euclaise/mathqa_programs huggingface dataset:
Problem: youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 12 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 10 , d ) 15 , e ) 18
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 720 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 7200 - - - - > 40 x = 720 - - > x = 18 . option e"
Answer: e
Python program:
a = 12 * 3
b = a / 2
Problem: buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of buffalos ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 ans : 3 buffalos answer : c"
Answer: c
Python program:
a = 4 - 2
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1400 . the difference between the profit shares of a and c is ?
Options: a ) 288 , b ) 560 , c ) 155 , d ) 600 , e ) 441
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1400 = > 5 parts out of 15 parts is rs . 1400 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1400 ) = rs . 560 answer : b"
Answer: b
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 1400
Problem: of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 1 / 3 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?
Options: a ) 7 / 15 , b ) 1 / 5 , c ) 4 / 15 , d ) 1 / 3 , e ) 2 / 5
Rationale: tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 3 ( 1 / 5 ( x / 2 ) ) = 1 / 30 ( x ) - - - > non major = x / 2 - 1 / 30 ( x ) = 7 / 15 ( x ) hence 7 / 15 a
Answer: a
Python program:
a = 1 / 2
b = 3 * 10
c = 1 / b
d = a - c
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 72 . what is sum of the numbers ?
Options: a ) 42 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 72 = > 12 x = 72 = > x = 72 / 12 = 6 sum of the numbers = 3 x + 4 x = 7 x = 7 x 6 = 42 answer : option a"
Answer: a
Python program:
a = 3 * 4
b = a * 100
c = 4 * 72
d = b + c
Problem: a sum of money deposited at c . i . amounts to rs . 9000 in 10 years and to rs . 9990 in 11 years . find the rate percent ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 13 %
Rationale: "9000 - - - 990 100 - - - ? = > 11 % answer : c"
Answer: c
Python program:
a = 9990 - 9000
b = a / 9000
c = b * 100
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 250 more than the correct answer . find the number .
Options: a ) 125 , b ) 280 , c ) 384 , d ) 480 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 250 25 * x / 48 = 250 x = 480 answer d"
Answer: d
Python program:
a = 250 * 16
b = a * 6
c = 5 * 16
d = 5 * 6
e = c - d
f = b / e
Problem: if 2 ^ 5 , 3 ^ 3 , and 11 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 132 , b ) 39 , c ) 42 , d ) 65 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 11 rest of them must be in w so w = 11 * 3 * 4 = 132 smash a"
Answer: a
Python program:
a = 2 ** 2
b = a * 3
c = 11 / 2
d = b * c
e = d * 2
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 60 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 132 ° f , b ) 140 ° f , c ) 148 ° f , d ) 156 ° f , e ) 164 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 60 ) / 5 + 32 = 140 ° f the answer is b ."
Answer: b
Python program:
a = 212 - 32
b = a / 100
c = b * 60
d = c + 32
Problem: xy = 1 then what is ( 4 ^ ( x + y ) ^ 2 ) / ( 4 ^ ( x - y ) ^ 2 )
Options: a ) 2 , b ) 4 , c ) 8 , d ) 256 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 4 ^ 4 = 256 answer d"
Answer: d
Python program:
a = 4 * 1
b = 4 ** a
Problem: on my sister ' s birthday , she was 154 cm in height , having grown 10 % since the year before . how tall was she the previous year ?
Options: a ) 150 cm , b ) 140 cm , c ) 142 cm , d ) 148 cm , e ) 146 cm
Rationale: "let the previous year ' s height be x . 1.1 x = 154 x = 140 the answer is b ."
