euclaise/mathqa_programs huggingface dataset:
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent t of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is t = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Python program:
a = 9 / 12
b = a * 100
c = 100 - b
Problem: in a throw of a coin find the probability of getting a head ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5
Rationale: s = { h , t } e = { h } p ( e ) = 1 / 2 answer is a
Answer: a
Python program:
a = 1 / 2
Problem: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 12 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 9 days , e ) 18 days
Rationale: explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 12 x = 18 days answer : option e
Answer: e
Python program:
a = 1/(12)
b = 1/(15)
c = 5 * b
d = 1 - c
e = a * d
f = 1/(e)
Problem: evaluate : 460 - 12 * 3 * 2 = ?
Options: a ) 878 , b ) 545 , c ) 434 , d ) 442 , e ) 452
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 460 - 12 * 3 * 2 = 460 - 8 = 452 correct answer e"
Answer: e
Python program:
a = 12 * 3
b = a * 2
c = 460 - b
Problem: in a km race , a beats bby 28 metres or 7 seconds . find a ' s timeoverthe course
Options: a ) 4 min , b ) 3 min 3 sec , c ) 4 min 4 sec , d ) 5 min 3 sec , e ) 4 min 3 sec
Rationale: clearly , b covers 28 m in 7 seconds . : . b ' s time over the course = ( 278 x 1000 ) sec = 250 seconds . : . a ' s time over the course = ( 250 - 7 - ) sec = 243 sec = 4 min . 3 sec . answer e 4 min 3 sec
Answer: e
Python program:
a = 7 / 28
b = a * 1000
c = b - 7
d = 2 * 100
e = c - d
Problem: a thief is spotted by a policeman from a distance of 200 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 800 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 200 m / 1000 ) x 1 / 2 hr = 1 / 10 hr . in 1 / 10 hrs , the thief covers a distance of 8 x 1 / 10 km = 4 / 5 km = 800 m answer is d ."
Answer: d
Python program:
a = 200 * 8
b = 10 - 8
c = a / b
Problem: set x consists of 10 integers and has median of 30 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 50 this is possible . hence it is the greatest such number . answer ( e )
Answer: e
Python program:
a = 30 + 20
Problem: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.25 hrs , e ) 11.25 hrs
Rationale: "net part filled in 1 hour = 1 / 5 - 1 / 9 = 4 / 45 therefore the cistern will be filled in 45 / 4 hours or 11.25 hours . answer : e"
Answer: e
Python program:
a = 1 / 5
b = 1 / 9
c = a - b
d = 1 / c
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 650 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 400 , d ) 589 , e ) 171
Rationale: "explanation : 650 = p ( 21 / 20 ) 2 p = 589.56 answer : d"
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 650 / c
Problem: there are 456 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 264 , b ) 209 , c ) 57 , d ) 171 , e ) 181
Rationale: given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 456 = 264 answer : a
Answer: a
Python program:
a = 11 - 8
b = 8 * a
c = b * 11
Problem: find the simple interest on rs . 70,400 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 8800 , e ) s . 6500
Rationale: "p = rs . 70400 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 70,400 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8800 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 3 + 2 
g = f * 2
h = e * g
i = c + h 
j = 16 * 3
k = j + 2 
l = k / 3
m = i * l
n = 3 * 3
o = 2 * 3
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 153 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1275 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 153 . ∴ x 16 x 9 / 12 x 1 / 100 } = 153 or x = 1275 . ∴ p . w . = rs . 1275 . answer c"
Answer: c
Python program:
a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 153 / d
f = e + 153
Problem: a voltage will influence current only if the circuit is :
Options: a ) 2
b ) 7
c ) 6
d ) 889
e ) 1
Rationale: answer : b
Answer: b
Python program:
a = 3 * 2
b = a + 1
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 2 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1166.7 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 90 % 102 % - - - - - - - - 12 % - - - - 140 100 % - - - - ? = > rs . 1166.7 answer : c"
Answer: c
Python program:
a = 140 * 100
b = 100 + 2 
c = 100 - 10
d = b - c
e = a / d
Problem: in the junior basketball league there are 15 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 9 . , e ) 5 .
Rationale: "total teams = 16 bad teams = ( 2 / 3 ) * 15 = 10 rich teams = 8 so maximum value that the both rich and bad can take will be 8 . so e = 9 can not be that value . ans d ."
