a ) 365 , b ) 52 , c ) 1024 , d ) 8760 , e ) no one knows
Rationale: the day has 24 hours , and the year contains 365 days . so the hours exist in one year is the multiplication of 24 by 365 . so the answer = 365 * 24 = 8760 hours so the correct answer is d
Answer: d
Python program:
a = 3600 / 10
b = 10 / 2
c = a + b 
d = 4 * 3
e = d * 2
f = c * e
Problem: if k is a non - negative integer and 15 ^ k is a divisor of 759,325 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 37 , d ) 118 , e ) 513
Rationale: "at first we should understand whether 759325 divisible by 15 . 15 is equal to 3 * 5 so 759325 should be divisible on these integers 759325 is divisible by 5 because of last digit 5 but not divisible by 3 because sum of its digits does n ' t divisible by 3 : 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 does n ' t divisible by 3 so 759325 can be divisible by 15 ^ k only if k = 0 and 15 ^ k = 1 so 3 ^ k - k ^ 3 = 1 - 0 = 1 answer is b"
Answer: b
Python program:
a = 1 - 1
b = 3 ** a
c = 1 - 1
d = c ** 3
e = b - d
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land once on heads and twice tails ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 5
Rationale: "must be once on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 answer : d"
Answer: d
Python program:
a = 2 ** 3
b = 1 / a
Problem: what is the smallest integer that is multiple of 7 , 9 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 1260 , e ) 1420
Rationale: "correct answer : d it is the lcm of 7 , 9 and 20 which is 1260"
Answer: d
Python program:
a = 20 / 3
b = math.floor(a)
c = b + 1
Problem: if a man lost 4 % by selling oranges at the rate of 36 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 1 , b ) 8 , c ) 9 , d ) 24 , e ) 3
Rationale: "96 % - - - - 36 144 % - - - - ? 96 / 144 * 36 = 24 answer : d"
Answer: d
Python program:
a = 100 - 4
b = a * 36
c = 100 + 44 
d = b / c
Problem: the fisherman sale , all of the prices of the fishes sold were different . if the price of a radio sold at the fisherman sale was both the 4 th highest price and the 13 th lowest price among the prices of the fishes sold , how many fishes were sold at the fisherman sale ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 41 , e ) 16
Rationale: 3 + 12 + 1 = 16 answer : e
Answer: e
Python program:
a = 4 + 13 
b = a - 1
Problem: in a school of 600 students , 45 % wear blue shirts , 23 % wear red shirts , 15 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 102 , b ) 112 , c ) 122 , d ) 132 , e ) 142
Rationale: "45 + 23 + 15 = 83 % 100 – 83 = 17 % 600 * 17 / 100 = 102 the answer is a ."
Answer: a
Python program:
a = 45 / 100
b = a * 600
c = 23 / 100
d = c * 600
e = b + d 
f = 15 / 100
g = f * 600
h = e + g 
i = 600 - h
Problem: the average of the marks of 10 students in a class is 80 . if the marks of each student are doubled , find the new average ?
Options: a ) 80 , b ) 120 , c ) 160 , d ) 270 , e ) 110
Rationale: "sum of the marks for the 10 students = 10 * 80 = 800 . the marks of each student are doubled , the sum also will be doubled . the new sum = 800 * 2 = 1600 . so , the new average = 1600 / 10 = 160 . answer : c"
Answer: c
Python program:
a = 80 * 2
Problem: in a forest 250 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 250 tagged deers comprise 10 % of total # of deers - - > total # of deers = 250 * 10 = 2,500 . answer : e"
Answer: e
Python program:
a = 50 * 5
Problem: the area of a sector of a circle of radius 5 cm formed by an arc of length 5.5 cm is ?
Options: a ) 13.78 , b ) 13.67 , c ) 13.75 , d ) 13.98 , e ) 13.28
Rationale: "( 5 * 5.5 ) / 2 = 13.75 answer : c"
Answer: c
Python program:
a = 1 / 2
b = 5 * 5
c = a * b
Problem: jane makes toy bears . when she works with an assistant , she makes 60 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 70 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 70 % a"
Answer: a
Python program:
a = 100 - 60
b = a - 10
c = 10 / b
d = c * 100
Problem: there were totally 100 men . 83 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: 100 - ( 100 - 83 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 17 - 25 - 15 - 30 = 100 - 87 = 13 answer : c
Answer: c
Python program:
a = 100 - 83
b = 100 - 75
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 70
g = e + f 
h = 100 - g
Problem: a 450 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 600 , b ) 525 , c ) 360 , d ) 370 , e ) 380
Rationale: "speed = 450 / 18 = 25 m / sec . let the length of the platform be x meters . then , ( x + 450 ) / 39 = 25 = > x = 975 m . l = 975 - 450 = 525 answer : option b"
Answer: b
Python program:
a = speed * (
b = a - 39
Problem: the distance between west - town to east - town is 15 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 , e ) 15 .