Answer: b
Python program:
a = 154 * 10
b = a / 100
c = 154 - b
Problem: an empty wooden vessel weighs 16 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 3 / 5 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 7 / 15
Rationale: "an empty wooden vessel weighs 16 % of its total weight when filled with paint : vessel = 0.16 ( vessel + paint ) ; 16 v = v + p ( so the weight of completely filled vessel is 16 v ) p = 15 v ( so the weight of the paint when the vessels is completely filled is 15 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 16 v ; p ' = 7 v ( so the weight of the paint when the vessels is partially filled is 7 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 7 v / 15 v = 7 / 15 . answer : e ."
Answer: e
Python program:
a = 16 / 2
b = a - 1
c = 16 - 1
d = b / c
Problem: in what time will a train 120 meters long cross an electric pole , if its speed is 184 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.3 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 184 * ( 5 / 18 ) = 51 m / sec time = distance / speed = 120 / 51 = 2.3 seconds option d"
Answer: d
Python program:
a = 184 * const_0_2778
b = 120 / a
Problem: if x is a positive integer with fewer than 3 digits , what is the probability r that x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability r that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Python program:
a = 100 / 4
b = a * 2
c = 100 / 5
d = c * 2
e = b + d 
f = e - 4
g = 100 - 1
h = f / g
Problem: the length of rectangle is thrice its breadth and its perimeter is 96 m , find the area of the rectangle ?
Options: a ) 432 , b ) 288 , c ) 376 , d ) 397 , e ) 592
Rationale: "2 ( 3 x + x ) = 96 l = 36 b = 12 lb = 36 * 12 = 432 answer : a"
Answer: a
Python program:
a = 3 * 2
b = 1 * 2
c = a + b 
d = 96 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g 
i = 96 / h
j = e * i
Problem: there are 12 pieces of radioactive metal a that look identical . 11 of the pieces give the same radiation count when measured , the 12 th piece is a counterfeit and gives a different radiation level , which may be more or less than the other 11 . we are given a radiation scale , which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different , which set has the higher level of radiation . what is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: first of all if you are down to just 3 pieces and you know that if the offending piece is less or more active , then it takes exactly 1 measurement to find out the offending piece . so you know you have to reduce the problem to three . now when you are down to either a or b after measurement 1 , you need the next measurement to ( a ) reduce the problem set to 3 and ( b ) to know whether anser is more or less . now you can not compare a group of 4 to 4 , as in the best case it will only reduce the problem to 4 elements which is not good enough . if you have to choose a set of 3 to compare , you can not pick any 3 on the same side from the same set ( a or b ) because if you do this , a quick check will show you that in every choice there is a case where you can only get down to 4 elements . eg . if you weighed { 1 , 23 } v / s { 5 , 910 } and they were equal you ' re problem would only reduce to { 46 , 78 } the easiest way to solve this then is to compare 3 to 3 , and make sure each side has elements from both ab such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only . which is why the sets { 1 , 59 } and { 2 , 67 } or { a , b , c } { a , b , b } . the extra element from c is just taken to make the problem symmetric so to say , we have 8 elements and we make it 9 , to compose 3 sets of 3 each . = b
Answer: b
Python program:
a = 12 - 11
b = a + 2
Problem: in a bag containing 5 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initiallyin the bag wereequally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 4 , d ) 5 / 6 , e ) 6 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Python program:
a = 1 / 2
b = 1 + 5 
c = 1 / b
d = 1 + 5 
e = 5 / d
f = c + e 
g = a + f 
h = 1 + g 
i = 1 + 5 
j = h / i
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 5 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 60 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 5 books / month = 60 books a year total number of books = 60 cs"
Answer: c
Python program:
a = 5 * 12
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 44 now , the son age 5 years back was
Options: a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99
Rationale: "let the son ' s present age be x years . then , ( 44 - x ) = x x = 22 . son ' s age 5 years back = ( 22 - 5 ) = 17 years answer : b"
Answer: b
Python program:
a = 44 / 2
b = a - 5
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 16 weavers in 16 days ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 96 , e ) 128
Rationale: "1 weaver can weave 1 mat in 4 days . 16 weavers can weave 16 mats in 4 days . 16 weavers can weave 64 mats in 16 days . the answer is c ."
