euclaise/mathqa_programs huggingface dataset:
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 4 more than the average of 10 , 70 , and what number ?
Options: a ) 28 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 4 = 36 sum of second list = 36 * 3 = 108 therefore the number = 108 - 80 = 28 answer : a"
Answer: a
Python program:
a = 20 + 40 
b = a + 60 
c = 4 * 3
d = c + 10 
e = d + 70 
f = b - e
Problem: what is the least number . which should be added to 221 to make it a perfect square ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 6 , e ) 7
Rationale: "221 + 4 = 225 15 ^ 2 answer : c"
Answer: c
Python program:
a = 12 + 4 
b = a + 2 
c = b / 100
d = 12 + 4 
e = d + 2 
f = e / 100
g = c * f
h = g - 221
Problem: when positive integer n is divided by positive integer j , the remainder is 42 . if n / j = 204.07 , what is value of j ?
Options: a ) 200 , b ) 400 , c ) 800 , d ) 600 , e ) 1200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.07 here 204 is the quotient . given that remainder = 42 so , 204.07 = 204 + 42 / j so , j = 600 answer : d"
Answer: d
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 204 - 7
e = 42 / d
Problem: 8796 x 223 + 8796 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 2658560 , d ) 2716740 , e ) none of them
Rationale: "= 8796 x ( 223 + 77 ) ( by distributive law ) = 8796 x 300 = 2638800 answer is b"
Answer: b
Python program:
a = 223 ** 8796
b = 8796 * a
Problem: an agent , gets a commission of 5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 887 , d ) 250 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 5 % . of x = 12.50 < = > ( 5 / 100 * x ) = 125 / 10 < = > x = 250 . answer : d"
Answer: d
Python program:
a = 5 / 100
b = 12 / 50
Problem: 121 x 5 ^ 4 = ?
Options: a ) 75625 , b ) 68225 , c ) 72325 , d ) 71225 , e ) 72225
Rationale: explanation : 121 × 5 ^ 4 = 121 × ( 10 / 2 ) ^ 4 = ( 121 × 10000 ) / 16 = 7.5625 × 10000 = 75625 answer is a
Answer: a
Python program:
a = 5 ** 4
b = 121 * a
Problem: the number n is h , 284 , where h represents the 10 ' s digit . if n is divisible by 6 , what is the value of h ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: if the number is divisible by 6 , then the sum of the digits must also be divisible by both 3 and 2 . only 1 yields such a number . answer : a
Answer: a
Python program:
a = 6 * 10
b = 6 * 10
c = a / b
Problem: a 360 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 140 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 360 / 9 = 500 / 9 = > x + 360 = 500 = > x = 140 so the length of the train is 140 meters option c"
Answer: c
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 360
Problem: how long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length ?
Options: a ) 22 sec , b ) 20 sec , c ) 15 sec , d ) 23 sec , e ) 16 sec
Rationale: "d = 100 + 245 = 345 m s = 54 * 5 / 18 = 15 t = 345 * 1 / 15 = 23 sec answer : d"
Answer: d
Python program:
a = 100 + 250 
b = 54 * const_0_2778
c = a / b
Problem: the ratio of efficiency of a is to c is 5 : 3 . the ratio of no . of days taken by b is to c is 2 : 3 . a takes 6 days less than c , when a and c completes the work individually . b and c left the work after 2 days . the no of days taken by a to finish the remaining work ?