Rationale: "by end of 1 st min : distance covered by 1 st bird is 4 km and 2 nd is 1 km . total distance = 5 km . by end of 2 nd min : distance covered by 1 st bird is 8 km and 2 nd is 2 km . total distance = 10 km . by end of 3 rd min : distance covered by 1 st bird is 12 km and 2 nd is 3 km . total distance = 15 km . so , meeting point is 12 kms from west - town ( from where 1 st bird started ) hence , answer will be d ."
Answer: d
Python program:
a = 4 * 4
Problem: if an integer n is to be chosen at random from the integers 1 to 94 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 59 / 94
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 47 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 47 + 12 ) / 94 = 59 / 94 = 5 / 8 ans is e"
Answer: e
Python program:
a = 94 / 2
b = 94 / 8
c = a + b 
d = c / 94
Problem: what is x if x + 2 y = 10 and y = 1 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: x = 10 - 2 y x = 10 - 2 . x = 8 answer : b
Answer: b
Python program:
a = 2 * 1
b = 10 - a
Problem: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 50 ?
Options: a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 50 / 2 = 25 answer is b"
Answer: b
Python program:
a = 50 / 2
Problem: set j consists of 15 consecutive even numbers . if the smallest term in the set is - 10 , what is the range of the positive integers in set j ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: "since there are only 15 integers , another approach is the just list all 15 . we get : - 10 , - 8 , - 6 , - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 range of positive integers = 18 - 2 = 16 answer : d"
Answer: d
Python program:
a = negate + ( 
b = 15 - 1
c = b * 2
d = a - c
Problem: a number is selected at random from the first 40 natural numbers . what is the probability that the number is a multiple of either 2 or 21 ?
Options: a ) 21 / 40 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Rationale: "number of multiples of 2 from 1 through 40 = 40 / 2 = 20 number of multiples of 21 from 1 through 40 = 40 / 21 = 1 number of multiples of 2 and 21 both from 1 through 40 = number of multiples of 21 * 2 ( = 42 ) = 0 total favourable cases = 20 + 1 - 0 = 21 probability = 21 / 40 answer : option a"
Answer: a
Python program:
a = 40 / 2
b = math.floor(a)
c = 40 / 21
d = b + c 
e = d / 40
Problem: if a , b , c and d are positive integers less than 4 , and 4 ^ a + 3 ^ b + 2 ^ c + 1 ^ d = 78 then what is the value of b / c ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 1 / 2 , e ) 1 / 3
Rationale: since a , b and c are positive integers less than 4 we have the following possibilities : 4 ^ a = 416 , or 64 3 ^ b = 39 , or 27 2 ^ c = 24 , or 8 trial and error gives us quite quick the solution of 4 ^ a = 64 3 ^ b = 9 2 ^ c = 4 64 + 9 + 4 = 77 i . e . c = 2 and b = 2 - - - - > b / c = 1 / 1 = 1 the correct answer is c
Answer: c
Python program:
a = 2 / 2
Problem: on a school â € ™ s annual day sweets were to be equally distributed amongst 112 children . but on that particular day , 32 children were absent . thus the remaining children got 6 extra sweets . how many sweets was each child originally supposed to get ?
Options: a ) 28 , b ) 27 , c ) 11 , d ) 15 , e ) 19
Rationale: explanation : let ' k ' be the total number of sweets . given total number of students = 112 if sweets are distributed among 112 children , let number of sweets each student gets = ' l ' = > k / 112 = l . . . . ( 1 ) but on that day students absent = 32 = > remaining = 112 - 32 = 80 then , each student gets ' 6 ' sweets extra . = > k / 80 = l + 6 . . . . ( 2 ) from ( 1 ) k = 112 l substitute in ( 2 ) , we get 112 l = 80 l + 480 32 l = 480 l = 15 therefore , 15 sweets were each student originally supposed to get . answer : d
Answer: d
Python program:
a = 112 - 32
b = a * 6
c = b / 32
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 16 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 6400 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2 / 100 = 10 and ci = 100 ( 1 + 5 / 100 ) 2 − 100 ∴ = 100 × 21 × 21 / 20 × 20 − 100 = 41 / 4 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 16 , the sum = 400 × 16 = 6400 answer d"
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 5 / 100
e = 2 * d
f = 1 + e 
g = c - f
h = 16 / g
Problem: there are two numbers . if 50 % of the first number is added to the second number , then the second number increases to its 5 - fourth . find the ratio of the first number to the second number ?
Options: a ) a ) 1 / 2 , b ) b ) 5 / 8 , c ) c ) 6 , d ) d ) 6 / 7 , e ) e ) 7
Rationale: let the two numbers be x and y . 50 / 100 * x + y = 5 / 4 y = > 1 / 2 x = 1 / 4 y = > x / y = 1 / 2 a )
Answer: a
Python program:
a = 5 / 4
b = a - 1
c = 50 / 100
d = b / c