euclaise/mathqa_programs huggingface dataset:
Problem: a cistern 10 m long and 6 m wide contains water up to a breadth of 1 m 35 cm . find the total area of the wet surface .
Options: a ) 100 m sqaure , b ) 103 m sqaure , c ) 152 m sqaure , d ) 164 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 1.35 + 10 * 1.35 ) ] + 10 * 6 = 103 m square option b"
Answer: b
Python program:
a = 35 / 100
b = a + 1 
c = b * 6
d = 35 / 100
e = d + 1 
f = e * 10
g = c + f 
h = 2 * g
i = 6 * 10
j = h + i
Problem: a city with a population of 173,460 is to be divided into 9 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 17,400 , b ) 17,500 , c ) 17,600 , d ) 17,700 , e ) 17,800
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 173,460 = p + 8 ( 1.1 ) p 9.8 p = 173,460 p = 17,700 the answer is d ."
Answer: d
Python program:
a = 1000 * 100
b = 3600 - 100
c = b - 1000
d = a - c
e = d / 1000
f = 10 / 100
g = 1 + f 
h = 9 - 1
i = g * h
j = i + 1 
k = e / j
Problem: car q and car y traveled the same 80 - mile route . if car q took 2 hours and car y traveled at an average speed that was 50 percent faster than the average speed of car q , how many hours did it take car y to travel the route ?
Options: a ) 2 / 3 , b ) 1 , c ) 4 / 3 , d ) 8 / 5 , e ) 3
Rationale: the speed of car q is ( distance ) / ( time ) = 80 / 2 = 40 miles per hour . the speed of car y = 3 / 2 * 40 = 60 miles per hour - - > ( time ) = ( distance ) / ( speed ) = 80 / 60 = 4 / 3 hours . answer : c . or : to cover the same distance at 3 / 2 as fast rate 2 / 3 as much time is needed - - > ( time ) * 2 / 3 = 2 * 2 / 3 = 4 / 3 hours . answer : c .
Answer: c
Python program:
a = 80 / 2
b = a * 50
c = b / 100
d = 80 / 2
e = c + d 
f = 80 / e
Problem: 3 pig ’ s and 10 hens are brought for rs . 1200 . if the average price of a hen be rs . 30 . what is the average price of a pig .
Options: a ) 300 , b ) 350 , c ) 400 , d ) 425 , e ) 275
Rationale: explanation : average price of a hen = rs . 30 total price of 10 hens = 10 * 30 = rs . 300 but total price of 3 pigs and 10 hens = rs . 1200 total price of 3 pigs is = 1200 - 300 = 900 average price of a pig = 900 / 3 = rs . 300 answer : a
Answer: a
Python program:
a = 10 * 30
b = 1200 - a
c = b / 3
Problem: how many factors of 240 are also multiples of 3 ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 20
Rationale: "take factors of 240 240 = 2 ^ 4 * 3 ^ 1 * 5 ^ 1 total factors of 240 = ( 4 + 1 ) * ( 1 + 1 ) * ( 1 + 1 ) = 5 * 2 * 2 = 20 out of total factors of 20 , half will have 0 as power of 3 and half will have 1 as power of 3 . it is because we have considered only 0 and 1 as power of 3 to compute total factors of 240 . therefore factors that are multiple of 3 = 20 / 2 = 10 ans - d"
Answer: d
Python program:
a = 10 * 2
b = 240 / a
Problem: mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 46800 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 9691.2 , d ) 4845.6 , e ) 3900
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 46800 ⁄ 12 = 3900 answer e"
Answer: e
Python program:
a = 100 - 60
b = a * 50
c = b / 100
d = c / 100
e = 46800 / d
f = 3 * 4
g = e / f
h = 100 - 60
i = h * 50
j = i / 100
k = j / 100
l = g * k
Problem: a train 605 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 81 , b ) 16 , c ) 33 , d ) 54 , e ) 12
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 605 * 3 / 55 = 33 sec . answer : c"
Answer: c
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 605 / b
Problem: tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 6300 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 3500 , b ) 2800 , c ) 3251 , d ) 4251 , e ) 3508
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 6300 = 3500 a"
Answer: a
Python program:
a = 2 * 3
b = 2 * a
c = 3000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 4500 * f
h = 2 * 3
i = 2 * h
j = 3000 * i
k = g + j 
l = c / k
m = 1 - l
n = 6300 * m
Problem: the simple form of the ratio 2 / 3 : 2 / 5 is
Options: a ) 5 : 7 , b ) 5 : 2 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 4
Rationale: "2 / 3 : 2 / 5 = 10 : 6 = 5 : 3 answer : d"
Answer: d
Python program:
a = 2 / 5
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 83 . how much was lent at 5 % ?