Options: a ) 4.5 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: a : b : c efficiency 10 : 9 : 6 no of days 9 x : 10 x : 15 x given = > 15 x - 9 x = 6 hence , x = 1 number of days taken by a = 9 and daily work done = 10 number of days taken by b = 10 and daily work done = 9 ( total work = 90 ) number of days taken by c = 15 and daily work done = 6 work done by b and c in initial 2 days = 30 rest work = 60 number of days required by a to finish = 60 / 10 = 6 days answer : c
Answer: c
Python program:
a = 5 - 3
b = 6 / a
c = b * 3
d = 5 - 3
e = 6 / d
f = 5 * e
g = f / 3
h = 2 * g
i = 1 / h
j = 5 - 3
k = 6 / j
l = 5 * k
m = 1 / l
n = i + m 
o = n * 2
p = 1 - o
q = c * p
Problem: a train covers a distance of 16 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 16 / 10 * 60 ) km / hr = ( 96 * 5 / 18 ) m / sec = 80 / 3 m / sec . length of the train = 80 / 3 * 6 = 160 m . answer : c"
Answer: c
Python program:
a = 16 / 10
b = a - 6
c = 16 / b
Problem: a man sitting in a train which is traveling at 70 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 42 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 70 ) kmph = 42 kmph . answer : e"
Answer: e
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 70
Problem: if s = { 8 , 16 , 24 , 32 , 40 , 48 } , what is the product of mean and median of the numbers in s ?
Options: a ) 652 , b ) 589 , c ) 456 , d ) 620 , e ) 784
Rationale: mean = ( 8 + 16 + 24 + 32 + 40 + 48 ) / 6 = 28 median = ( 24 + 32 ) / 2 = 28 product = 28 * 28 = 784 option e
Answer: e
Python program:
a = 16 + 8 
b = a + 24 
c = b + 32 
d = c + 40 
e = d + 48 
f = 2 + 4 
g = e / f
h = 24 + 32 
i = h / 2
j = g * i
Problem: after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.2 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.2 , c ) 4.0 , d ) 6.5 , e ) 8.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.2 x = 3.2 alternate solution : try to backsolve . initial volume = 3.2 after one hour - - > ( 1 / 4 ) 3.2 = 0.8 after two hours - - > ( 1 / 4 ) 0.8 = 0.2 answer : b"
Answer: b
Python program:
a = 0 / 2
b = a / const_0_25
Problem: one fourth of a solution that was 22 % sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.22 + 1 / 4 * x = 1 * 0.35 - - > x = 0.74 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.22 + 25 * x = 100 * 0.35 - - > x = 0.74 . answer : a ."
Answer: a
Python program:
a = 35 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 22 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: if 2994 ã · 14.5 = 171 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 171 in the place of 2994 / 14.5 ] = 171 / 10 = 17.1 answer is a ."
Answer: a
Python program:
a = 14 / 5
b = 171 / a
Problem: when positive integer n is divided by positive integer j , the remainder is 27 . if n / j = 204.09 , what is value of j ?
Options: a ) 300 , b ) 320 , c ) 360 , d ) 410 , e ) 420
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.09 here 204 is the quotient . given that remainder = 27 so , 204.09 = 204 + 27 / j so , j = 300 answer : a"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 204 - 9
e = 27 / d
Problem: there are 840 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 140 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 840 - x x / 2 + 840 - x / 4 = 1 / 3 * ( 840 ) = 280 x = 280 x / 2 = 140 is supposed to be the answer m is missing something correct option a"
Answer: a
Python program:
a = 840 / 3
b = a * 4
c = b - 840
d = c / 2
Problem: p alone can complete a job in 7 days . the work done by q alone in one day is equal to one - sixth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "p ' s rate is 1 / 7 q ' s rate is 1 / 42 the combined rate is 1 / 7 + 1 / 42 = 1 / 6 if they work together , the job will take 6 days . the answer is e ."
Answer: e
Python program:
a = 1 / 7
b = 1 / 7
c = b / 3
d = a + c 
e = 1 / d
Problem: there are 4 members in a family . their average income is rs . 10000 per month . 3 members get rs . 8000 , rs . 15000 , rs . 6000 respectively . therefore what is the income of the fourth member of the family ?
