euclaise/mathqa_programs huggingface dataset:
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.2 – 6.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 6.2 * = 4 ( the greatest positive even integer less than or equal to 6.2 is 4 ) . hence , 6.2 – 6.2 * = 6.2 - 4 = 2.2 answer : d ."
Answer: d
Python program:
a = math.floor(6, 2)
b = a - 1
c = 6 - 2
Problem: 108 . triangle a ’ s base is 20 % greater than the base of triangle b , and a ’ s height is 20 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 0.25 % less
b ) 1 % less
c ) equal to each other
d ) 1 % more
e ) 9 % more
Rationale: wish the question specified that we are talking about corresponding height . base of a = 21 / 20 * base of b height of a = 19 / 20 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 21 / 20 * 19 / 20 * area of b = 399 / 400 * area of b area of a is 0.25 % less than the area of b . answer ( a )
Answer: a
Python program:
a = 100 * 100
b = 100 + 20 
c = 100 - 20
d = b * c
e = a - d
f = 100 / e
Problem: a circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter . if the smaller rim makes x revolutions per second , how many revolutions per second does the larger rim makes in terms of x ?
Options: a ) 4 x / 5
b ) 75 x
c ) 48 x
d ) 24 x
e ) x / 75
Rationale: let ' s try the explanation . we have two wheels . one with 28 pi and the other one with 35 pi . they have the same speed . in the smaller wheel it ' s 28 pi * x , which must be equal to the speed of the bigger one ( 35 pi * a number of revolutions ) . they are asking that number of revolutions ( but in minutes , which makes the question even harder ) . anyway , we have 28 pi * x = 35 pi * a . ( 28 pi * x ) / ( 35 pi ) . = 4 x / 5 . ans : a
Answer: a
Python program:
a = 2 * 3
b = a * 10
c = 28 / 35
d = b * c
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 11 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 11 = > m = 33 answer b"
Answer: b
Python program:
a = 2 / 3
b = 11 / a
c = b - 11
Problem: walking with 5 / 4 of my usual speed , i miss the bus by 5 minutes . what is my usual time ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 22 , e ) 24
Rationale: "speed ratio = 1 : 5 / 4 = 4 : 5 time ratio = 5 : 4 1 - - - - - - - - 5 4 - - - - - - - - - ? è 20 answer : c"
Answer: c
Python program:
a = 4 / 5
b = 3 / 0
c = b * 4
Problem: if n = 2 ^ 0.25 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 16 , e ) 80 / 3
Rationale: "25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 4 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 4 b = 16 answer : d"
Answer: d
Python program:
a = math.log(16)
b = 2 ** 0
c = math.log(b)
d = a / c
Problem: in how many q ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ?
Options: a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 1296
Rationale: total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value q = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d
Answer: d
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = a / b
d = math.factorial(2)
e = c / d
f = math.factorial(4)
g = math.factorial(2)
h = f / g
i = math.factorial(2)
j = h / i
k = e * j
l = 2 * 3
m = l - 1
n = 2 * 3
o = n - 1
p = m * o
q = k * p
Problem: the distance between delhi and mathura is 150 kms . a starts from delhi with a speed of 25 kmph at 5 a . m . for mathura and b starts from mathura with a speed of 40 kmph at 6 p . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 77 , c ) 8 , d ) 10 , e ) 12
Rationale: d = 150 – 25 = 125 rs = 40 + 25 = 65 t = 125 / 65 = 2 hours 6 a . m . + 2 = 8 a . m . . answer : c
Answer: c
Python program:
a = 25 + 40 
b = 150 / a
c = 6 + b
Problem: water boils at 212 ° f or 100 ° c and melts at 32 ° f or 0 ° c . if the temperature of the particular day is 35 ° c , it is equal to
Options: a ) 50 ° f , b ) 76 ° f , c ) 95 ° f , d ) 110 ° f , e ) 120 ° f
Rationale: let f and c denotes the temparature in fahrenheit anid celcsius respectively . then , ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) , if c = 35 , then f = 95 . c
Answer: c
Python program:
a = 35 / 100
b = 212 - 32
c = a * b
d = c + 32
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 96 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 96 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 96 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 96 r 2 = ( 96 * 2 ) / 3 = 64 = > r = 8 rate = 8 % answer : a"
Answer: a
Python program:
a = math.sqrt(96)
Problem: a monkey ascends a greased pole 26 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options: a ) 50 th minute , b ) 41 st minute , c ) 45 th minute , d ) 42 nd minute , e ) 49 th minute
Rationale: "the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 24 meters . i mean this will continue for first 24 * 2 = 48 mins . he would have reached 24 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 48 + 1 = 49 mins . so , asnwer will be e"
Answer: e
Python program:
a = 4 * 2
b = a * 2
c = b + 1
Problem: a man distributed rs . 100 equally among his friends . if there had been 5 more friends , each would have received one rupee less . how many friends had he ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: firstly we have 20 friends and money wiill be distribute each of them 5 rupee then 5 more friends it means total no frnd = 25 each recv 4 rupee which means all recv 1 less rupee answer : b
Answer: b
Python program:
a = 100 / 5
b = a + 5
Problem: a , b and c can do a work in 6 , 9 and 12 days respectively doing the work together and get a payment of rs . 1800 . what is b ’ s share ?
