euclaise/mathqa_programs huggingface dataset:
Problem: set a of 8 positive integers may have the same element and have 36 . and set b of 8 positive integers must have different elements and have 36 . when m and n are the greatest possible differences between 36 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 36 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 29 and 36 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 8 . so , 29 - 8 = 21 . the correct answer is b .
Answer: b
Python program:
a = 8 + 2 
b = a + 8 
c = 36 - b
Problem: how many times digit 6 is used while writing numbers from 100 to 1100 ?
Options: a ) 648 , b ) 320 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 320 . hence b ."
Answer: b
Python program:
a = 1100 - 100
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 6 * 2
h = f + g
Problem: what is the total cost of 2 sandwiches at $ 3.49 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.46 , e ) $ 11.85
Rationale: "answer = d 2 * 3.49 + 4 * 0.87 = 2 ( 3.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 7 + 4 - 0.02 - 0.52 = 11 - 0.54 = 10.46"
Answer: d
Python program:
a = 2 * 3
b = 4 * 0
c = a + b
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 7 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 2 : 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 * 7 w 10 + 5 x = 7 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is e"
Answer: e
Python program:
a = 7 - 5
b = 10 - 7
c = a / b
Problem: find the ratio in which rice at rs . 7.00 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 6 : 7 , e ) none of these
Rationale: "solution required ratio = 60 : 70 = 6 : 7 answer d"
Answer: d
Python program:
a = 6 - 30
b = 7 - 0
c = a / b
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 6 ) and ( 9 , 6 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 3 , b ) 2 , c ) 1 / 4 , d ) 3 / 5 , e ) 5 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 3 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 3 ) is 3 / 5 . the answer is d ."
Answer: d
Python program:
a = 9 - 1
b = a + 6 
c = b / 6
d = 1 / c
Problem: calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 5 , 6 , 10 and 12 seconds . ?
Options: a ) 61 , b ) 60 , c ) 79 , d ) 70 , e ) 78
Rationale: "lcm of 5 , 6 , 10 and 12 is 60 lcm = 60 answer : b"
Answer: b
Python program:
a = 10 / 2
b = 5 * 6
c = a * b
Problem: a water tank is one - fifth full . pipe a can fill a tank in 15 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the combined rate of filling / emptying the tank = 1 / 15 - 1 / 6 = - 1 / 10 since the rate is negative , the tank will be emptied . a full tank would take 10 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 10 = 2 minutes the answer is a ."
Answer: a
Python program:
a = 1 + 4 
b = 1 / a
c = 1 / 6
d = 1 / 15
e = c - d
f = 1 / e
g = b * f
Problem: a jar contains 4 black and 3 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Rationale: "p ( 1 st black , 2 nd white ) = 4 / 7 * 3 / 6 = 4 / 14 ; p ( 1 st white , 2 nd black ) = 3 / 7 * 4 / 6 = 4 / 14 . p = 4 / 14 + 4 / 14 = 4 / 7 . answer : c ."
Answer: c
Python program:
a = 4 + 3 
b = 4 / a
c = 4 + 3 
d = c - 1
e = 3 / d
f = b * e
Problem: a can do a work in 3 days . b can do the same work in 6 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 3 b rate = 1 / 6 ( a + b ) rate = ( 1 / 3 ) + ( 1 / 6 ) = 1 / 2 a & b finish the work in 2 days correct option is d"
Answer: d
Python program:
a = 3 * 6
b = 3 + 6 
c = a / b
Problem: in an it company , there are a total of 100 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 50 , c ) 55 , d ) 35 , e ) 65
Rationale: "you could pick 50 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 55 . c"
Answer: c
Python program:
a = 80 - 100
b = 50 - 35
c = a + b
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 390 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 84 , b ) 96 , c ) 104 , d ) 112 , e ) 120
Rationale: "the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 390 = 104 the answer is c ."
Answer: c
Python program:
a = 3 * 2
b = a + 4 
c = b + 5 
d = 390 / c
e = d * 4
Problem: a train 280 m long , running with a speed of 36 km / hr will pass a tree in
Options: a ) 12 sec , b ) 15 sec , c ) 16 sec , d ) 28 sec , e ) none
Rationale: "sol . speed = ( 36 x 5 / 18 ) m / sec . = 10 m / sec . time taken = ( 280 x 1 / 10 ) sec = 28 sec answer d"
Answer: d
Python program:
a = 36 * 1000
b = 280 / a
c = b * 3600
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 4 , then v =
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 4 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 9 the answer is b ."
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 4 / b
d = 1 / 3
e = 1 - d
f = c / e
Problem: a person buys an article at rs . 340 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 600 , b ) 882 , c ) 374 , d ) 356 , e ) 521
Rationale: "cost price = rs . 340 profit = 10 % of 340 = rs . 34 selling price = cost price + profit = 340 + 34 = 374 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 340 * a
c = 340 + b
Problem: on dividing 12401 by a certain number , we get 76 as quotient and 13 as remainder . what is the divisor ?
Options: a ) 163 , b ) 785 , c ) 852 , d ) 456 , e ) 852
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 12401 - 13 ) / 76 = 163 answer ( a )"
Answer: a
Python program:
a = 12401 - 13
b = a / 76
Problem: the average of the marks of 10 students in a class is 40 . if the marks of each student are doubled , find the new average ?
