euclaise/mathqa_programs huggingface dataset:
Problem: last year , company x paid out a total of $ 1 , 050,000 in salaries to its 21 employees . if no employee earned a salary that is more than 8 % greater than any other employee , what is the lowest possible salary that any one employee earned ?
Options: a ) $ 40,000 , b ) $ 41,667 , c ) $ 42,000 , d ) $ 46 , 460.17 , e ) $ 60,000
Rationale: employee 1 earned $ x ( say ) employee 2 will not earn more than $ 1.08 x therfore , to minimize the salary of any one employee , we need to maximize the salaries of the other 20 employees ( 1.08 x * 20 ) + x = 1 , 050,000 solving for x = $ 46 , 460.17 answer d
Answer: d
Python program:
a = 8 / 100
b = a + 1 
c = 1000 + const_60 
d = c - 10
e = d * 1000
f = b * e
g = 21 - 1
h = 8 / 100
i = h + 1 
j = g * i
k = j + 1 
l = f / k
m = 8 / 100
n = m + 1 
o = l / n
p = o / 100
q = 100 * 2
r = q + 3 
s = p + r
Problem: a part - time employee ’ s hourly wage was increased by 40 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 29 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 40 % wage increase , the employee makes $ 1.40 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.40 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.40 to get : new # of hours = 100 / 1.40 ≈ 71 hours so , the number of hours decreases from 100 hours to ( approximately ) 71 hours . this represents a 29 % decrease ( approximately ) . answer : c"
Answer: c
Python program:
a = 40 / 100
b = 40 + 100 
c = b / 100
d = a / c
e = d * 100
Problem: a boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 9 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 1.85 kmph
Rationale: "rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate dowm stream = 1 / 9 * 60 = 6.7 kmph rate of the current = ½ ( 6.7 - 3 ) = 1.85 kmph answer : e"
Answer: e
Python program:
a = 1 / 9
b = a * const_60
c = 1 / 20
d = c * const_60
e = b - d
f = e / 2
Problem: if the selling price of 10 articles is same as the cost price of 12 articles . find the gain or loss percentage ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 32 % , e ) none
Rationale: "let the c . p of each article be re 1 . then , s . p of 10 articles = c . p of 12 articles = rs . 12 now , c . p of 10 articles = rs . 10 , s . p of 10 articles = rs 12 gain = rs ( 12 - 10 ) = rs 2 . gain % = ( 2 / 10 × 100 ) % = 20 % b )"
Answer: b
Python program:
a = 10 - 12
Problem: a man swims downstream 51 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8.5 , c ) 9.5 , d ) 6.5 , e ) 11.5
Rationale: "51 - - - 3 ds = 17 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 17 + 6 ) / 2 = 11.5 answer : e"
Answer: e
Python program:
a = 18 / 3
b = 51 / 3
c = a + b 
d = c / 2
Problem: a jar of 312 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "312 = 24 * 13 = 26 * 12 there are 24 people in the group today . the answer is d ."
Answer: d
Python program:
a = 312 * 2
b = a * 4
c = 2 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 2
g = f / 2
Problem: find the simple interest on rs . 422 for 3 months at 2 paisa per month ?
Options: a ) s . 27.5 , b ) s . 34 , c ) s . 26 , d ) s . 25.28 , e ) s . 25.32
Rationale: "explanation : i = ( 422 * 3 * 2 ) / 100 = 25.32 answer : option e"
Answer: e
Python program:
a = 3 / 100
b = 422 * a
Problem: the radius of a semi circle is 6.7 cm then its perimeter is ?
Options: a ) 32.75 , b ) 32.45 , c ) 22.45 , d ) 34.45 , e ) 32.15
Rationale: "36 / 7 r = 6.7 = 34.45 answer : d"
Answer: d
Python program:
a = circumface / (
b = a + 2
Problem: john was 19 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 8 of john ' s . how old is betty ?