Options: a ) 299 , b ) 566 , c ) 678 , d ) 700 , e ) 8277
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 83 5 x / 100 + 90 – 6 x / 100 = 83 x / 100 = 7 = > x = 700 answer : d"
Answer: d
Python program:
a = 5 + 6 
b = a * 100
Problem: a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is ?
Options: a ) 25 % , b ) 26 % , c ) 27 % , d ) 28 % , e ) 29 %
Rationale: "explanation : let original length = x and original width = y decrease in area will be = xy − ( 80 x / 100 × 90 y / 100 ) = ( xy − 18 / 25 xy ) = 7 / 25 xy decrease = ( 7 xy / 25 xy × 100 ) % = 28 option d"
Answer: d
Python program:
a = 100 - 20
b = a / 100
c = 100 - 10
d = c / 100
e = b * d
f = 1 - e
g = f * 100
Problem: gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 6 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 4 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 6 w 10 + 5 x = 6 ( x + 1 ) x = 4 ratio of gold with copper = 1 : 4 = 1 : 4 answer is b
Answer: b
Python program:
a = 6 - 5
b = 10 - 6
c = a / b
Problem: calculate how many days it will take for 8 boys to paint a 50 m long wall if 6 boys can paint a 60 m long wall in 5 days ,
Options: a ) 4.13 days , b ) 3.13 days , c ) 513 days , d ) 9.13 days , e ) 2 days
Rationale: the length of wall painted by one boy in one day = 60 / 6 * 1 / 5 = 2 m no . of days required to paint 50 m cloth by 8 boys = 50 / 8 * 1 / 2 = 3.13 days . b
Answer: b
Python program:
a = 6 * 5
b = a * 50
c = 60 * 8
d = b / c
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 20 % goods during theft . his loss percent is :
Options: a ) 10 , b ) 13 , c ) 12 , d ) 18 , e ) 19
Rationale: "c 12 % suppose he has 100 items . let c . p . of each item be $ 1 . total cost = $ 100 . number of items left after theft = 80 . s . p . of each item = $ 1.10 total sale = 1.10 * 80 = $ 88 hence , loss % = 12 / 100 * 100 = 12 %"
Answer: c
Python program:
a = 100 + 10 
b = 100 + 10 
c = b * 20
d = c / 100
e = a - d
f = 100 - e
Problem: a customer went to a shop and paid a total of $ 40 , out of which 90 cents was for sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) $ 22.70 , b ) $ 23.20 , c ) $ 24.10 , d ) $ 25.50 , e ) $ 26.90
Rationale: "the total cost was $ 40 . the tax was $ 0.90 let the original price of the taxable items = x given that tax rate = 6 % 0.06 x = 0.90 x = $ 15 the cost of the tax free items was $ 40 - $ 15 - $ 0.90 = $ 24.10 the answer is c ."
Answer: c
Python program:
a = 40 - 90
b = 6 * 2
c = a - b
Problem: albert buys 4 horses and 9 cows for rs . 13,400 . if he sells the horses at 10 % profit and the cows at 20 % profit , then he earns a total profit of rs . 1880 . the cost of a horse is :
Options: a ) rs . 2007 , b ) rs . 2000 , c ) rs . 2089 , d ) rs . 2067 , e ) rs . 2098
Rationale: "let c . p . of each horse be rs . x and c . p . of each cow be rs . y . then , 4 x + 9 y = 13400 - - ( i ) and , 10 % of 4 x + 20 % of 9 y = 1880 2 / 5 x + 9 / 5 y = 1880 = > 2 x + 9 y = 9400 - - ( ii ) solving ( i ) and ( ii ) , we get : x = 2000 and y = 600 . cost price of each horse = rs . 2000 . answer : b"
Answer: b
Python program:
a = 20 * 100
Problem: two motor bikes cover the same distance at the speed of 60 and 64 kmps respectively . find the distance traveled by them if the slower bike takes 1 hour more than the faster bike ?
Options: a ) 860 km , b ) 870 km , c ) 960 km , d ) 260 km , e ) 840 km
Rationale: explanation : 60 ( x + 1 ) = 64 x x = 15 60 x 16 = 960 km answer : c
Answer: c
Python program:
a = 64 - 60
b = 60 / a
c = b + 1 
d = 60 * c
Problem: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value s of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] s = z - x = x + 9 - x = 9 ans : d"
Answer: d
Python program:
a = 5 + 2 
b = a + 2
Problem: if renee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 2 / 25 , e ) 1 / 20
Rationale: 5 % is 5 / 100 = 1 / 20 10 % is 10 / 100 = 1 / 10 the increase must be greater than 1 / 20 and less than 1 / 10 . 1 / 4 , 1 / 5 , and 1 / 10 are not less than 1 / 10 . 1 / 20 is not greater than 1 / 20 . the only option left is 2 / 25 , which is in the specified range . answer : d
Answer: d
Python program:
a = 5 - 1
b = 5 * 10
c = a / b
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent r of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit r = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Python program:
a = 100 - 20
b = a - 20
c = 100 - b
Problem: in δ pqs above , if pq = 5 and ps = 6 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 16 / 5 , d ) 30 / 7 , e ) 50 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 5 * 6 / 2 = pr * 7 / 2 pr = 30 / 7 d"
Answer: d
Python program:
a = 6 / 5
Problem: in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the male students is single ?