Options: a ) rs . 245.8 , b ) rs . 653.8 , c ) rs . 300 , d ) rs . 400 , e ) rs . 748.5
Rationale: "wc = 1 / 6 : 1 / 9 : 1 / 12 = > 6 : 4 : 3 4 / 13 * 1800 = 653.8 answer : b"
Answer: b
Python program:
a = 1/(9)
b = 1/(12)
c = 1/(6)
d = 1/(9)
e = c + d 
f = b + e 
g = a / f
h = 1800 * g
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 6270 . what was his original salary ?
Options: a ) 6000 , b ) 2999 , c ) 1000 , d ) 2651 , e ) 1971
Rationale: x * ( 110 / 100 ) * ( 95 / 100 ) = 6270 x * ( 11 / 10 ) * ( 1 / 100 ) = 66 x = 6000 answer : a
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = 5 / 100
d = 1 - c
e = b * d
f = 6270 / e
Problem: the true discount on a bill of rs . 270 is rs . 45 . the banker ' s discount is
Options: a ) 54 , b ) 55 , c ) 56 , d ) 57 , e ) none of these
Rationale: solution p . w = rs . ( 270 - 45 ) = rs . 225 s . i on rs . 270 = rs . ( 45 / 225 x 270 ) = rs . 54 . answer a
Answer: a
Python program:
a = 270 - 45
b = 45 / a
c = b * 270
Problem: a part of certain sum of money is invested at 9 % per annum and the rest at 21 % 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 ) 7 : 3 , d ) 4 : 0 , e ) 4 : 9
Rationale: "21 : 9 = 7 : 3 answer : c"
Answer: c
Python program:
a = 21 / 100
b = a * 9
Problem: a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter made instead a sandbox which was twice as long , twice as wide and twice as high as the original , what would the capacity be of the new larger sandbox ?
Options: a ) 20
b ) 40
c ) 60
d ) 80
e ) 100
Rationale: explanation : when all the dimensions of a three dimensional object are in fact doubled , then the capacity increases by a factor of 2 x 2 x 2 = 2 ^ 3 = 8 . thus the capacity of the new sandbox is 8 x 10 = 80 cubic feet . answer : option d
Answer: d
Python program:
a = 2 ** 3
b = a * 10
Problem: a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 4 / 9 , d ) 5 / 7 , e ) 4 / 11
Rationale: "2 / 3 - - - - 12 ? - - - - - 8 = = > 4 / 9 c"
Answer: c
Python program:
a = 2 / 3
b = a * 8
c = b / 12
Problem: the toll for crossing a certain bridge is $ 0.75 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 12.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : a"
Answer: a
Python program:
a = 0 - 75
b = a * 2
c = 12 / 0
d = c * 2
e = d / 10
f = e * 2
g = 0 - 75
h = g * 2
i = 12 / 0
j = i * 2
k = f + j
Problem: if 20 % of a is the same as 25 % of b , then a : b is :
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 7 , e ) 5 : 7
Rationale: "expl : 20 % of a i = 25 % of b = 20 a / 100 = 25 b / 100 = 5 / 4 = 5 : 4 answer : c"
Answer: c
Python program:
a = 25 / 100
b = 20 / 100
c = a / b
Problem: 4 , 7 , 16 , 43 , 124 , ( . . . )
Options: a ) 22 , b ) 367 , c ) 27 , d ) 32 , e ) 25
Rationale: "explanation : 4 4 × 3 - 5 = 7 7 × 3 - 5 = 16 16 × 3 - 5 = 43 43 × 3 - 5 = 124 124 × 3 - 5 = 367 answer : option b"
Answer: b
Python program:
a = negate - (
Problem: a man buys an article for $ 100 . and sells it for $ 120 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 120 gain = $ 20 gain % = 20 / 100 * 100 = 20 % answer is d"
Answer: d
Python program:
a = 100 / 100
b = 120 / a
c = b - 100
Problem: the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is
Options: a ) 45 kg , b ) 50 kg , c ) 53 kg , d ) 55 kg , e ) none of these
Rationale: "solution weight of the teacher = ( 35.4 × 25 - 35 × 24 ) kg = 45 kg . answer a"
Answer: a
Python program:
a = 400 / 1000
b = 35 + a 
c = 24 + 1 
d = b * c
e = 24 * 35
f = d - e
Problem: what percent of 200 is 55 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 27.5 % , e ) 250 %
Rationale: "200 * x / 100 = 55 x = 27.5 ans : d"
Answer: d
Python program:
a = 200 / 55
b = a * 100
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 25 % ?
