euclaise/mathqa_programs huggingface dataset:
Problem: if a large pizza has a radius that is 40 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 40 % , b ) 80 % , c ) 96 % , d ) 112 % , e ) 124 %
Rationale: let the radius of medium pizza be r . then the radius of large pizza is 1.4 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.4 * r ) ^ 2 = 1.96 * pi * r ^ 2 , an increase of 96 % . the answer is c .
Answer: c
Python program:
a = 40 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: if tim had lunch at $ 60.50 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 72.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 60.50 = ( 20 / 100 ) * 60.50 = $ 12.1 total spent 60.50 + 12.1 = $ 72.6 correct answer b"
Answer: b
Python program:
a = 60 * 50
b = a / 100
c = 60 + 50
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 14000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8600 , d ) rs . 9000 , e ) none
Rationale: answer average salary = 8000 + 5000 + 14000 + 7000 + 9000 / 5 = rs . 8600 correct option : c
Answer: c
Python program:
a = 8000 + 5000 
b = a + 14000 
c = b + 7000 
d = c + 9000 
e = 4 + 1 
f = d / e
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 162 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 144
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is in 162 grams of water . 2 x + 16 x = 162 18 x = 162 x = 9 since x is 9 , we know that there are 16 x 9 = 144 grams of oxygen in 162 grams of water . answer e ."
Answer: e
Python program:
a = 2 + 16 
b = 162 / a
c = 2 * b
Problem: a can do a piece of work in 20 days and b can do it in 30 days and c can do it 10 days . they started the work together and a leaves after 2 days and c leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 13 , b ) 16 , c ) 25 , d ) 14 , e ) 15
Rationale: 2 / 20 + x / 30 + 4 / 10 = 1 x = 300 / 20 = 15 answer : e
Answer: e
Python program:
a = 4 - 2
b = 1/(30)
c = 1/(10)
d = b + c 
e = a * d
f = 1/(10)
g = 1/(20)
h = 1/(30)
i = g + h 
j = f + i 
k = j * 2
l = e + k 
m = 1 - l
n = 1/(30)
o = m / n
p = o + 4
Problem: find the least number which when divided by 18,32 , 48,52 leaves remainder 14,28 , 44,48 respectively .
Options: a ) 2845 , b ) 3250 , c ) 3740 , d ) 4150 , e ) 5140
Rationale: "the difference of 18 - 14 = 4 , 32 - 28 = 4 , 48 - 44 = 4 , 52 - 48 = 4 lcm of 18,32 , 48,52 = 3744 required number = 3744 - 4 = 3740 answer is c"
Answer: c
Python program:
a = math.lcm(18, 32)
b = 14 + 28
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Python program:
a = 40 / 100
b = 25 / 100
c = 40 / 100
d = b * c
e = a - d
f = 25 / 100
g = 40 / 100
h = f * g
i = 1 - h
j = e / i
k = j * 100
Problem: if 0.75 : x : : 7 : 8 , then x is equal to :
Options: a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 0.95 , d ) d ) 0.85 , e ) e ) 0.9
Rationale: "( x * 7 ) = ( 0.75 * 8 ) x = 6 / 7 x = 0.85 answer = d"
Answer: d
Python program:
a = 0 * 75
b = a / 7
Problem: tom drives from town r to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between r and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point r to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Python program:
a = 1 + 2 
b = a / 36
c = 2 / 60
d = b - c
e = 1 / d
Problem: of the 3,600 employees of company x , 1 / 3 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 3 are clerical out of 3600 so 1200 are clerical 1200 reduced by 1 / 3 is 1200 * 1 / 3 so it reduced 400 people , so there is 800 clerical people left but since 400 people left , it also reduced from the total of 3600 so there are 3200 people total since 800 clerical left / 3200 people total you get ( a ) 25 %"
Answer: a
Python program:
a = 1 / 3
b = 1 / 3
c = 1 - b
d = a * c
e = 1 / 3
f = 1 / 3
g = 1 - f
h = e * g
i = 1 / 3
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: a and b can do a piece of work in 6 days , b and c in 7 days , c and a in 8 days . how long will c take to do it ?
