euclaise/mathqa_programs huggingface dataset:
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 40 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 112 mtr . , e ) 17 mtr .
Rationale: "20 men is 6 days can build 112 metres 25 men in 3 days can build = 112 * ( 40 / 20 ) x ( 3 / 6 ) = 112 meters answer : d ."
Answer: d
Python program:
a = 40 * 3
b = 20 * 6
c = a / b
d = 112 * c
Problem: a certain junior class has 1,000 students and a certain senior class has 400 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 20,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 400 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 400 * 1000 ) = 3 / 20,000 a"
Answer: a
Python program:
a = 1 / 3
Problem: a train running at the speed of 180 km / hr crosses a pole in 8 seconds . find the length of the train .
Options: a ) 150 , b ) 88 , c ) 480 , d ) 288 , e ) 400
Rationale: "speed = 180 * ( 5 / 18 ) m / sec = 50 m / sec length of train ( distance ) = speed * time 50 * 8 = 400 meter answer : e"
Answer: e
Python program:
a = 180 * 1000
b = a / 3600
c = b * 8
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds b in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out b : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Python program:
a = 25 + 25 
b = a / 2
c = 10 + b
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 600 , find the original price per kg ?
Options: a ) s . 11 , b ) s . 14 , c ) s . 15 , d ) s . 21 , e ) s . 29
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 600 - - - 80 ? - - - 2 = > rs . 15 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 600
c = b / 10
d = 20 / 100
e = d * 600
f = c / e
g = f * 100
Problem: what is the remainder when 3 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 3 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? d
Answer: d
Python program:
a = 5 / 2
b = 3 * 3
c = a - b
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 42 years , was replaced by a new person . find the age of the new person ?
Options: a ) 22 , b ) 18 , c ) 12 , d ) 88 , e ) 66
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 - 42 + q = > q = 12 answer : c"
Answer: c
Python program:
a = 10 * 3
b = 42 - a
Problem: what is the sum of the squares of the first 20 natural numbers ( 1 to 20 ) ?
Options: a ) 2870
b ) 2000
c ) 5650
d ) 6650
e ) 7650
Rationale: n ( n + 1 ) ( 2 n + 1 ) / 6 20 ( 21 ) ( 21 ) / 6 = 2870 answer : a
Answer: a
Python program:
a = 20 + 1 
b = 20 * a
c = 2 * 20
d = c + 1 
e = b * d
f = 2 * 3
g = e / f
Problem: the average of 9 observations was 7 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 27 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 7 = 63 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 63 = 27 option a"
Answer: a
Python program:
a = 10 * 5
b = 7 * 5
c = a + b 
d = 7 * 9
e = c - d
Problem: the guests at a football banquet consumed a total of 319 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 159 * 2 ( max possible amount of food a guest could consume ) = 318 pounds , so there must be more than 159 guests , next integer is 160 . answer : a ."
Answer: a
Python program:
a = 319 / 2
b = math.floor(a)
c = b + 1
Problem: 8 persons can build a wall 140 m long in 42 days . in how many days can 30 persons complete a similar wall 100 m long ?
Options: a ) 12 , b ) 10 , c ) 8 , d ) 6 , e ) 5
Rationale: explanation : more persons , less days ( indirect proportion ) more length of the wall , more days ( direct proportion ) ⇒ 8 × 100 × 42 = 30 × 140 × x ⇒ x = ( 8 × 100 × 42 ) / ( 30 × 140 ) = ( 8 × 100 × 14 ) / ( 10 × 140 ) = ( 8 × 100 ) / ( 10 × 10 ) = 8 . answer : option c
Answer: c
Python program:
a = 8 * 42
b = 140 / a
c = 30 * b
d = 100 / c
Problem: what is the prime factors ’ number of 48 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 4 * 3 ^ 1 prime factors ’ number will be 4 + 1 = 5 . hence , answer is d .