Options: a ) 600 , b ) 887 , c ) 625 , d ) 654 , e ) 712
Rationale: "cost price = rs . 500 profit = 25 % of 500 = rs . 125 selling price = cost price + profit = 500 + 125 = 625 answer : c"
Answer: c
Python program:
a = 25 / 100
b = 500 * a
c = 500 + b
Problem: if 28 a + 30 b + 31 c = 545 . then a + b + c = ? . a , b , c are natural numbers
Options: a ) 12 , b ) 14 , c ) 8 , d ) 25 , e ) 18
Rationale: have a look on your calender since , we all knw a year consist of 365 days february is d only month which has 28 days 4 months in a year has 30 days and , rest 7 months has 31 days . . so , following d given eq . we can write 28 * 1 + 30 * 10 + 31 * 7 . . hence values of a , b and c are 1 , 10 and 7 respectively . . a + b + c = 18 answer : e
Answer: e
Python program:
a = 545 / 31
Problem: p and q started a business investing rs 75000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 5 : 1 , b ) 17 : 3 , c ) 5 : 6 , d ) 17 : 7 , e ) 3 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 75000 : 15000 = 75 : 15 = 5 : 1 option a"
Answer: a
Python program:
a = 75000 / 15000
Problem: evaluate : 55 - 12 * 3 * 2 = ?
Options: a ) 47 , b ) 52 , c ) 32 , d ) 12 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 55 - 12 * 3 * 2 = 55 - 8 = 47 correct answer a"
Answer: a
Python program:
a = 12 * 2
b = a * 2
c = 55 - b
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 42 ° is ?
Options: a ) 56.8 m 2 , b ) 82.9 m 2 , c ) 52.8 m 2 , d ) 17.9 m 2 , e ) 72.9 m 2
Rationale: "42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c"
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 42 / g
i = f * h
Problem: if 2 x = 4 y = z , what is x - y , in terms of z ?
Options: a ) z / 4 , b ) z / 2 , c ) z , d ) 2 z , e ) 4 z
Rationale: "2 x = 4 y = z i . e . x = z / 2 and y = z / 4 x - y = z / 2 - z / 4 = z / 4 answer : option a"
Answer: a
Python program:
a = 2 * 100
b = a / 2
c = b - 2
d = 2 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: the average weight of a group of boys is 35 kg . after a boy of weight 40 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: let the number off boys in the group originally be x . total weight of the boys = 35 x after the boy weighing 40 kg joins the group , total weight of boys = 35 x + 40 so 35 x + 40 = 36 ( x + 1 ) = > x = 5 . answer : b
Answer: b
Python program:
a = 35 + 1 
b = 40 - a
c = b + 1
Problem: how many 13 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 1234567654321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 9000000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the 13 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 12 th 11 th 10 th , 9 th , 8 th , 7 th , we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 6 th , 5 th , 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 13 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 9000000 ways ) answer : e"
Answer: e
Python program:
a = 13 * 10
b = a * 10
c = b * 10
d = c * 10
Problem: 5216 × 51 = ?
Options: a ) 266015 , b ) 266014 , c ) 266016 , d ) 266116 , e ) 266226
Rationale: "normal way of multiplication may take time . here is one alternative . 5216 × 51 = ( 5216 × 50 ) + 5216 = ( 5216 × 1002 ) + 5216 = 5216002 + 5216 = 260800 + 5216 = 266016 answer is c ."
Answer: c
Python program:
a = 5216 / 51
b = a * 100
Problem: points x , y , and z lie , in that order , on a straight railroad track . the distance from point x to point y is twice the distance from point y to point z . a train traveled from point x to point z without stopping . the train ' s average speed when traveling from point x to point y was 100 miles per hour and the train ' s average speed when traveling from point y to point z was 75 miles per hour . what was the train ' s average speed , in miles per hour , when traveling from point x to point z ?