Options: a ) 12.6 days , b ) 14.4 days , c ) 15.2 days , d ) 16.8 days , e ) 18.2 days
Rationale: "2 c = 1 / 7 + 1 / 8 – 1 / 6 = 20 / 168 = 10 / 84 c = 5 / 84 = > 84 / 5 = 16.8 days the answer is d ."
Answer: d
Python program:
a = 6 * 3
b = 6 * 3
c = b / 8
d = 6 * 3
e = d / 6
f = 6 * 3
g = f / 7
h = e + g 
i = c + h 
j = i / 2
k = 6 * 3
l = k / 6
m = j - l
n = a / m
Problem: two trains are moving in opposite directions with speed of 210 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 48 , c ) 47 , d ) 26 , e ) 24
Rationale: explanation : relative speed = 210 + 90 = 300 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 300 hr = 1 / 150 hr = 3600 / 150 seconds = 24 seconds answer : option e
Answer: e
Python program:
a = 1 + 1 
b = 210 + 90 
c = a / b
d = c * 3600
Problem: pat , kate and mark charged a total of 216 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 120 , d ) 90 , e ) 108
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 216 - total hours charged for , x = 24 . mat charged 6 x - x or 5 x for more hours than kate , or for 120 hours . c is correct"
Answer: c
Python program:
a = 1 + 2 
b = 2 * 3
c = a + b 
d = 216 / c
e = 2 * 3
f = e - 1
g = d * f
Problem: find the principle on a certain sum of money at 5 % per annum for 5 years if the amount being rs . 1120 ?
Options: a ) 896 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 5 ) / 100 ] p = 896 answer : a"
Answer: a
Python program:
a = 5 * 5
b = a / 100
c = 1 + b 
d = 1120 / c
Problem: 10 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
Options: a ) 45 % , b ) 55 % , c ) 65 % , d ) 75 % , e ) 85 %
Rationale: science majors make up 0.4 of the class . 60 % of the class are women and 0.1 * 0.6 = 0.06 of the class are female science majors . then 0.34 of the class are male science majors . 0.4 x = 0.34 x = 0.85 = 85 % the answer is e .
Answer: e
Python program:
a = 60 + 40 
b = 10 * 2
c = a - b
d = c / 100
e = 10 / 2
f = e / 100
g = d + f 
h = g * 100
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 6.5 liters of alcohol and 3.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 6.5 ) / 50 = 8.5 / 50 = 17 % the answer is e ."
Answer: e
Python program:
a = 5 / 100
b = 40 * a
c = b + 6 
d = 6 + 5 
e = 40 + d 
f = c / e
g = f * 100
Problem: the area of a parallelogram is 243 sq m and its altitude is three times the corresponding base . what is the length of the base ?