Options: a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married . total females = 70 married males = 20 then single males = 70 - 20 = 50 we need to find the fraction of male students who are single i . e single male students / total male student = 50 / 70 = 5 / 7 [ e ]"
Answer: e
Python program:
a = 10 / 30
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 4 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 6.6 miles , c ) 4.8 miles , d ) 8 miles , e ) 10 miles
Rationale: "answer : b ) 6.6 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 4 * 20 / ( 4 + 20 ) = 6.6 m / hr the distance between schoolhome should be half of that . ie . 6.6 miles answer b"
Answer: b
Python program:
a = 1 / 4
b = 1 / 20
c = a + b 
d = 1 / c
e = d * const_1_6
Problem: an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 4 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 16 coaches are attached .
Options: a ) 66 , b ) 72 , c ) 80 , d ) 68 , e ) 73
Rationale: "1 . no . of coaches = 4 sqr root = 2 speed decreases by 12 12 = k * 2 k = 6 no . of coaches = 16 swr root = 4 decrease = 4 * 6 = 24 new speed = 90 - 24 = 66 a"
Answer: a
Python program:
a = math.sqrt(16)
b = 90 - 78
c = math.sqrt(4)
d = b / c
e = a * d
f = 90 - e
Problem: at what rate percent of simple interest will a sum of money double itself in 77 years ?
Options: a ) 6.54 % , b ) 2.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 1.29 %
Rationale: let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 77 ) = 100 / 77 = 1.29 % answer : e
Answer: e
Python program:
a = 100 / 77
Problem: what is the value of 10 ^ 7 - 6 ^ 5 ?
Options: a ) 99 , 91,223 , b ) 99 , 92,224 , c ) 99 , 94,265 , d ) 99 , 95,300 , e ) 99 , 96,307
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer b"
Answer: b
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 10
d = c / 100
Problem: dacid obtained 73 , 69 , 92 , 64 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 76
Rationale: "average = ( 73 + 69 + 92 + 64 + 82 ) / 5 = 380 / 5 = 76 answer : e"
Answer: e
Python program:
a = 73 + 69 
b = a + 92 
c = b + 64 
d = c + 82 
e = 10 / 2
f = d / e
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 30 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 66 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 130 / 100 = 78 in june total income = 78 + 40 = 118 % of mrs lee ' s income = 72 / 112 = 66.10 ( b )"
Answer: b
Python program:
a = 100 + 30 
b = 100 + 30 
c = b + 100 
d = a / c
e = d * 100
Problem: r and s together can plough a field in 10 hours but by himself r requires 15 hours . how long would s take to plough the same field ?
Options: a ) 24 hours , b ) 5 hours , c ) 10 hours , d ) 15 hours , e ) 20 hours
Rationale: f r and s together can do a piece of work in x days and r alone can do the same work in y days , then s alone can do the same work in x y / y â € “ x days . the no . of hours required by s = 10 ã — 20 / 20 â € “ 10 = 200 / 10 = 20 hours e
Answer: e
Python program:
a = 15 - 10
b = 15 + a
Problem: 36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203 . what is the first part ?
Options: a ) 19 , b ) 88 , c ) 267 , d ) 26 , e ) 28
Rationale: explanation : let the first part be x . 8 x + 3 ( 36 – x ) = 203 8 x + 108 – 3 x = 203 5 x + 108 = 203 5 x = 95 x = 19 answer : a
Answer: a
Python program:
a = 36 * 3
b = 203 - a
c = 8 - 3
d = b / c
Problem: roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be twice as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 160 , b ) 168 , c ) 176 , d ) 184 , e ) 192
Rationale: "r = j + 8 = k + 4 r + 2 = 2 ( j + 2 ) ( j + 8 ) + 2 = 2 j + 4 j = 6 r = 14 k = 10 in 2 years ( r + 2 ) ( k + 2 ) = 16 * 12 = 192 the answer is e ."