Answer: d
Python program:
a = 1 + 1 
b = 1 + a 
c = b + 1 
d = c + 1
Problem: in a group of cows and hens , the number of legs are 20 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 20 4 x + 2 y = 2 x + 2 y + 20 2 x = 20 x = 10 answer : c"
Answer: c
Python program:
a = 20 - 4
Problem: the compound interest on a sum of money for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound interest and simple interest for 3 years
Options: a ) 98.5 , b ) 08.56 , c ) 98.56 , d ) 98.86 , e ) 98.46
Rationale: explanation : difference in c . i and s . i in 2 years = rs . 32 s . i for 1 year = rs . 400 s . i for rs . 400 for one year = rs . 32 rate = [ 100 * 32 ) / ( 400 * 1 ) % = 8 % difference between in c . i and s . i for 3 rd year = s . i on rs . 832 = rs . ( 832 * 8 * 1 ) / 100 = rs . 66.56 answer : c ) rs . 98.56
Answer: c
Python program:
a = 800 / 2
b = 832 - a
c = 800 / 2
d = b - c
e = d * 100
f = 800 / 2
g = e / f
h = 832 * g
i = h / 100
j = 800 / 2
k = 832 - j
l = 800 / 2
m = k - l
n = i + m
Problem: if 5 ^ 21 x 4 ^ 11 = 2 x 10 ^ n . what is the value of n ?
Options: a ) 11 , b ) 21 , c ) 22 , d ) 23 , e ) 32
Rationale: "if 5 ^ 21 x 4 ^ 11 = 2 x 10 ^ n what is the value of n 4 ^ 11 = ( 2 ^ 2 ) ^ 11 = 2 ^ 22 10 ^ n = ( 5 x 2 ) ^ n = 5 ^ n x 2 ^ n 5 ^ 21 x 2 ^ 22 = 2 x 2 ^ n x 5 ^ n = 2 ^ n + 1 x 5 ^ n = 2 ^ 22 x 5 ^ 21 n = 21 option b"
Answer: b
Python program:
a = 4 ** 11
b = 5 ** 21
c = a * b
d = math.log(c)
e = math.log(2)
f = d / e
Problem: from below option 51 is divisible by which one ?
Options: a ) a ) 4 , b ) b ) 5 , c ) c ) 6 , d ) d ) 3 , e ) e ) 7
Rationale: "51 / 3 = 17 d"
Answer: d
Python program:
a = math.sqrt(51)
Problem: each child has 2 pencils and 13 skittles . if there are 11 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 11 = 22 . answer is d .
Answer: d
Python program:
a = 2 * 11
Problem: . a car covers a distance of 390 km in 4 hours . find its speed ?
Options: a ) 104 , b ) 55 , c ) 66 , d ) 98 , e ) 100
Rationale: 390 / 4 = 98 kmph answer : d
Answer: d
Python program:
a = 390 / 4
Problem: find the sum of all 3 digit natural numbers , which are divisible by 8
Options: a ) 61376 , b ) 54411 , c ) 612314 , d ) 64170 , e ) 64171
Rationale: "the three digit natural numbers divisible by 8 are 104 , 112 , 120 , … . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 answer a 61376"
Answer: a
Python program:
a = 100 + 4 
b = 100 * 10
c = b - 8
d = a + c 
e = 100 * 10
f = e - 8
g = 100 + 4 
h = f - g
i = h / 8
j = i + 1 
k = j / 2
l = d * k
Problem: a man buys 25 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 25 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 55 , b ) 82 , c ) 73 , d ) 75 , e ) 85
Rationale: "20 % in 25 lts is 5 . so water = 25 - 5 = 20 lts . 30 % of 25 lts = 7.5 . so water in 2 nd mixture = 25 - 7.5 = 17.5 lts . now total quantity = 25 + 25 = 50 lts . total water in it will be 20 + 17.5 = 37.5 lts . % of water = ( 100 * 37.5 ) / 50 = 75 . answer : d"
Answer: d
Python program:
a = 25 - 20
b = 25 * a
c = 25 - 30
d = 25 * c
e = b + d 
f = 25 + 25 
g = e / f
Problem: john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 45 * 2 + 3 * 55 = 255 miles . answer c"
Answer: c
Python program:
a = 45 * 2
b = 3 * 55
c = a + b
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 555 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 6 , e ) 19
Rationale: "30 * 25 = 750 455 - - - - - - - - - - - 195 25 + 7.50 = 32.5 195 / 32.5 = 6 d"
Answer: d
Python program:
a = 7 * 50
b = a + 555 
c = 7 + 50 
d = b / c
e = 30 - d
Problem: a does 4 / 5 th of a work in 20 days . he then calls in b and they together finish the remaining work in 3 days . how long b alone would take to do the whole work ?