Answer: c
Python program:
a = 4 * 4
b = 4 / a
c = 16 * b
d = 16 * c
Problem: a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 65 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 20 , c ) 32 , d ) 40 , e ) 48
Rationale: lets say x ounces of p is mixed with q . = > 65 - x ounces of q is present in the mixture ( as the total = 65 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 65 - x ) = 15 = > x = 25 = > 65 - 25 = 40 ounces of q is present in the mixture . answer is d .
Answer: d
Python program:
a = 20 / 100
b = a * 65
c = 15 - b
d = 25 / 100
e = 20 / 100
f = d - e
g = c / f
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability q that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Python program:
a = 3 + 2 
b = 4 * 4
c = a / b
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 330 m long platform ?
Options: a ) 37 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min
Rationale: "e 45 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 330 ) / 36 * 5 / 18 = 45 min ."
Answer: e
Python program:
a = const_0_2778 * 36
b = a * 12
c = 330 + b 
d = const_0_2778 * 36
e = c / d
Problem: if 3 < x < 6 < y < 10 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 < x < 6 < y < 10 ; 3 < x y < 10 3 + y < x + 10 y - x < 7 . positive integer difference is 6 ( for example y = 9.5 and x = 3.5 ) answer : d ."
Answer: d
Python program:
a = 10 - 3
b = a - 1
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 14 ) ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) - 2
Rationale: the expression considers all even numbers between 10 and - 14 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , and - 14 now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 = 42 - 44 = - 2 hence the correct answer choice is e .
Answer: e
Python program:
a = 6 - 8
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 1000 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 22500 , d ) rs . 16108 , e ) rs . 16011
Rationale: "explanation : manager ' s monthly salary rs . ( 2500 * 21 - 1500 * 20 ) = rs . 22500 . answer : c"
Answer: c
Python program:
a = 1500 + 1000 
b = 20 + 1 
c = a * b
d = 1500 * 20
e = c - d
Problem: stacy and heather are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 15 mile , b ) 14 mile , c ) 11 mile , d ) 10 mile , e ) 12.5 mile
Rationale: "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 30 - 2.4 = 17.6 time taken = distance / speed = 27.6 / 11 = 2.5 hrs heather will cover = 5 * 2.5 = 12.5 miles . answer e"
Answer: e
Python program:
a = 1 + 5 
b = a / const_60
c = 24 * b
d = 30 - c
e = 1 + 5 
f = 5 + e 
g = d / f
h = g * 5
Problem: for a race a distance of 224 meters can be covered by p in 8 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 672 m , b ) 6738 m , c ) 634 m , d ) 671 m , e ) 636 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 8 = 28 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 24 seconds therefore , distance covered by p in that time = 28 m / s x 24 seconds = 672 metres answer : a"
Answer: a
Python program:
a = 8 * speed
b = 224 - a
Problem: in a single throw of a die , what is the probability of getting a number greater than 4 ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: s = { 1,2 , 3,4 , 5,6 } e = { 5,6 } probability = 2 / 6 = 1 / 3 answer is a
Answer: a
Python program:
a = 4 + 2 
b = 2 / a
Problem: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 6 year . find what was the original average age of the class ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 4
Rationale: let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 34 â ‡ ’ 40 y + 384 = 34 y + 408 â ‡ ’ 6 y = 24 â ˆ ´ y = 4 e
Answer: e
Python program:
a = 40 - 6
b = 12 * a
c = 12 * 32
d = b - c
e = d / 6
Problem: a car takes 6 hours to cover a distance of 180 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 10 kmph , b ) 20 kmph , c ) 15 kmph , d ) 30 kmph , e ) 25 kmph
Rationale: "time = 6 distance = 280 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 180 / 9 = 20 kmph b )"
Answer: b
Python program:
a = 6 * 3
b = a / 2
c = 180 / b
Problem: 5 n + 2 > 12 and 7 n - 19 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 2 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: 5 n + 2 > 12 5 n > 10 n > 2 7 n - 19 < 44 7 n < 63 n < 9 so n must be between 2 and 9 2 < n < 9 correct answer c
Answer: c
Python program:
a = 2 * 10
b = 44 + 19 
c = b / 7
d = a + c
Problem: the price of a consumer good increased by pp % during 20122012 and decreased by 1212 % during 20132013 . if no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010 % higher than the price at the beginning of 20122012 , what was the value of pp ?