Answer: e
Python program:
a = 8 - 2
b = 8 + a 
c = b + 2 
d = 8 - 2
e = 8 + d 
f = 8 / 2
g = e - f
h = g + 2 
i = c * h
Problem: mike works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 500 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 62,500 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 13000 , b ) 12500 , c ) 13500 , d ) 14000 , e ) 15000
Rationale: let the rate be x , then population of the bacteria after each hour can be given as 500,500 x , 500 ( x ^ 2 ) , 500 ( x ^ 3 ) now population at 4 pm = 62,500 thus we have 500 ( x ^ 3 ) = 62,500 = 125 thus x = 5 therefore population at 3 pm = 500 ( 25 ) = 12500 answer : b
Answer: b
Python program:
a = 2 + 3 
b = a ** 2
c = b * 500
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 35 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 35 kg joins the group , total weight of boys = 20 x + 35 so 20 x + 35 = 21 ( x + 1 ) = > x = 14 . answer : b"
Answer: b
Python program:
a = 20 + 1 
b = 35 - a
c = b + 1
Problem: at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 1.75 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 1.75 = 7.02 - > ~ 7 . answer : a ."
Answer: a
Python program:
a = 12 - 80
b = a / 1
Problem: the ratio of number of boys and girls in a school is 3 : 5 . if there are 320 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 200 , e ) 280
Rationale: "let the number of boys and girls be 3 x and 5 x total students = 320 number of girls in the school = 5 * 320 / 8 = 200 answer is d"
Answer: d
Python program:
a = 320 / 3
b = a * 5
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.5 - 2 * 1.5 = 11.5 . answer : c ."
Answer: c
Python program:
a = 2 * 1
b = 14 - 5
Problem: a girl sitting in a train which is travelling at 100 kmph observes that a goods train travelling in a opposite direction , takes 6 seconds to pass him . if the goods train is 560 m long , find its speed .
Options: a ) 230 , b ) 232 , c ) 234 , d ) 236 , e ) 238
Rationale: "relative speed = ( 560 / 6 ) m / s = ( 560 / 6 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 100 = 236 kmph answer is e"
Answer: e
Python program:
a = 560 / 6
b = a / const_0_2778
c = b - 100
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 20 years , b ) 22 years , c ) 24 years , d ) 25 years , e ) 27 years
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 4 + 16 * 9 ) ] = ( 225 - 200 ) = 25 years . answer : d"
Answer: d
Python program:
a = 15 * 15
b = 4 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: a can do a piece of work in 10 days and b alone can do it in 15 days . how much time will both take to finish the work ?
Options: a ) 2 days , b ) 7 days , c ) 6 days , d ) 9 days , e ) 3 days
Rationale: "c 6 days time taken to finish the job = xy / ( x + y ) = 10 x 15 / ( 10 + 15 ) = 150 / 25 = 6 days"
Answer: c
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / c
Problem: in a class of 25 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.6
Rationale: "explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 17 * 45 = 1240 average marks of whole class = 1240 / 25 = 49.6 answer : option e"
Answer: e
Python program:
a = 3 + 5 
b = 25 - a
c = 45 * b
d = 95 * 5
e = c + d 
f = e / 25
Problem: if | 20 x - 10 | = 190 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 90
Rationale: "| 20 x - 10 | = 190 20 x - 10 = 190 or 20 x - 10 = - 190 20 x = 200 or 20 x = - 180 x = 10 or x = - 9 product = - 9 * 10 = - 90 answer is e"
Answer: e
Python program:
a = 190 - 10
b = 190 + 10 
c = a - b
d = c - 10
Problem: how many positive integers between 1 and 400 are there such that they are multiples of 25 ?
Options: a ) 12 , b ) 13 , c ) 16 , d ) 15 , e ) 11
Rationale: "multiples of 25 = 25 , 50,75 , - - - - - 400 number of multiples of 25 = > 25 * 16 = 400 answer is c"
Answer: c
Python program:
a = 400 - 1
b = a / 25
Problem: if the range w of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?
Options: a ) 0 , b ) 2 , c ) 12 , d ) 13 , e ) 15
Rationale: the range w of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d .
Answer: d
Python program:
a = 12 + 3 
b = 10 + 4 
c = b - 12
d = a - c
Problem: how many 7 digit number contain number 3 ?
Options: a ) 2748472 , b ) 3748472 , c ) 4748472 , d ) 5748472 , e ) 6748472
Rationale: "total 7 digit no . = 9 * 10 * 10 * 10 * 10 * 10 * 10 = 9000000 not containing 3 = 8 * 9 * 9 * 9 * 9 * 9 * 9 = 4251528 total 7 digit number contain 3 = 9000 - 4251528 = 4748472 answer : c"
Answer: c
Python program:
a = 1000 - 10
b = 7 * 7
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10