Options: a ) 23 days , b ) 37 days , c ) 37 ½ days , d ) 40 days , e ) 41 days
Rationale: explanation : a can finish the whole work in 20 × 5 / 4 days = 25 days a and b together finish the whole work in 5 × 3 days = 15 days therefore , b can finish the whole work in 25 b / 25 + b = 15 25 b = 15 ( 25 + b ) = 375 + 15 b 10 b = 375 and b = 375 / 10 = 37 ½ days . answer : option c
Answer: c
Python program:
a = 3 * 5
b = 1/(a)
c = 5 / 4
d = c * 20
e = 1/(d)
f = b - e
g = 1/(f)
Problem: a and b can do a work in 12 days and 36 days respectively . if they work on alternate days beginning with b , in how many days will the work be completed ?
Options: a ) 11 , b ) 17 , c ) 10 , d ) 17 , e ) 18
Rationale: the work done in the first two days = 1 / 12 + 1 / 36 = 1 / 9 so , 9 such two days are required to finish the work . i . e . , 18 days are required to finish the work . answer : e
Answer: e
Python program:
a = 1/(36)
b = 1/(12)
c = a + b 
d = 1/(c)
e = d + 12 
f = e - 3
Problem: a train , 140 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 140 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 140 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 140 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 140 + x = > 45 ã — 10 ã — 10 / 12 = 140 + x = > 15 ã — 10 ã — 10 / 4 = 140 + x = > 15 ã — 25 = 140 + x = 375 = > x = 375 - 140 = 235 answer : option c"
Answer: c
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 140
Problem: if 12 : 18 : : x : 9 , then find the value of x
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: explanation : treat 12 : 18 as 12 / 18 and x : 9 as x / 9 , treat : : as = so we get 12 / 18 = x / 9 = > 18 x = 108 = > x = 6 option c
Answer: c
Python program:
a = 18 * 12
b = a + 18 
c = b / 9
Problem: a can do a piece of work in 30 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 30 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: 10 / 30 + 10 / 30 + 10 / x = 1 x = 30 days answer : a
Answer: a
Python program:
a = 10 + 10 
b = a / 30
c = 1 - b
d = 10 / c
Problem: the distance between towns a and b is 300 km . one train departs from town a and another train departs from town b , both leaving at the same moment of time and heading towards each other . we know that one of them is 10 km / hr faster than the other . find the speeds of both trains if 2 hours after their departure the distance between them is 40 km .