Options: a ) 21 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "assume betty ' s age on marriage = x years . john ' s age on marriage = 19 john ' s age after 5 years = 24 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 24 ) = 21 therefore betty ' s current age = 21 option a"
Answer: a
Python program:
a = 7 / 8
b = 19 + 4 
c = a * b
Problem: a train 70 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 140 sec , b ) 160 sec , c ) 176 sec , d ) 150 sec , e ) 170 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 70 * 2 / 35 = 140 sec answer : a"
Answer: a
Python program:
a = 63 * 1000
b = 70 / a
c = b * 3600
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 10 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 10 more blue balls than white balls . . . equation # 2 : y = 10 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 10 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 10 ) = 100 5 y - 10 = 100 5 y = 110 y = 22 there are 22 blue balls . this is 10 more than the number of white balls , so z = 12 . that ' s the answer . just as a check , x = 66 , and 66 + 22 + 12 = 100 . answer = 12 , ( c )"
Answer: c
Python program:
a = 10 * 3
b = 100 - a
c = b / 4
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 21 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 120 , c ) $ 180 , d ) $ 220 , e ) $ 210
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 21 + 1.2 e = = > 11 a = 210 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 210 + 12 e = = > e = 210 e"
Answer: e
Python program:
a = 21 * 100
b = 12 + 1 
c = b * 10
d = 100 + 20 
e = c - d
f = a / e
Problem: at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 35 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 320 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000
Rationale: i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 8 ) + 30 ( y - 8 ) = r - . 25 r = > 20 x + 160 + 30 y - 240 = . 75 r = > 20 x + 30 y = . 75 r + 80 . . . . . . . . . . . . ( 2 ) so , r = . 75 r + 80 = > r = 320 the answer is a .
Answer: a
Python program:
a = 20 * 8
b = 30 * 8
c = a - b
d = negate / (
e = 35 / 100
f = d - e
Problem: in a group of houses , 40 had dogs , 30 had cats and 10 houses having both dogs and cats . what is the number of houses ?
Options: a ) 30 , b ) 60 , c ) 40 , d ) 45 , e ) 50
Rationale: make a venn diagram , and enter your data . let the number of houses be x 30 + 10 + 20 = x x = 60 so number of houses were = 60 answer b
Answer: b
Python program:
a = 40 + 30 
b = a - 10
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 8
Rationale: "required run rate = 282 - ( 3.2 x 10 ) = 250 = 6.25 40 40 b"
Answer: b
Python program:
a = 3 * 2
b = 282 - a
c = b / 40
Problem: the product of x and y is a constant . if the value of x is increased by 30 % , by what percentage must the value of y be decreased ?
Options: a ) 16 % , b ) 23.07 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.3 x ( 130 ) i . e . 130 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 130 = 76.92 i . e . y decreases from 100 to 76.92 i . e . decrease of 23.07 % b"
Answer: b
Python program:
a = 100 + 30 
b = 100 / a
c = 1 - b
d = c * 100
Problem: two employees a and b are paid a total of rs . 550 per week by their employer . if a is paid 120 percent of the sum paid to b , how much is b paid per week ?
Options: a ) rs . 150 , b ) rs . 190 , c ) rs . 200 , d ) rs . 250 , e ) rs . 300
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 550 ⇒ y [ 12 / 10 + 1 ] = 550 ⇒ 22 y / 10 = 550 ⇒ 22 y = 5500 ⇒ y = 5500 / 22 = 500 / 2 = rs . 250 d )"
Answer: d
Python program:
a = 120 / 100
b = a + 1 
c = 550 / b
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.6 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 3 , b ) 1 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.6 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.6 ) < = > k = 0.2 / 0.6 = 1 / 3 . required ratio = 1 / 3 : 1 = 1 : 3 . answer : b"
Answer: b
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that all three will miss ?
Options: a ) 3 / 8 , b ) 5 / 8 , c ) 7 / 16 , d ) 9 / 16 , e ) 23 / 32
Rationale: "the probability that all three will miss is 5 / 6 * 6 / 7 * 7 / 8 = 5 / 8 . the answer is b ."
Answer: b
Python program:
a = 1 / 7
b = 1 / 8
c = a * b
d = 1 / 6
e = 1 - d
f = c * e
Problem: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 9720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 3159 , d ) 2777 , e ) 2991
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 9720 32.5 k = 32.5 k / 100 k * 9720 = 3159 the number of valid votes polled in favour of b is 3159 . answer : c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = b * 9720
d = 15 * 9720
e = d / 100
f = c - e
g = f / 2
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 3 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 3 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 3 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 9 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 9 w = 9 the answer is c ."