Options: a ) rs . 10000 , b ) rs . 11000 , c ) rs . 12000 , d ) rs . 9000 , e ) rs . 8500
Rationale: explanation total income of 3 members = rs . ( 8000 + 15000 + 6000 ) = rs . 29000 . required income = rs . [ ( 10000 x 4 ) – 29000 ] = rs . ( 40000 – 29000 ) = rs . 11000 . answer b
Answer: b
Python program:
a = 4 * 10000
b = 8000 + 15000 
c = b + 6000 
d = a - c
Problem: if ( 3 / 2 ) x - 3 = 15 what is the value of x ?
Options: a ) - 12 , b ) 12 , c ) - 1 / 12 , d ) 1 / 12 , e ) 3
Rationale: ( 3 / 2 ) x - 3 = 15 = > 3 x - 6 = 30 = > 3 x = 36 = > x = 12 answer : b
Answer: b
Python program:
a = 15 + 3 
b = a * 2
c = b / 3
Problem: a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 3.58 , b ) 3.68 , c ) 3.78 , d ) 3.88 , e ) 3.98
Rationale: "m = 8 s = 1.2 ds = 8 + 1.2 = 9.2 us = 8 - 1.2 = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.68 . answer : b"
Answer: b
Python program:
a = 8 + 1 
b = 8 - 1
c = a * b
d = 8 + 1 
e = 8 - 1
f = d + e 
g = c / f
h = g * 2
Problem: a and b invests rs . 3000 and rs . 8000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 16 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 8 * 12 ) 54 : 96 = > 9 : 16 . answer : c"
Answer: c
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 8000 * e
g = d / f
Problem: a rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 34 , b ) 77 , c ) 36 , d ) 56 , e ) 91
Rationale: "explanation : perimeter of the plot = 2 ( 90 + 50 ) = 280 m no of poles = 280 / 5 = 56 m answer : d"
Answer: d
Python program:
a = 90 + 50 
b = a * 2
c = b / 5
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 9.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 9.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 9.80 - 3.20 = 6.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 6.6 = t ( 5.4 x ) - > t = ( 6.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 6.6 / 5.4 = 9.3 answer c ."
Answer: c
Python program:
a = 9 - 80
b = math.sqrt(2)
c = b - 1
d = 5 + c 
e = a / d
f = e * 5
g = 3 + 20
Problem: how many two - element subsets of { 1,2 , 3,4 } are there that do not contain the pair of elements 2 and 4 ?
Options: a ) one , b ) two , c ) four , d ) five , e ) six
Rationale: "{ 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } , { 3,4 } . or : c 24 − 1 = 5 answer : d ."
Answer: d
Python program:
a = 4 - 4
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 16 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 39 = 19 + 16 + 12 - 4 - 2 x 2 x = 19 + 16 + 12 - 4 - 39 = 43 - 39 = 4 x = 2 a
Answer: a
Python program:
a = 19 + 16 
b = a + 12 
c = b - 4
d = c - 39
e = d / 2
Problem: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle ?
Options: a ) 6
b ) 5
c ) 8
d ) 6
e ) 3
Rationale: let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c
Answer: c
Python program:
a = square_edge_by_area / (
b = a / 2
c = 3 + 4 
d = c / 3
e = b + d
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to z . what is the value of 5.2 – 5.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b ."
Answer: b
Python program:
a = math.floor(5, 2)
b = 5 - 2
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 17,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900
Rationale: "5000 * r * t / 100 = 250 rt = 5 17000 * 5 / 100 = 850 answer is d"
Answer: d
Python program:
a = 2 * 100
b = a * 100
c = 250 * b
d = 2 * 100
e = d * 100
f = e / 4
g = c / f
Problem: 30 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 36 , e ) 10
Rationale: binders books days 30 1400 21 x 1600 20 x / 30 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 36 answer : d
Answer: d
Python program:
a = 1600 / 20
b = 30 * 21
c = 1400 / b
d = a / c
Problem: if the radius of a circle is decreased 30 % , what happens to the area ?