Options: a ) 4 , b ) 9 , c ) 10 , d ) 4 , e ) 12
Rationale: "3 x * x = 243 = > x = 9 answer : b"
Answer: b
Python program:
a = 243 / 2
b = math.sqrt(a)
Problem: rs . 730 were divided among punith , michael , suresh in such a way that if punith gets rs . 3 , then michael gets rs . 4 and if michael gets rs . 3.50 then suresh gets rs . 3 . the share of michael exceeds that of suresh by
Options: a ) rs 30 , b ) rs 40 , c ) rs 70 , d ) rs 210 , e ) rs 310
Rationale: explanation : let a = punith , b = michael , c = suresh . a : b = 3 : 4 and b : c = 7 / 2 : 3 = ( 8 / 7 ) * ( 7 / 2 ) * ( 8 / 7 ) * 3 = 4 : ( 24 / 7 ) a : b : c = 3 : 4 : 24 / 7 = 21 : 28 : 24 . bs share = rs . [ 730 * ( 28 / 73 ) ] = rs . 280 . cs share = rs . [ 730 * ( 24 / 73 ) ] = rs . 240 . difference of their shares = 40 answer : b
Answer: b
Python program:
a = 4 * 3
b = 3 * 3
c = 4 * 3
d = b + c 
e = 4 * 3
f = d + e 
g = 730 / f
h = a * g
i = 4 * 3
j = 3 * 3
k = 4 * 3
l = j + k 
m = 4 * 3
n = l + m 
o = 730 / n
p = i * o
q = h - p
Problem: the value of log 5 ( 1 / 125 ) is :
Options: a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none of these
Rationale: "log 5 ( 1 / 125 ) = log 5 ( 1 / 5 ) ^ 3 = 3 log 5 ( 1 / 5 ) = 3 ( log 5 1 - log 5 5 ) = 3 ( 0 - 1 ) = - 3 answer : b"
Answer: b
Python program:
a = 4 + 1 
b = a * 1000
c = 1 - b
d = math.log(c)
e = 4 + 1 
f = math.log(e)
g = d / f
h = math.log(g)
Problem: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 222 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 148 , c ) 130 , d ) 160 , e ) 210
Rationale: "125 % of 120 % of a = 222 125 / 100 * 120 / 100 * a = 222 a = 222 * 2 / 3 = 148 . answer b"
Answer: b
Python program:
a = 20 / 100
b = 1 + a 
c = 25 / 100
d = 1 + c 
e = b * d
f = 222 / e
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 90 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 90 = 0.833 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 0.833 + t » 100 / 40 = 0.833 + t » 2.5 = 0.833 + t » t = 1.667 back to 2 nd part of the trip formula : 25 / s = 1.667 » s = 15 ans a"
Answer: a
Python program:
a = 40 + 90 
b = a - 75
c = 40 + 90 
d = c / 40
e = 75 / 90
f = d - e
g = b / f
Problem: there are 190 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 94 , d ) 105 , e ) 108
Rationale: "you had the answer almost right . the x = 82 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 82 + set ab = 82 + 23 = 105 d"
Answer: d
Python program:
a = 190 - 59
b = a + 23 
c = b - 49
Problem: in a 240 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 23 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 240 m in 7 / 56 * 240 = 30 seconds since a beats b by 7 seconds , a runs 240 m in ( 30 - 7 ) = 23 seconds hence , a ' s time over the course = 23 seconds answer : a"
Answer: a
Python program:
a = 7 / 56
b = a * 240
c = b - 7
Problem: a man is 40 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is
Options: a ) 31 years , b ) 32 years , c ) 33 years , d ) 34 years , e ) 35 years
Rationale: "explanation : let ' s son age is x , then father age is x + 40 . = > 2 ( x + 6 ) = ( x + 40 + 6 ) = > 2 x + 12 = x + 46 = > x = 34 years answer : option d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 40 - b
d = 2 - 1
e = c / d
Problem: the perimeter of a semi circle is 198 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 98 , d ) 38.5 , e ) 13
Rationale: "36 / 7 r = 198 = > r = 38.5 answer : d"
Answer: d
Python program:
a = 2 + math.pi 
b = 198 / a
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.35 – 6.35 * ?
Options: a ) 0.35 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.35 * = 6 ( the greatest positive even integer less than or equal to 6.35 is 6 ) . hence , 6.35 – 6.35 * = 6.35 - 6 = 0.35 answer : a ."
Answer: a
Python program:
a = math.floor(6, 35)
b = 6 - 35
Problem: joe drives 360 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 53 , c ) 50 , d ) 54 , e ) 56
Rationale: t 1 = 360 / 60 = 6 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 9 hours avg speed = total distance / t = 480 / 9 = 53 mph = b
Answer: b
Python program:
a = 360 + 120 
b = 360 / 60
c = 120 / 40
d = b + c 
e = a / d
Problem: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 8 .