Options: a ) − 2 % , b ) 2 % , c ) 22 % , d ) 25 % , e ) can not be determined
Rationale: as per question = > price was simple 10 percent greater hence x [ 1 + 10 / 100 ] must be the final price . equating the two we get = > x [ 110 / 100 ] = x [ 1 + p / 100 ] [ 88 / 100 ] = > 44 p + 4400 = 5500 = > 44 p = 1100 = > p = 1100 / 44 = > 100 / 4 = > 25 . so p must be 25 answer : d
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = 12 / 100
d = 1 - c
e = b / d
f = e - 1
g = 100 * f
Problem: two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer .
Options: a ) 4 , b ) 6 , c ) 12 , d ) 24 , e ) 30
Rationale: "assume the integers to be x and y , where x < y given x / y = 1 / 4 - ( i ) or y = 4 x and x + 6 / y = 1 / 2 - ( ii ) or y = 2 x + 12 substituting the value of y from ( i ) , 4 x = 2 x + 12 x = 6 hence y = 4 * 6 = 24 answer d"
Answer: d
Python program:
a = 2 * 6
b = 4 - 2
c = a / b
d = c * 4
Problem: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 12 days , working 16 hours a day , the number of men required is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 16 : 8 : : 12 : x = > 12 x 16 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 12 x 16 ) = > x = 5 answer : b"
Answer: b
Python program:
a = 12 * 8
b = a * 10
c = b / 16
d = c / 12
Problem: find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm .
Options: a ) 952 cm ^ 2
b ) 957 cm ^ 2
c ) 954 cm ^ 2
d ) 958 cm ^ 2
e ) none of them
Rationale: volume = ∏ r 2 h = ( ( 22 / 7 ) x ( 7 / 2 ) x ( 7 / 2 ) x 40 ) = 1540 cm ^ 3 . . curved surface area = 2 ∏ rh = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x 40 ) = 880 cm ^ 2 . total surface area = 2 ∏ rh + 2 ∏ r 2 = 2 ∏ r ( h + r ) = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x ( 40 + 3.5 ) ) cm 2 = 957 cm ^ 2 answer is b
Answer: b
Python program:
a = 7 / 2
b = a ** 2
c = b * math.pi
d = c * 2
e = 7 * math.pi
f = e * 40
g = d + f
Problem: how many positive integers less than 5,000 are evenly divisible by neither 15 nor 23 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4521 answer c ."
Answer: c
Python program:
a = 4 + 15 
b = a - 1
c = math.factorial(b)
d = math.factorial(15)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 4 years at 20 % per annum is rs . 50 of money ?
Options: a ) 1000 , b ) 6000 , c ) 5000 , d ) 8000 , e ) 1900
Rationale: "p = 50 ( 100 / 20 ) 4 = > p = 1000 answer : a"
Answer: a
Python program:
a = 20 * 4
b = 50 / a
c = b * 100
d = 20 * 4
e = c * d
Problem: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 52,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 26,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 52,000 i . e . rs . 26,000 answer : b"
Answer: b
Python program:
a = 4 * 2
b = 2 + 3 
c = b * 2
d = a * c
e = d * 100
f = 2 + 3 
g = f * 100
h = g * 100
i = e + h 
j = 2 + 3 
k = j * 2
l = k / 2
m = 4 * 3
n = l / m
o = i * n