Options: a ) 22 , b ) 27 , c ) 236 , d ) 90 , e ) 81
Rationale: let the speed of the slower train be xx km / hr . then the speed of the faster train is ( x + 10 ) ( x + 10 ) km / hr . in 2 hours they cover 2 x 2 x km and 2 ( x + 10 ) 2 ( x + 10 ) km , respectively . therefore if they did n ' t meet yet , the whole distance from a to b is 2 x + 2 ( x + 10 ) + 40 = 4 x + 602 x + 2 ( x + 10 ) + 40 = 4 x + 60 km . however , if they already met and continued to move , the distance would be 2 x + 2 ( x + 10 ) − 40 = 4 x − 202 x + 2 ( x + 10 ) − 40 = 4 x − 20 km . so we get the following equations : 4 x + 60 = 3004 x + 60 = 300 4 x = 2404 x = 240 x = 60 x = 60 or 4 x − 20 = 3004 x − 20 = 300 4 x = 3204 x = 320 x = 80 x = 80 hence the speed of the slower train is 60 km / hr or 80 km / hr and the speed of the faster train is 70 km / hr or 90 km / hr . answer : d
Answer: d
Python program:
a = 300 - 40
b = 2 + 2 
c = a / b
d = c - 10
e = d - 10
f = 300 - 40
g = 2 + 2 
h = f / g
i = h - 10
j = i - 10
k = e + j
Problem: tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 2 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 12 , b ) 15 , c ) 10 , d ) 20 , e ) 14
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 480 ( we want to find the days , sop = 480 / d ) 2 ) ( p + 16 ) ( d - 2 ) = 480 = > pd - 2 p + 16 d - 32 = 480 as the 1 ) stated u can put 1 ) into 2 ) = > 480 - 2 p + 16 d - 32 = 480 = > 16 d - 2 p = 32 put the bold one into it = > 16 d - 2 ( 480 / d ) = 80 the we get the final equation 16 d ^ 2 - 960 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 60 = 0 ( d - 12 ) ( d + 5 ) = 0 so d = 12 days ans : a"
Answer: a
Python program:
a = 16 * 2
b = a * 4
c = 16 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 16
g = f / 2
Problem: a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 00000 and the monthly manufacturing expenses is rs 1 , 50000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 69 / 70 ) â ˆ ’ 150000 ã — ( 69 / 70 ) â ˆ ’ 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,000 = > rs . 5,000 . answer : d
Answer: d
Python program:
a = 75000 - 50000
b = 2 + 3 
c = a / b
Problem: a fruit seller sells mangoes at the rate of rs . 14 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 15 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 18.94 , d ) rs . 12.31 , e ) none
Rationale: "solution 85 : 14 = 115 : x x = ( 14 ã — 115 / 85 ) = rs . 18.94 hence , s . p per kg = rs . 18.94 answer c"
Answer: c
Python program:
a = 100 + 15 
b = 14 * a
c = 100 - 15
d = b / c
Problem: for a 3 - digit number xyz , where x , y , and z are the digits of the number , f ( xyz ) = 5 ^ x 2 ^ y 3 ^ z . if f ( abc ) = 3 * f ( def ) , what is the value of abc - def ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 27
Rationale: since f ( abc ) = 3 * f ( def ) , i would assume that f = c - 1 from the function above . the answer should be ( a )
Answer: a
Python program:
a = 3 - 2
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length
Options: a ) 33 , b ) 44 , c ) 55 , d ) 77 , e ) 22
Rationale: "t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer : c"
Answer: c
Python program:
a = 165 + 660 
b = 54 * const_0_2778
c = a / b
Problem: a truck covers a distance of 392 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 70 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 392 / 8 = 49 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 48 + 18 ) = 66 kmph distance travelled by car = 392 + 70 = 462 km time taken by car = distance / speed = 462 / 66 = 7 hours . answer – c"
Answer: c
Python program:
a = 392 + 70 
b = 392 / 8
c = b + 18 
d = a / c
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 70 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220070
Rationale: "( 555 + 445 ) * 2 * 110 + 70 = 220000 + 70 = 220070 e"
Answer: e
Python program:
a = 555 + 445 
b = a * 2
c = 555 - 445
d = b * c
e = d + 70
Problem: the average of 45 results is 10 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 10 * 45 - 15 * 22 + 20 * 22 = 450 - 330 + 440 = 560 answer is e"
Answer: e
Python program:
a = 45 * 10
b = 22 * 20
c = a - b
d = 22 * 15
e = c - d
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 140 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,260
Rationale: "10 / 100 p = 140 > > p = 140 * 100 / 10 = 1400 1400 - 140 = 1260 answer : e"
Answer: e
Python program:
a = 100 / 10
b = 140 * a
c = b - 140
Problem: a professional janitor can clean a certain high school in ( 4 + 4 ) hours , working at a constant rate . a student sentenced to detention can clean that same high school in 20 hours , also working at a constant rate . if the student is paid $ 7 total per hour and the janitor is paid $ 21 per hour , how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together ?