Answer: d
Python program:
a = 1 / 2
b = 15 * a
c = b + 1
Problem: a movie buff buys movies on dvd and on blu - ray in a ratio of 17 : 4 . if she returns 4 blu - ray movies , that ratio would change to 9 : 2 . if she buys movies on no other medium , what was the original number of movies purchased ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 378
Rationale: if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 17 x and b ( d ) = 4 x now from the next line the new eqn becomes 17 x / ( 4 x - 4 ) = 9 / 2 solving it 34 x = 36 x - 36 x = 18 which means m ( d ) = 306 and b ( d ) = 72 so total initially is m ( d ) + b ( d ) = 378 e
Answer: e
Python program:
a = 4 * 9
b = a / 2
c = 17 + 4 
d = b * c
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 15 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "let ' s test : 1998 revenues = $ 100 profits = $ 10 next we ' re told that , in 1999 , revenue fell by 20 % , but profits were 15 % of revenues . using the numbers from 1998 ( above ) , we end up with . . . 1999 revenues = $ 80 profits = $ 12 we ' re asked to compare the profits in 1999 to the profits in 1998 ( as a percentage ) : $ 12 / $ 10 = 1.2 = 120 % answer : c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 15 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: a cube has two of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 5 , b ) 3 : 6 , c ) 1 : 2 , d ) 2 : 9 , e ) 1 : 3
Rationale: "let x be the area of each face of the cube . the area painted red is 2 ( x / 2 ) = x the area painted white is 2 ( x / 2 ) + 4 x = 5 x the ratio of red to white is x : 5 x which is 1 : 5 . the answer is a ."
Answer: a
Python program:
a = 1 + 4 
b = 1 / 2
c = a * b
d = c * 2
e = 1 + 4 
f = 1 / 2
g = e * f
h = g + 1 
i = h * 2
j = d / i
Problem: if athul rows 16 km upstream and 24 km down steam taking 4 hours each , then the speed of the stream
Options: a ) 1 kmph , b ) 2 kmph , c ) 1.5 kmph , d ) 12 kmph , e ) 15 kmph
Rationale: speed upstream = 16 / 4 = 4 kmph speed down stream = 24 / 4 = 6 kmph speed of stream = ½ ( 6 - 4 ) = 1 kmph answer : a
Answer: a
Python program:
a = 24 / 4
b = 16 / 4
c = a - b
d = c / 2
Problem: the average age of 30 students in a class is 5 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 45 , e ) 36
Rationale: "total age of 50 students = 30 * 5 = 150 total age of 51 persons = 31 * 6 = 186 age of teacher = 186 - 150 = 36 years answer is e"
Answer: e
Python program:
a = 30 * 5
b = a + 1 
c = b + 30 
d = 30 * 5
e = c - d
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 11000 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3000 , c ) rs . 6750 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 11000 ] = rs . 3000 answer : option b"
Answer: b
Python program:
a = 2 / 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 1 
f = 1/(e)
g = 11000 * f
Problem: a batsman scored 120 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 30 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b"
Answer: b
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 120 - c
e = d / 120
f = e * 100
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job
Options: a ) 49 , b ) 249 , c ) 349 , d ) 449 , e ) none of these
Rationale: explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 449 answer : d
Answer: d
Python program:
a = 1/(8)
b = 1/(10)
c = a + b 
d = 1/(c)
Problem: 4.036 divided by 0.04 gives :
Options: a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 100.9 , e ) 100.6
Rationale: "= 4.036 / 0.04 = 403.6 / 4 = 100.9 answer is d ."
Answer: d
Python program:
a = 4 / 36
Problem: find the constant k so that : - x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) - 11 , b ) - 12 , c ) - 13 , d ) - 14 , e ) - 15
Rationale: "- x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 7 ) x - 8 = - x 2 + 6 x - 8 - ( k + 7 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 13 : solve the above for k correct answer c"
Answer: c
Python program:
a = 4 + 2 
b = 7 + a
Problem: a car takes 4.5 hours to travel from a to b , which is 360 miles apart . what is the average speed of the car ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 85
Rationale: average speed = 360 / 4.5 hours = 360 / 270 = 1.33 miles per min = 80 miles per hour answer : d
Answer: d
Python program:
a = 360 / 4
Problem: there are 20 balls which are red , blue or green . if 7 balls are green and the sum of red balls and green balls is less than 13 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : given : red + green + blue = 20 green = 7 solution : r + g < 13 therefore r + 7 < 13 so r < 6 ans : at most 5 red balls b . 5 hence ( b ) is correct . answer : b"
Answer: b
Python program:
a = 7 - 1
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 1 / 2 % , then the amount invested at 11 % was ?
Options: a ) 23777 , b ) 25000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 19 / 2 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 950000 x = 75000 sum invested at 9 % = rs . 75000 sum invested at 11 % = rs . ( 100000 - 75000 ) = rs . 25000 . answer : b"
Answer: b
Python program:
a = 1 / 2
b = 9 + a 
c = b / 100
d = 100000 * c
e = 9 / 100
f = 100000 * e
g = d - f
h = 11 / 100
i = 9 / 100
j = h - i
k = g / j
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 64.5 , c ) 62.5 , d ) 82.5 , e ) 60.5
Rationale: c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.5 b
Answer: b
Python program:
a = 100 + 25 
b = 47 * 5
c = b / 100
d = 100 - 8
e = c / d
f = e * 100
Problem: exactly 36 % of the numbers in set s are even multiples of 3 . if 40 % of the even integers in set s are not multiples of 3 , what percent of the numbers in set s are not even integers ?