Options: a ) 161 , b ) 152 , c ) 154 , d ) 158 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 8 d = 153 + 8 d = 161 answer a"
Answer: a
Python program:
a = 17 * 9
b = a + 8
Problem: car a runs at the speed of 55 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 11 : 7 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 55 × 8 = 440 km car b travels 70 × 4 = 280 km the ratio is 440 : 280 = 44 : 28 = 11 : 7 the answer is c ."
Answer: c
Python program:
a = 55 * 8
b = 70 * 4
c = a / b
Problem: a train running at the speed of 70 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 700 , b ) 770 , c ) 707 , d ) 710 , e ) 720
Rationale: "speed = ( 70 * 5 / 18 ) m / sec = ( 175 / 9 ) m / sec length of the train = ( speed x time ) = ( 175 / 9 * 36 ) m = 700 m . answer : a"
Answer: a
Python program:
a = 70 * 1000
b = a / 3600
c = b * 36
Problem: a jeep takes 3 hours to cover a distance of 440 km . how much should the speed in kmph be maintained to cover the same direction in 1 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 252 kmph , c ) 293 kmph , d ) 263 kmph , e ) 265 kmph
Rationale: "time = 3 distance = 340 1 / 2 of 3 hours = 6 * 1 / 2 = 1.5 hours required speed = 440 / 1.5 = 293 kmph c )"
Answer: c
Python program:
a = 1 / 2
b = a * 3
c = 440 / b
Problem: what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 4 , and 5 if each digit can be used only once in each number ?
Options: a ) 2442 , b ) 2552 , c ) 2662 , d ) 2772 , e ) 2882
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 444 ) + 2 ( 555 ) = 2442 the answer is a ."
Answer: a
Python program:
a = 5 + 4 
b = a + 2 
c = b * 100
d = 4 + 0 
e = d + 2 
f = e * 10
g = c + f 
h = 5 + 4 
i = h + 2 
j = g + i 
k = j * 4
Problem: the difference between the ages of two persons is 20 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the younger person is ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 28 , e ) 32
Rationale: let their ages be x years and ( x + 20 ) years then , ( x + 20 ) - 15 = 2 ( x - 15 ) x + 5 = 2 x - 30 x = 35 answer is b
Answer: b
Python program:
a = 3 + 2 
b = 20 - a
c = 20 - b
d = 3 + 2 
e = 20 - d
f = e * 2
g = c + f
Problem: if 70 percent of 600 is 40 percent of x , then x = ?
Options: a ) 105 , b ) 168 , c ) 342 , d ) 660 , e ) 1050
Rationale: "given : 0.7 * 600 = 0.4 x - - > 420 = 4 / 10 * x - - > x = 1,050 . answer : e ."
Answer: e
Python program:
a = 70 * 600
b = a / 40
Problem: find the sum of divisors of 544 which are perfect squares
Options: a ) 21
b ) 22
c ) 23
d ) 24
e ) 25
Rationale: perfect squares divisiors are 1 , 2 ^ 2 & 2 ^ 4 only sum of divisors of 544 which are perfect squares = 1 + 2 ^ 2 + 2 ^ 4 = 21 answer : a
Answer: a
Python program:
a = 544 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 544 / e
g = f / 2
h = 544 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 544 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: find compound interest on $ 6000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 2331.75 , b ) 2209.75 , c ) 2108.75 , d ) 2107.75 , e ) 2100.75
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 6000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 6000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 8331.75 . : . c . i . = rs . ( 8331.75 - 6000 ) = $ 2331.75 answer a ."
