euclaise/mathqa_programs huggingface dataset:
Problem: the total of 344 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 277 , c ) 278 , d ) 200 , e ) 300
Rationale: explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 344 - x ) . 0.20 * ( x ) + 0.25 ( 344 - x ) = 71 = > x = 300 . . answer : e ) 300
Answer: e
Python program:
a = 344 * 25
b = 71 * 100
c = a - b
d = 25 - 20
e = c / d
Problem: a man buys a cycle for rs . 800 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 680 , d ) s . 520 , e ) s . 700
Rationale: "s . p . = 85 % of rs . 800 = rs . 85 / 100 x 800 = rs . 680 answer : c"
Answer: c
Python program:
a = 100 - 15
b = a * 800
c = b / 100
Problem: a math teacher has 26 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 26 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 26 - 17 = 9 answer ( a )"
Answer: a
Python program:
a = 26 * 8
b = a / 10
c = b / 2
d = c - const_0_25
e = d - const_0_25
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 7 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 1.5
Rationale: "6 * 15 * 3 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 7 + 1 ) = ( √ 8 * 18 ) / 8 = ( √ 144 ) / 8 = 12 / 8 = 1.5 answer is e"
Answer: e
Python program:
a = 6 + 2 
b = 15 + 3 
c = a * b
d = math.sqrt(c)
e = 7 + 1 
f = d / e
Problem: if 3 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 3 z / 5 , e ) z / 9
Rationale: "3 x = 6 y = z x = z / 3 and y = z / 6 x + y = z / 3 + z / 6 = z / 2 answer is a"
Answer: a
Python program:
a = 3 * 100
b = a / 2
c = b - 2
d = 3 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1400 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 20000 , d ) 12197 , e ) 12012
Rationale: "[ 1400 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 20000 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 600 / a
Problem: how many bricks each measuring 21 cm x 10 cm x 8 cm , will be needed to build a wall 9 m x 5 m x 18.5 m
Options: a ) 4955 , b ) 4899 , c ) 4650 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 900 x 500 x 18.5 ) / ( 21 x 10 x 8 ) = 4955 answer : a"
Answer: a
Python program:
a = 9 * 5
b = a * 18
c = 21 * 10
d = c * 8
e = d / 100
f = e / 100
g = b / f
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 62.8 , c ) 62.1 , d ) 62.9 , e ) 32.5
Rationale: "explanation : cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5 answer : a"
Answer: a
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 5
f = d / e
Problem: during a certain two - week period , 64 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 10 a , b ) 12 a , c ) 14 a , d ) 16 a , e ) 18 a
Rationale: total movies = 100 . comedies = 64 . action + drama = 36 . since there were 5 times as many dramas as action movies , then action + 5 * action = 36 - - > action = a = 6 . comedies = 60 = 10 a . a
Answer: a
Python program:
a = 5 + 1 
b = 64 / a
c = math.floor(b)
Problem: find the greatest 4 digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24 . a . 9974
Options: a ) 388 , b ) 282 , c ) 378 , d ) 292 , e ) 281
Rationale: explanation : since the difference between the divisors and the respective remainders is not constant , back substitution is the convenient method . none of the given numbers is satisfying the condition . answer : e
Answer: e
Python program:
a = 15 * 24
b = 5 * 15
c = a - b
d = c - 4
Problem: p has $ 35 more than what q and r together would have had if both b and c had 1 / 7 of what p has . how much does p have ?
Options: a ) $ 45 , b ) $ 47 , c ) $ 49 , d ) $ 51 , e ) $ 53
Rationale: "p = ( 2 / 7 ) * p + 35 ( 5 / 7 ) * p = 35 p = 49 the answer is c ."