Options: a ) 90 , b ) 85 , c ) 85.5 , d ) 70 , e ) 90
Rationale: "average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 100 speed y - z = 75 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 100 ) + ( d / 75 ) 3 d / ( 6 d / 300 ) + ( 4 d / 300 ) 3 d / ( 10 d / 300 ) 900 d / 10 d average speed = 90 answer : a"
Answer: a
Python program:
a = 100 / 75
b = 2 / a
c = b + 1 
d = 3 / c
e = d * 75
Problem: if there are 200 questions in a 3 hr examination . among these questions are 20 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 ) 72 min , b ) 62 min , c ) 70 min , d ) 32.72727 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 180 x + 20 * 2 x = 180 x = 180 / 220 x = 0.818182 time taken for type a problem = 20 * 2 * 0.818182 = 32.72727 min answer : d"
Answer: d
Python program:
a = 3 * const_60
b = 200 - 20
c = 2 * 20
d = b + c 
e = a / d
f = 2 * e
g = f * 20
Problem: an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 2 ) will be divisible by 2 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 2 ) to be divisible by 2 either n or n + 2 must be a multiples of 2 . in each following group of numbers : { 1 , 2 , 3 , 4 } , { 5 , 6 , 7 , 8 } , . . . , { 97 , 98 , 99 , 100 } there are exactly 2 numbers out of 4 satisfying the above condition . for example in { 1 , 2 , 3 , 4 } n can be : 2 , or 4 . thus , the overall probability is 2 / 4 = 1 / 2 . answer : c ."
Answer: c
Python program:
a = 100 / 2
b = a / 100
c = b * 2
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 36 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 68 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 36 % is one st . dev , then on either side of m we have 36 / 2 = 18 % . so , 18 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 18 = 68 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 68 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c"
Answer: c
Python program:
a = 100 - 36
b = a / 2
c = 100 - b
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 4 / 5 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 13 / 20 , b ) 11 / 3 , c ) 5 / 13 , d ) 12 / 17 , e ) 17 / 20
Rationale: "let total number of juniors = j total number of seniors = s ( 4 / 5 ) j = ( 1 / 2 ) s = > s = 8 / 5 j total number of students = j + s = ( 13 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 13 / 5 ) j ] = 5 / 13 answer c"
Answer: c
Python program:
a = 5 * 2
b = 5 * 5
c = 2 + b 
d = a / c
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 1 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 3 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 12 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 1 - - > e : s = 4 : 1 = 12 : 3 . thus , l : s = 8 : 3 . answer : b ."
Answer: b
Python program:
a = 4 * 1
b = 1 * 1
c = a / b
d = 1 * 4
e = 2 * 4
f = d / e
g = c / f
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 40 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 41.00 , b ) s . 51.22 , c ) s . 51.219 , d ) s . 41.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 40 * 100 ) / ( 2 * 5 ) = rs . 400 amount = [ 400 * ( 1 + 5 / 100 ) 2 ] = rs . 441 c . i . = ( 441 - 400 ) = rs . 41 answer : a"
Answer: a
Python program:
a = 5 / 100
b = a * 2
c = 40 / b
d = c * 5
e = d / 100
f = 5 / 100
g = f * 2
h = 40 / g
i = e + h 
j = 5 / 100
k = j * 2
l = 40 / k
m = l * 5
n = m / 100
o = 5 / 100
p = o * 2
q = 40 / p
r = n + q 
s = r * 5
t = s / 100
u = i + t 
v = 5 / 100
w = v * 2
x = 40 / w
y = u - x
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 18000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3629 , c ) rs . 3279 , d ) rs . 3629 , e ) rs . 3283
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 18000 = > x = 3600 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3600 . answer : a"
Answer: a
Python program:
a = 4 / 5
b = a * 18000
c = 18000 - b
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 79.36
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.8 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.8 + 8.5 ) = 24.8 point of value of the dive = 24 * 3.2 = 79.36 answer e"
Answer: e
Python program:
a = 7 + 5 
b = a + 8 
c = b * 3
Problem: at the faculty of aerospace engineering , 310 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 430 , b ) 432 , c ) 440 , d ) 442 , e ) 446
Rationale: "310 + 232 - 112 ( since 112 is counted twice ) = 430 a is the answer"
Answer: a
Python program:
a = 112 / 2
b = 310 - a
c = 112 / 2
d = 232 - c
e = b + d
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 12 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 7 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 12 w 19 + 9 x = 12 ( x + 1 ) x = 7 / 3 ratio of gold with copper = 1 : 7 / 3 = 3 : 7 answer is b"
Answer: b
Python program:
a = 12 - 9
b = 19 - 12
c = a / b