Answer: c
Python program:
a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
Problem: the average runs scored by a batsman in 20 matches is 30 . in the next 10 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?
Options: a ) 25 , b ) 46 , c ) 88 , d ) 13 , e ) 12
Rationale: "total score of the batsman in 20 matches = 600 . total score of the batsman in the next 10 matches = 150 . total score of the batsman in the 30 matches = 750 . average score of the batsman = 750 / 30 = 25 . answer : a"
Answer: a
Python program:
a = 30 * 20
b = 15 * 10
c = a + b 
d = 20 + 10 
e = c / d
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 14 heads and 41 legs . how many cats does the ship host ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "sa ' s + co + ca + cats = 14 . sa ' s + 1 + 1 + cats = 14 or sa ' s + cats = 12 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 41 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 12 - cats + cat * 2 = 19 then cats = 7 c"
Answer: c
Python program:
a = 41 - 1
b = 14 - 1
c = b * 2
d = a - c
e = 14 - 1
f = e * 4
g = 14 - 1
h = g * 2
i = f - h
j = d / i
k = 14 - 1
l = j * k
Problem: a ladder learning against a wall makes an angle of 60 ° with the ground . if the length of the ladder is 19 m , find the distance of the foot of the ladder from the wall .
Options: a ) 9 m , b ) 9.5 m , c ) 10.5 m , d ) 12 m , e ) none
Rationale: let ab be the wall and bc be the ladder . then , < abc = 60 ° and , bc = 19 m . ; ac = x metres ac / bc = cos 60 ° = x / 19 = 1 / 2 x = 19 / 2 = 9.5 m . answer b
Answer: b
Python program:
a = 19 + 3 
b = 4 + 3 
c = a / b
d = 60 * c
e = const_60 * 3
f = d / e
g = cosine * (
Problem: 12.5 * 5.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 224 , d ) 646 , e ) 572
Rationale: "e 572 ? = 12.5 * 5.2 * 8.8 = 572"
Answer: e
Python program:
a = 12 * 5
Problem: if x + ( 1 / x ) = 5 , what is the value of t = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) t = 21 , b ) t = 22 , c ) t = 23 , d ) 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Python program:
a = 5 ** 2
b = a - 2
Problem: a certain company had a total annual expenditure of 2.1 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 50,000
Rationale: "given : total annual expenditure of 2.1 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 5 = 2100 therefore try to bring the numerator in terms of 2100 average salary = ( 2100 * 10 ^ 4 ) / 420 = 5 * 10 ^ 4 = 50,000 option e"
Answer: e
Python program:
a = 10 * 7
b = 2 * 1
c = b / 420
d = c * 100
Problem: on dividing 181 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 20
Rationale: "d = ( d - r ) / q = ( 181 - 1 ) / 9 = 180 / 9 = 20 e )"
Answer: e
Python program:
a = 181 / 9
b = math.floor(a)
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 9 . the true discount is
Options: a ) rs . 75 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 9 x 100 / 12 x 1 ) = rs . 75 . answer a"
Answer: a
Python program:
a = 12 / 100
b = 9 / a
Problem: a farmer spent $ 36 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.60 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 36 = $ 14.4 on chicken feed , thus he spent the remaining 36 - 14.4 = $ 21.6 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14.4 - - > x = $ 18 therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 18 + 21.6 = $ 39.6 . answer : d ."
Answer: d
Python program:
a = 40 / 100
b = 36 * a
c = b + 36
Problem: a garrison of 300 men had a provision for 31 days . after 28 days 280 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 45 days , b ) 55 days , c ) 35 days , d ) 25 days , e ) 40 days
Rationale: "400 - - - 31 400 - - - 3 120 - - - ? 300 * 3 = 20 * x = > x = 45 days answer : a"
Answer: a
Python program:
a = 31 - 28
b = a * 300
c = b / 280
Problem: what is the speed of the stream if a canoe rows upstream at 6 km / hr and downstream at 10 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph
Rationale: sol . speed of stream = 1 / 2 ( 10 - 6 ) kmph = 2 kmph . answer d
Answer: d
Python program:
a = 10 - 6
b = a / 2
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 25 % . what was its profit on the items sold in february ?