Answer: c
Python program:
a = 1 / 7
b = a * 2
c = 1 - b
d = 35 / c
Problem: a can do a work in 20 days and b in 30 days . if they work on it together for 4 days , then the fraction of the work that is left is :
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3
Rationale: "ans is : b a ' s 1 day ' s work = 1 / 20 b ' s 1 day ' s work = 1 / 30 ( a + b ) ' s 1 day ' s work = ( 1 / 20 + 1 / 30 ) = 1 / 12 ( a + b ) ' s 4 day ' s work = ( 1 / 12 * 4 ) = 1 / 3 therefore , remaining work = ( 1 - 1 / 3 ) = 2 / 3"
Answer: b
Python program:
a = 1 / 20
b = 1 / 30
c = a + b 
d = c * 4
e = 1 - d
Problem: 3 candidates in an election and received 1136 , 7636 and 10628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 54.8 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 7636 + 10628 ) = 19400 so , required percentage = 10628 / 19400 * 100 = 54.8 % c"
Answer: c
Python program:
a = 1136 + 7636 
b = a + 10628 
c = 10628 / b
d = c * 100
Problem: a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 4 a = 2 b = c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
Options: a ) 124 , b ) 297 , c ) 394 , d ) 421 , e ) 842
Rationale: ratio of a : b : c = 1 : 2 : 4 two possible greatest single digit values for c are 8 and 4 if c is 8 , then x = 248 if c is 4 , then x = 124 difference = 248 - 124 = 124 a is the answer
Answer: a
Python program:
a = 4 * 3
b = a * 10
c = b + 4
Problem: if albert ’ s monthly earnings rise by 27 % , he would earn $ 567 . if , instead , his earnings rise by only 26 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 562 , d ) 578 , e ) 693
Rationale: "= 567 / 1.27 ∗ 1.26 = 562 = 562 answer is c"
Answer: c
Python program:
a = 27 / 100
b = 1 + a 
c = 567 / b
d = 26 / 100
e = 1 + d 
f = c * e
Problem: indu gave bindu rs . 1250 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 5 , b ) 2 , c ) 9 , d ) 5 , e ) 1
Rationale: "1250 = d ( 100 / 4 ) 2 d = 2 answer : b"
Answer: b
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 1250 * c
e = d - 1250
f = 4 / 100
g = 1250 * f
h = g * 2
i = e - h
Problem: when n is divided by 24 , the remainder is 4 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 0 , e ) 7
Rationale: "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 4 n = 4 ( 4 ) = 16 , which leaves a remainder of 0 when divided by 8 . answer d"
Answer: d
Python program:
a = 4 - reminder
Problem: tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 3 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 60 , b ) 72 , c ) 84 , d ) 96 , e ) 108
Rationale: "d is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 3 t ) = 8 t = = > t = 2 / 5 = = > 24 minutes to travel double distance , 2 ( 2 + 3 t ) = 8 t = = > 2 = = > 120 minutes difference , 96 minutes d"
Answer: d
Python program:
a = 2 * 2
b = 2 * 3
c = 8 - b
d = a / c
e = 8 - 3
f = 2 / e
g = d - f
h = g * const_60
Problem: 35 - [ 23 - { 15 - x } ] = 12 × 2 ÷ 1 / 2
Options: a ) 34 , b ) 32 , c ) 17 , d ) 27 , e ) 28
Rationale: explanation : 35 - [ 23 - { 19 - ( 15 - x ) } ] = 12 × 2 × 2 = 48 = > 35 - 23 + ( 19 - 15 + x ) = 48 = > 12 + 4 + x = 48 = > x = 48 - ( 4 + 12 ) = 32 answer : option b
Answer: b
Python program:
a = 35 - 3
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.2 km ?
Options: a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "c 300 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1200 ) = 300 m answer is c"
Answer: c
Python program:
a = 1 * 2
b = 18 * a
c = b / 48
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 20 . what is the value of f ( 6 ) ?
Options: a ) 9 , b ) 0 , c ) 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 20 then f ( 5 ) = 20 - 5 = 15 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 15 - 6 = 9 . answer : a . questions on funtions to practice :"
Answer: a
Python program:
a = 1 + 4 
b = 20 - a
c = b - 6
Problem: a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?
Options: a ) 22 hours , b ) 21 hours , c ) 23 hours , d ) 20 hours , e ) 28 hours
Rationale: "d 20 hours | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 50 40 d = 20 rs = 50 – 40 = 10 t = 20 / 10 = 2 hours"
Answer: d
Python program:
a = 1 / 2
b = a * 40
c = 50 - 40
d = b / c
e = 1 / 2
f = d - e
Problem: what is the smallest 5 digit number that is divisible by 15 , 32 , 45 , and 54 ?
Options: a ) 11260 , b ) 11860 , c ) 12360 , d ) 12960 , e ) 13560
Rationale: 15 = 3 * 5 32 = 2 ^ 5 45 = 3 ^ 2 * 5 54 = 2 * 3 ^ 3 lcm = 2 ^ 5 * 3 ^ 3 * 5 = 4320 the smallest five - digit number that is a multiple of 4320 is 3 * 4320 = 12,960 the answer is d .