Options: a ) 76 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 24 %
Rationale: let s be the total number of elements in set s . we know that 0.36 * s is the number of even multiples of three . let n be the number of even numbers . we know 0.40 * n are even numbers not multiple of three . this also means , 0.60 * n are even numbers that are multiples of three . therefore : 0.06 * n = 0.36 * s n = ( 0.36 / 0.60 ) * s = ( 36 / 60 ) * s = ( 6 / 10 ) * s = 0.60 * s = 60 % of s so even numbers are 60 % of s . that means , 40 % of s are not even integers . answer = d
Answer: d
Python program:
a = 100 - 40
b = 36 / a
c = b * 100
d = 100 - c
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 48 + q = > q = 18 answer : a"
Answer: a
Python program:
a = 10 * 3
b = 48 - a
Problem: a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 3.00 , b ) 5.00 , c ) 4.50 , d ) 5.50 , e ) 6.75
Rationale: "we are given that a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution , we can set up a proportion . we can say : “ 10 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 45 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 10 / 100 = x / 45 when we cross multiply we obtain : ( 10 ) ( 45 ) = 100 x 450 = 100 x 4.50 = x there are 4.5 grams of glucose in the solution in the container . the answer is c ."
Answer: c
Python program:
a = 10 / 100
b = 45 * a
Problem: find the two digit number , such that the ratio is 7 / 4 of original number to the number formed by reversing the digits .
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: here ratio is 7 / 4 . so lets check one by one . for 1 : 7 * 1 / 4 * 1 = 7 / 4 for 2 : 7 * 2 / 4 * 2 = 14 / 8 , which does n ' t satisfy the conditions . for 3 : 7 * 3 / 4 * 3 = 21 / 12 answer : b
Answer: b
Python program:
a = 7 * 4
b = a - 7
Problem: the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 7350 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6289 , b ) rs . 6298 , c ) rs . 6681 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 7350 ( 100 / 110 ) = rs . 6681 . answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = 7350 / b
Problem: a can do a piece of work in 4 days . b can do it in 5 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 16 days , d ) 19 days , e ) 36 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 5 = 1 / 20 = > 20 days answer : b"
Answer: b
Python program:
a = 4 * 5
b = 4 * 5
c = 4 * 5
d = c / 4
e = 4 * 5
f = e / 5
g = d + f 
h = g * 2
i = b - h
j = i / 2
k = a / j
Problem: what least no . must be subtracted from 10154 so that remaining no . is divisible by 30 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 10154 by 30 we get the remainder 14 , so 14 should be subtracted option c"
Answer: c
Python program:
a = 10154 / 30
b = math.floor(a)
c = b * 30
d = 10154 - c
Problem: the present population of a town is 240 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 264
Rationale: "p = 240 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 240 * ( 1 + 10 / 100 ) = 240 * ( 11 / 10 ) = 264 answer is e"
Answer: e
Python program:
a = 240 * 10
b = a / 100
c = 240 + b
Problem: a batsman makes a score of 74 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 31 , c ) 26 , d ) 29 , e ) 39
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 74 = total runs scored in 17 innings = > 16 ( x - 3 ) + 74 = 17 x = > 16 x - 48 + 74 = 17 x = > x = 26 answer is c"
Answer: c
Python program:
a = 17 * 3
b = 74 - a
c = b + 3
Problem: a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number q of ways this can be done is :
Options: a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225
Rationale: we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = q answer : c .
Answer: c
Python program:
a = math.factorial(5)
b = a * 2
c = math.factorial(4)
d = b - c
Problem: the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 156 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) .
Options: a ) 168.58 cm , b ) 158.58 cm , c ) 179.29 cm , d ) 168.58 cm , e ) 178.58 cm
Rationale: "calculated average height of 35 boys = 180 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 156 cm . correct total height of 35 boys = 180 * 35 cm - 156 cm + 106 cm = 180 * 35 cm - 156 cm + 106 cm / 35 = 180 cm - 50 / 35 cm = 180 cm - 1.42 cm = 178.58 cm . answer : e"
Answer: e
Python program:
a = 35 * 180
b = a - 156
c = b + 106 
d = c / 35
e = math.floor(d)
Problem: in a group of 100 cars , 37 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 48 , d ) 49 , e ) 53
Rationale: "lets assume ac = 63 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 14 tocars with ac and racing stripes . hence ac = 63 - 14 = 49 . the answer is d"
Answer: d
Python program:
a = 100 - 51
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability r that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . r = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %
Answer: b
Python program:
a = 2 * 5
b = 2 * 5
c = a * b
d = 60 / c
e = 2 * 5
f = 2 * 5
g = e * f
h = 20 / g
i = 1 - h
j = d / i
k = 1 - j
l = 2 * 5
m = 2 * 5
n = l * m
o = k * n
Problem: john purchased 1365 large bottles at $ 1.89 per bottle and 720 small bottles at $ 1.42 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.73 , e ) $ 1.76
Rationale: ( 1365 * 1.89 + 720 * 1.42 ) / ( 1365 + 720 ) = ~ 1.73 option ( d )
Answer: d
Python program:
a = 1365 * 1
b = 720 * 1
c = a + b 
d = 1365 + 720 
e = c / d
Problem: a train 100 meters long completely crosses a 300 meters long bridge in 15 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 96 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 45 = 400 / 15 * 18 / 5 = 96 answer : b"
Answer: b
Python program:
a = 100 + 300 
b = a / 1000
c = 15 / 3600
d = b / c