Options: a ) 12.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.75 * 150 x = 112.5 x hence total profit = 12.5 % option a"
Answer: a
Python program:
a = 100 - 25
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 100 , e ) 11
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 5 = rs . 100 . answer : d"
Answer: d
Python program:
a = 8925 / 85
b = a - 5
Problem: the length of a rectangle is halved , while its breadth is tripled . wa tis the % changein area ?
Options: a ) 34 %
b ) 45 %
c ) 50 %
d ) 60 %
e ) 67 %
Rationale: let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c
Answer: c
Python program:
a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
Problem: if k ^ 3 is divisible by 84 , what is the least possible value of integer k ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 56 , e ) 60
Rationale: "k ^ 3 = 84 * x = 2 ^ 2 * 3 * 7 * x the factors of k must at minimum include 2 * 3 * 7 = 42 . the answer is b ."
Answer: b
Python program:
a = 84 / 2
b = a / 2
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 5 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 450 km , b ) 500 km , c ) 360 km , d ) 550 km , e ) 600 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bike in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 5 h is 90 × 5 = 450 km ans . ( a )"
Answer: a
Python program:
a = 4 / 5
b = 1 + a 
c = 575 / 23
d = 2 * c
e = b * d
f = e * 5
Problem: a train 650 m long is running at a speed of 117 km / hr . in what time will it pass a bridge 325 m long ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "speed = 117 * 5 / 18 = 65 / 2 m / sec total distance covered = 650 + 325 = 975 m required time = 975 * 2 / 65 = 30 sec answer : a"
Answer: a
Python program:
a = 117 - 325
b = a * const_0_2778
c = 650 / b
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 363 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 101 , e ) 1322
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 363 3 b 2 = 363 b 2 = 121 = 11 ( b > 0 ) b = 11 m . answer : a"
Answer: a
Python program:
a = 363 / 3
b = math.sqrt(a)
Problem: in a class of 40 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "answer let a be the set of students who have enrolled for english and b be the set of students who have enrolled for german . then , ( a u b ) is the set of students who have enrolled at least one of the two subjects . as the students of the class have enrolled for at least one of the two subjects , a u b = 40 we know a u b = a + b - ( a n b ) i . e , 40 = a + 22 - 12 or a = 30 which is the set of students who have enrolled for english and includes those who have enrolled for both the subjects . however , we need to find out the number of students who have enrolled for only english = students enrolled for english - students enrolled for both german and english = 30 - 12 = 18 . choice is ( c )"
Answer: c
Python program:
a = 40 + 12 
b = a - 22
c = b - 12
Problem: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 98 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 50 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after some water evaporates the cucumbers become 98 % water and 2 % of non - water , so now 1 pound of non - water composes 2 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.02 = 50 pounds . answer : b ."
Answer: b
Python program:
a = 100 - 99
b = 100 - 98
c = a / b
d = c * 100
Problem: how much 60 % of 50 is greater than 45 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 16.5 , d ) 17 , e ) 12
Rationale: "( 60 / 100 ) * 50 – ( 45 / 100 ) * 30 30 - 13.5 = 16.5 answer : c"
Answer: c
Python program:
a = 60 * 50
b = a / 100
c = 45 * 30
d = c / 100
e = b - d
Problem: rectangular tile each of size 50 cm by 40 cm must be laid horizontally on a rectangular floor of size 120 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 9 , b ) 15 , c ) 12 , d ) 11 , e ) 10
Rationale: "area of tile = 50 * 40 = 2000 area of floor = 120 * 150 = 18000 no of tiles = 18000 / 2000 = 9 so , the no of tile = 9 answer : a"
Answer: a
Python program:
a = 120 * 150
b = 50 * 40
c = a / b
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 60 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 60 / 50 = 18 minutes to print 60 pages ( answer b )"
Answer: b
Python program:
a = 4 * 2
b = a + 4 
c = 60 * b
d = c / 40