Answer: d
Python program:
a = 100 * 100
b = math.lcm(5, 15)
c = math.lcm(b, 32)
d = math.lcm(c, 45)
e = math.lcm(d, 54)
f = 100 * 100
g = math.lcm(5, 15)
h = math.lcm(g, 32)
i = math.lcm(h, 45)
j = math.lcm(i, 54)
k = e - reminder
l = a + k
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 45 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 , b ) 88 , c ) 77 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 45 km with stoppages . stoppage time = time take to travel ( 60 - 45 ) km i . e 15 km at 60 km / hr . stoppage time = 15 / 60 hrs = 15 min . answer : a"
Answer: a
Python program:
a = 1 * const_60
b = 45 / 60
c = b * const_60
d = a - c
Problem: a rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 14 cms
b ) 21 cms
c ) 42 cms
d ) none of these
e ) can not be determined
Rationale: solution largest size of the tile . h . c . f of 378 cm and 525 cm = 21 cms . answer b
Answer: b
Python program:
a = 100 * 3
b = a / 3
c = b / 3
d = c / 3
e = d / 2
f = e * 3
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel five times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 5 and w = 5 s then we have 1 / ( 5 * s ) + 1 / s = 1 / 5 < = > 6 / ( 5 * s ) = 1 / 5 < = > s = 6 ans : b"
Answer: b
Python program:
a = 2 * 4
b = 1/(a)
c = b + 1 
d = c * 3
e = 2 * 4
f = d * e
Problem: 3 bodies x , y and z start moving around a circular track of length 960 m from the same point simultaneously in the same direction at speeds of 12 m / s , 20 m / s and 36 m / s respectively . when will they meet for the first time after they started moving ?
Options: a ) 240 seconds , b ) 120 seconds , c ) 60 seconds , d ) 180 seconds , e ) 100 seconds
Rationale: if they all meet after t seconds , it means they covered the distances 12 t , 20 t , and 36 t respectively . since they all arrive to the same spot , it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track , which is 960 m . so , 8 t , 16 t , and 24 t must all be multiples of 960 . 8 t multiple of 960 means t multiple of 120 . the smallest t with this property is 120 and is on the list of answers . answer b .
Answer: b
Python program:
a = 20 - 12
b = 960 / a
Problem: a part of certain sum of money is invested at 10 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 2 , b ) 4 : 8 , c ) 4 : 3 , d ) 4 : 0 , e ) 6 : 5
Rationale: "12 : 10 = 6 : 5 answer : e"
Answer: e
Python program:
a = 12 / 100
b = a * 10
Problem: kelly and chris are moving into a new city . both of them love books and thus packed several boxes with books . if chris packed 60 % of the total number of boxes , what was the ratio of the number of boxes kelly packed to the number of boxes chris packed ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 4 , e ) 1 / 4
Rationale: the ratio of the number of boxes kelly packed to the number of boxes chris packed = 40 / 60 = 2 / 3 answer : b
Answer: b
Python program:
a = 100 - 60
b = a / 60
Problem: there are 6 more women than there are men on a local co - ed softball team . if there are a total of 24 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 9 / 15 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 6 w + m = 24 m + 6 + m = 24 2 m = 18 m = 9 w = 15 ratio : 9 : 15 ans : b"
Answer: b
Python program:
a = 24 - 6
b = 1 + 1 
c = a / b
d = 24 - 6
e = 1 + 1 
f = d / e
g = f + 6 
h = c / g
Problem: two cars start at the same time from opposite ends of a highway that is 60 miles long . one car is riding at 13 mph and the second car is riding at 17 mph . how long after they begin will they meet ?
Options: a ) 0.75 , b ) 1 , c ) 1.25 , d ) 1.5 , e ) 2.0
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 17 + 13 = 30 mph total distance to be covered = 60 miles . time taken would be : 60 miles / 30 mph = 2.0 hours e is the answer ."
Answer: e
Python program:
a = 13 + 17 
b = 60 / a
Problem: ( x + 6 ) is a factor in x ^ 2 - mx - 42 . what is the value of m ?
Options: a ) 2 , b ) 2.2 , c ) 1 , d ) 4 , e ) 5
Rationale: i solved the second degree equation and found it like this : x ^ 2 - mx - 42 = 0 ( x - 7 ) ( x + 6 ) = 0 x = 7 or x = - 6 substituting both values for x in the equation we find : x ^ 2 - mx - 42 = > ( - 6 ) ^ 2 - m ( - 6 ) = 42 = > 36 + 6 m = 42 = > 6 m = 42 - 36 = 6 = > m = 1 and with 7 , using a similar process we end up with : ( 7 ) ^ 2 - m ( 7 ) = 42 - 7 m = 42 - 49 = - 7 m = - 1 ao , ans c
Answer: c
Python program:
a = 42 / 6
b = a - 6
Problem: local kennel has cats and dogs in the ratio of 6 : 8 . if there are 10 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 30 , b ) 35 , c ) 45 , d ) 50 , e ) 40
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 6 : 8 or cats 6 dogs 8 we can write number of cats as 6 x and number of dogs as 8 x and we know that 8 x - 6 x = 10 ( therefore 2 x = 10 = > x = 5 ) then # of dogs = 8 x 5 = 40 answer is e"
Answer: e
Python program:
a = 10 * 8
Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 144 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 ( too high ) 18 * 8 = 144 the length is 18 meters . the answer is b ."