Answer: a
Python program:
a = 15 / 100
b = 6000 * a
c = 15 / 100
d = 6000 * c
e = 6000 + d 
f = 15 / 100
g = e * f
h = b + g 
i = 15 / 100
j = 6000 * i
k = 6000 + j 
l = 15 / 100
m = 6000 * l
n = 6000 + m 
o = 15 / 100
p = n * o
q = k + p 
r = 15 / 100
s = r / 3
t = q * s
u = h + t
Problem: a towel , when bleached , lost 30 % of its length and 40 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 30 % , c ) 44 % , d ) 58 % , e ) 64 %
Rationale: "percentage change in area = ( − 30 − 40 + ( 30 × 40 ) / 100 ) % = − 58 % i . e . , area is decreased by 58 % answer : d"
Answer: d
Python program:
a = 100 * 100
b = 100 - 30
c = 100 - 40
d = b * c
e = a - d
f = e / 100
Problem: in order to obtain an income of rs . 3800 from 70 % stock at rs . 280 , one must make an investment of
Options: a ) rs . 16000 , b ) rs . 15000 , c ) rs . 15250 , d ) rs . 15200 , e ) rs . 15300
Rationale: "explanation : market value = rs . 280 required income = rs . 3800 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 70 ( ie , 70 % of the face value 100 ) , investment = rs . 280 to obtain rs . 3800 , investment = 280 / 70 ã — 3800 = rs . 15200 answer : option d"
Answer: d
Python program:
a = 280 / 70
b = a * 3800
Problem: a train 300 m long can cross an electric pole in 15 sec and then find the speed of the train ?
Options: a ) 65 kmph , b ) 70 kmph , c ) 72 kmph , d ) 75 kmph , e ) 78 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 15 s = 20 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 72 kmph answer : c"
Answer: c
Python program:
a = 300 / 1000
b = 15 / 3600
c = a / b
Problem: a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 5 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 5 / 18 , c ) 4 / 9 , d ) 3 / 8 , e ) 4 / 7
Rationale: 2 / 3 - - - - 12 ? - - - - - 5 = = > 5 / 18 b
Answer: b
Python program:
a = 2 / 3
b = a * 5
c = b / 12
Problem: jane and thomas are among the 8 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "the total number of ways to choose 3 people from 8 is 8 c 3 = 56 . the number of committees without jane or thomas is 6 c 3 = 20 . there are 56 - 20 = 36 possible committees which include jane and / or thomas . the answer is d ."
Answer: d
Python program:
a = math.comb(8, 1)
b = math.comb(8, 1)
c = a + b 
d = math.comb(4, 1)
e = c + d
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 6 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 225 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 6 people . so $ 150 . but , he also has to put in the average for himself ( the seventh person ) , so add $ 75 . so $ 225 is your answer . answer a"
Answer: a
Python program:
a = 6 + 1 
b = a * 75
c = 6 + 1 
d = c * 50
e = b - d
f = e + 50
Problem: what is the least value of x . so that 30 x 55 is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 1 , d ) 2 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 3 + 0 + x + 5 + 5 = 13 + x least value of x may be 2 therefore 13 + 2 = 15 is divisible by 3 . d"
Answer: d
Python program:
a = math.lcm(30, 55)
b = a / 55
c = b / 4
d = c / 4
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 4 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 4 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 140 ans c"
Answer: c
Python program:
a = 70 - 4
b = a * 2
c = 2 * 10
d = b + c
Problem: 2 ^ ( 2 x / 3 ) = 2 ^ ( x / 2 ) what is the value of x ?
Options: a ) 2 , b ) 2 / 3 , c ) 1 , d ) 0 , e ) - 2
Rationale: 2 x / 3 = x / 2 4 x = 3 x 4 x - 3 x = 0 ; x = 0 ans : d
Answer: d
Python program:
a = 3 * 2
b = 2 * 2
c = a - b
Problem: a box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 54 , d ) 56 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 35 , 20 and 10 . thus side of cube must be 5 , and total number of cubes = 35 / 5 * 20 / 5 * 10 / 5 = 56 ans d it is ."
Answer: d
Python program:
a = 35 * 20
b = a * 10
c = 10 / 2
d = b / volume_cube
Problem: how many prime numbers between 1 and 100 are factors of 1771 ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "factor of 1771 = 7 * 11 * 23 - - - 3 prime numbers e"
Answer: e
Python program:
a = 4 * 1
Problem: what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 20 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "denote | x - 4 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 4 - - > x = 8 or x = - 1 . the sum = 7 . answer : d ."
Answer: d
Python program:
a = 4 + 4 
b = 4 - 4
c = a + b