Options: a ) - $ 56 , b ) - $ 6 , c ) $ 0 , d ) $ 6 , e ) $ 8
Rationale: a professional janitor can clean a certain high school in ( 4 + 4 ) or 8 hours so ( applying rule # 1 ) , the janitor can clean 1 / 8 of the school in one hour a student sentenced to detention can clean that same high school in 20 hours so ( applying rule # 1 ) , the student can clean 1 / 20 of the school in one hour so , combined , the student and janitor can clean ( 1 / 8 + 1 / 20 ) of the school in one hour 1 / 8 + 1 / 20 = 5 / 40 + 2 / 40 = 7 / 40 so , in one hour they can clean 7 / 40 of the school . applying rule # 2 , it will takethem 40 / 7 hoursto clean the entire school . the janitor earns $ 21 / hour and the student earns $ 7 / hour , so their combined rate is $ 28 / hour . theircombined wages = ( pay rate ) ( time ) = ( $ 28 / hour ) ( 40 / 7 hours ) = $ 160 working alone , the janitor takes 8 hours and earns $ 21 / hour so , working alone , the janitor ' s earnings = ( pay rate ) ( time ) = ( $ 21 / hour ) ( 8 hours ) = $ 168 $ 168 - $ 160 = $ 8 , so the answer is e
Answer: e
Python program:
a = 4 + 4 
b = a * 21
c = 7 + 21 
d = 4 + 4 
e = 1 / d
f = 1 / 20
g = e + f 
h = 1 / g
i = c * h
j = b - i
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 2 men and 3 women will do that task .
Options: a ) 1 / 2 , b ) 1 / 10 , c ) 1 / 18 , d ) 1 / 16 , e ) 1 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 2 m + 3 w = 7 w answer is 7 / 14 = 1 / 2 answer : a"
Answer: a
Python program:
a = 8 - 2
b = 6 - 3
c = a / b
d = c * 2
e = d + 3 
f = 8 - 2
g = 6 - 3
h = f / g
i = 6 * h
j = i + 2 
k = e / j
Problem: a light has a rating of 60 watts , it is replaced with a new light that has 12 % higher wattage . how many watts does the new light have ?
Options: a ) 105 , b ) 67 , c ) 80 , d ) 60 , e ) 100
Rationale: "final number = initial number + 12 % ( original number ) = 60 + 12 % ( 60 ) = 60 + 7 = 67 answer b"
Answer: b
Python program:
a = 12 / 100
b = 1 + a 
c = 60 * b
Problem: a sum of money becomes 7 / 6 of itself in 6 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 9 , b ) 50 / 13 , c ) 50 / 17 , d ) 25 / 9 , e ) 5 5 / 1
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 6 years . rate = ( 100 * x ) / ( x * 6 * 6 ) = 25 / 9 % . answer : d"
Answer: d
Python program:
a = 7 / 6
b = a - 1
c = b / 6
d = c * 100
Problem: find the missing figures : 0.3 % of ? = 0.15
Options: a ) 50 , b ) 45 , c ) 150 , d ) 450 , e ) 500
Rationale: let 0.3 % of x = 0.15 . then , 0.30 * x / 100 = 0.15 x = [ ( 0.15 * 100 ) / 0.3 ] = 50 . answer is a .
Answer: a
Python program:
a = 0 / 3
b = 0 / 15
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 265 , then the mean profit for the last 15 days would be
Options: a ) rs . 435 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: average would be : 350 = ( 265 + x ) / 2 on solving , x = 435 . answer : a
Answer: a
Python program:
a = 30 * 350
b = 15 * 265
c = a - b
d = c / 15
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 5 females and 5 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 5 ) = 2 x - 5 x = 10 there were 3 x = 30 people at the party originally . the answer is c ."
Answer: c
Python program:
a = 5 * 2
b = a * 3
c = 5 * 2
d = b - c
e = d / 2
f = 5 * 2
g = f * 3
h = 5 * 2
i = g - h
j = e + i
Problem: the least number which when increased by 8 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 869 , d ) 856 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 8 = 864 - 8 = 856 . answer d"
Answer: d
Python program:
a = math.lcm(24, 32)
b = math.lcm(a, 36)
c = math.lcm(b, 54)
d = c - 8