Answer: b
Python program:
a = 144 / 10
b = a / 2
c = const_0_33 + b 
d = const_0_25 + c 
e = 10 + d
Problem: add 15 % of 25 and 12 % of 45 .
Options: a ) 9.2 , b ) 10.5 , c ) 11.5 , d ) 12.3 , e ) 15
Rationale: 15 % of 25 + 12 % of 45 25 * 15 / 100 + 45 * 12 / 100 3.8 + 5.4 = 9.2 answer a
Answer: a
Python program:
a = 15 * 25
b = a / 100
c = 12 * 45
d = c / 100
e = b + d
Problem: there are cats got together and decided to kill the mice of 999919 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009
Rationale: "999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 9 ) * ( 1000 - 9 ) = ( 1009 ) * ( 991 ) given that number of cats is less than number if mice . so number of cats is 991 and number of mice were 1009 answer c"
Answer: c
Python program:
a = 100 * 10
b = 3 + 2 
c = a + b 
d = 999919 / c
Problem: a crate measures 4 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "to fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet now since the limiting number in the base is 8 feet ; therefore a cylinder { we can visualise that a cylinder ' s width is its diameter } can only fit inside the crate if it is 8 feet or less . therefore the radius of the cylinder will become diameter 2 = = = > 8 / 2 = 4 diameter answer : d"
Answer: d
Python program:
a = 8 * 12
b = a * 4
c = b / 12
d = c / 8
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 45 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm
Rationale: "we have 45 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 22.5 and continues . so we have 45 , 22.5 , 11.25 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 45 / 1 - ( 1 / 2 ) = 90 equilateral triangle perimeter is 3 a = 3 * 90 = 270 . so option d ."
Answer: d
Python program:
a = triangle_perimeter + (
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 120 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,080
Rationale: "10 / 100 p = 120 > > p = 120 * 100 / 10 = 1200 1200 - 120 = 1080 answer : e"
Answer: e
Python program:
a = 100 / 10
b = 120 * a
c = b - 120
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 6 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 27 , b ) 22 , c ) 24 , d ) 26 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : a"
Answer: a
Python program:
a = 3 ** 3
b = a - 1
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 3 years ?
Options: a ) 14300 , b ) 17280 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 3 = 17280 b )"
Answer: b
Python program:
a = 10000 * 20
b = a / 100
c = b * 3
d = 10000 + c
Problem: a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 18 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : b"
Answer: b
Python program:
a = 2 + 1 
b = 6 * a
c = b / 2
d = c * 2
Problem: how many even multiples of 15 are there between 149 and 301 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "150 = 10 * 15 300 = 20 * 15 the even multiples are 15 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Python program:
a = 301 - 149
b = 15 * 2
c = a / b
d = c + 1
Problem: what least number should be added to 1101 , so that the sum is completely divisible by 24
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1056 / 24 ) gives remainder 21 21 + 3 = 24 , so we need to add 3 . answer : option d"
Answer: d
Python program:
a = 24 - reminder
Problem: a and b can do a work in 6 days , b and c in 2 days and c and a in 8 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 12 / 24 , b ) 48 / 63 , c ) 45 / 56 , d ) 48 / 19 , e ) 28 / 12
Rationale: "one day work of a and b = 1 / 6 one day work of b and c = 1 / 2 one day work of c and a = 1 / 8 2 ( a + b + c ) = 1 / 6 + 1 / 2 + 1 / 8 2 ( a + b + c ) = 19 / 24 ( a + b + c ) = 19 / 48 number of days required = 48 / 19 days . answer : d"
Answer: d
Python program:
a = 1/(6)
b = 1/(2)
c = a + b 
d = 1/(8)
e = c + d 
f = e / 6
g = 1 / f
Problem: working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 10 % , but hillary becomes distracted and her rate decreases by 10 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 5 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 5 + ( 1 / 10 * 1 / 5 ) = 2 / 9 per hour hillary = 1 / 3 - ( 1 / 10 * 1 / 3 ) = 3 / 10 per hour together they work 2 / 9 + 3 / 10 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Python program:
a = 1 / 5
b = 10 / 100
c = b + 1 
d = a * c
e = 1 / 3
f = 10 / 100
g = e * f
h = d + g 
i = 1/(h)
Problem: how many 3 digit no ' s are between 100 - 500 , where sum of two digit is 3 rd ?
Options: a ) 24 , b ) 54 , c ) 60 , d ) 84 , e ) 94
Rationale: total permutations possible = 18 + 16 + 14 + 12 = 60 answer : c
Answer: c
Python program:
a = 4 + 4 
b = 500 / 100
c = a - b
d = c + 1 
e = 4 + 4 
f = d + e 
g = 500 / 100
h = f * g
i = 3 - 1
j = h / i
k = j * 2