Options: a ) 51 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.7 * old radius so new area = ( 0.7 ) ^ 2 old area = > 0.49 of old area = > 49 % old area ans : a"
Answer: a
Python program:
a = 30 / 100
b = a ** 2
c = b * 100
d = 100 - c
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 1671
Rationale: "5000 * 104 / 100 * 105 / 100 = > 5460 answer : c"
Answer: c
Python program:
a = 100 + 4 
b = 5000 * a
c = b / 100
d = 100 + 5 
e = c * d
f = e / 100
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 410 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 690 , c ) 287 , d ) 771 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 410 = 3690 salary of the new supervisor = 3690 â ˆ ’ 3000 = 690 answer : b"
Answer: b
Python program:
a = 410 * 9
b = 430 * 9
c = b - 870
d = a - c
Problem: if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: 6 + 4 = 10 correct answer is c ) 10
Answer: c
Python program:
a = 4 + 6
Problem: how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an a . p ( arithmetic progression ) with the first term being 103 and the last term being 999 . the common difference of the sequence is 7 . step 2 : compute the number of terms in an a . p , the last term l = a + ( n - 1 ) * d , where ' a ' is the first term , ' n ' is the number of terms of the series and ' d ' is the common difference . therefore , 999 = 103 + ( n - 1 ) * 7 or 999 - 103 = ( n - 1 ) * 7 or 896 = ( n - 1 ) * 7 so , n - 1 = 128 or n = 129 choice e is the correct answer ."
Answer: e
Python program:
a = 100 * 10
b = a - 1
c = 10 + 4 
d = c * 7
e = d + 5 
f = b - e
g = f / 7
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48
Rationale: "3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c ."
Answer: c
Python program:
a = 9 * 2
Problem: if c is 30 % of a and 25 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 120 % , d ) 35 % , e ) 250 %
Rationale: "answer = c 30 a / 100 = 25 b / 100 b = 30 a / 25 = 120 a / 100 = 120 %"
Answer: c
Python program:
a = 30 / 100
b = 25 / 100
c = a / b
d = c * 100
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 24 in two years , at the same percent rate per annum ?
Options: a ) s . 50 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 24 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 24 – 20 ) / 20 ] * 100 = 20 % p . a . let the principal be rs . x time = t = 2 years % rate = 20 % p . a . si = ( prt / 100 ) 20 = ( x * 20 * 2 ) / 100 x = rs . 50 answer : a"
Answer: a
Python program:
a = 24 - 20
b = a * 100
c = b / 2
Problem: the moon revolves around the earth at a speed of approximately 0.9 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 3240 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.9 * 3600 = 3240 kilometers per hour . option c is correct"
Answer: c
Python program:
a = 0 * 9
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a"
Answer: a
Python program:
a = 100 - 80
b = 100 / 60
c = 80 / 80
d = b - c
e = a * d
Problem: the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a ."
Answer: a
Python program:
a = 150 / 5
b = a * 12
c = b / 2
d = c - 150
Problem: divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325
Rationale: "a + b + c = 1300 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1300 = > 325 answer : e"
Answer: e
Python program:
a = 1300 / 3
Problem: a boy is travelling from his home to school at 4 km / hr and reached 7 min late . next day he traveled at 8 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 4 hr t 2 = x / 8 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 4 - x / 8 = 1 / 4 x / 8 = 1 / 4 x = 2 km answer is a"
Answer: a
Python program:
a = 7 / const_60
b = 8 / const_60
c = a + b 
d = 1 / 8
e = c / d
Problem: a , b and c , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ?
Options: a ) $ 1206.60 , b ) $ 1363.63 , c ) $ 1263.63 , d ) $ 1463.53 , e ) $ 1163.03
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2500 = $ 1363.63 hence : b"
Answer: b
Python program:
a = 1/(4)
b = 1/(6)
c = 1/(2)
d = 1/(4)
e = c + d 
f = b + e 
g = a / f
h = 2500 * g
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 5 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 60 , e ) 100
Rationale: orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 5 oz can = 300 oz / 5 oz = 60 answer d , 60 cans
Answer: d
Python program:
a = 6 * 200
b = 200 / 10
c = a / b