Options: a ) 78 , b ) 56 , c ) 80 , d ) 27 , e ) 40
Rationale: "sum of the marks for the 10 students = 10 * 40 = 400 . the marks of each student are doubled , the sum also will be doubled . the new sum = 400 * 2 = 800 . so , the new average = 800 / 10 = 80 . answer : c"
Answer: c
Python program:
a = 40 * 2
Problem: how much interest will $ 10,000 earn in 9 months at an annual rate of 6 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 650
Rationale: "soln : - 9 months = 3 / 4 of year ; 6 % = 6 / 100 = 3 / 50 ; $ 10,000 ( principal ) * 3 / 50 ( interest rate ) * 3 / 4 ( time ) = $ 450 . answer : c"
Answer: c
Python program:
a = 100 ** 2
b = 4 / 0
c = a * b
d = 3 / 6
e = c * d
Problem: what is the sum of the greatest common factor and the lowest common multiple of 72 and 36 ?
Options: a ) 120 , b ) 150 , c ) 145 , d ) 108 , e ) 112
Rationale: "prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 72 = 2 x 2 x 2 x 3 x 3 gcf = 36 lcm = 72 sum = 108 ans : d"
Answer: d
Python program:
a = 72 * 36
b = a / 4
Problem: at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 19.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 13.7 , b ) 14.0 , c ) 14.3 , d ) 14.6 , e ) 14.9
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 19.6 x ^ 2 = 1.96 x = 1.4 at 4 : 00 pm , the amount of bacteria was 10 ( 1.4 ) = 14 grams . the answer is b ."
Answer: b
Python program:
a = 19 / 6
b = math.sqrt(a)
c = b * 10
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 350 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 20289 , d ) 17500 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 350 = > x = 17500 answer : d"
Answer: d
Python program:
a = 5 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 10 / 100
f = 20 / 100
g = e * f
h = d - g
i = 350 / h
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( e ) ."
Answer: e
Python program:
a = 480 / 3840
b = a * 100
c = b * 100
d = c / 60
Problem: if 3 spiders make 3 webs in 3 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 3 webs 3 : 1 1 x 3 x x = 3 x 1 x 3 = > x = 3 answer is e"
Answer: e
Python program:
a = 1 * 3
Problem: three machines , each working at the same constant rate , together can complete a certain job in 18 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 9 days ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 8
Rationale: "rate of one machine = 1 job / ( 18 * 3 ) days let x = number of machines needed to complete the job in 9 days 1 / ( 3 * 18 ) * 9 * x = 1 job x = 6 6 - 3 = 3 answer : a"
Answer: a
Python program:
a = 4 + 1 
b = 18 * a
c = b / 9
d = 4 + 1 
e = c - d
Problem: light glows for every 30 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 142 times , c ) 382 times , d ) 392 times , e ) 165 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 30 ) = 165 times . answer : e"
Answer: e
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 30
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 2 : 5 . the first number is :
Options: a ) a ) 33 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 2 : 5 x = 11 = > 3 x = 33 answer : a"
Answer: a
Python program:
a = 3 * 5
b = 9 / a
c = 3 * b
d = 3 * 5
e = 9 / d
f = 5 * e
g = c + f
Problem: a man is 35 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 33 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 35 ) + 2 = 2 ( x + 2 ) x + 37 = 2 x + 4 x = 33 . answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 35 - b
d = 2 - 1
e = c / d
Problem: p and q invested in a business . the profit earned was divided in the ratio 4 : 6 . if p invested rs 60000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 90000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 60000 : q = 4 : 6 ⇒ 60000 × 6 = 4 q ⇒ q = ( 60000 × 6 ) / 4 = 90000 answer is c ."
Answer: c
Python program:
a = 60000 / 4
b = a * 6
Problem: on charlie ' s cell phone plan , he signed up for 8 gb of data per 4 week period . if he went over the 8 gb per month , it would cost him an extra $ 10.00 per gb . in the first week , he used 2 gb ; in the 2 nd week , he used 3 gb ; in the 3 rd week , he used 5 gb ; and in the 4 th week , he used a whopping 10 gb . how much extra did charlie need to pay on his cell phone bill ?
Options: a ) $ 120 , b ) $ 40 , c ) $ 80 , d ) $ 100 , e ) $ 140
Rationale: to determine how much extra he would need to pay , you have to add all 4 weeks of gb usage ( 2 + 3 + 5 + 10 = 20 ) . to determine the extra amount of gb usage , you have to subtract the the original amount of gb ( 8 ) allowed on his plan . 20 - 8 = 12 to determine the extra cost on his cell phone plan , you have to multiply $ 10.00 per extra usage ( 12 ) for a total of $ 120.00 . the correct answer is a
Answer: a
Python program:
a = 2 + 3 
b = a + 5 
c = b + 10 
d = c - 8
e = d * 10
Problem: a pipe can fill a cistern in 44 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 4 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 44 minutes 1 / 11 part filled in = 44 * 1 / 11 = 4 minutes answer is a"
Answer: a
Python program:
a = 1 / 11
b = 44 * a
Problem: 0.0003 x 0.3 = ?
Options: a ) 0.0009 , b ) 9.0 e - 05 , c ) 0.09 , d ) 0.009 , e ) 9.0
Rationale: "3 x 3 = 9 . sum of decimal places = 5 0.0003 x 0.3 = 0.00009 answer : option b"
Answer: b
Python program:
a = 0 / 3
b = a * 100
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams e ?
Options: a ) e = 16 , b ) e = 32 , c ) e = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Python program:
a = 8 * 4
Problem: a train running at the speed of 54 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 150 meter , b ) 105 meter , c ) 140 meter , d ) 135 meter , e ) none of these
Rationale: "explanation : speed = 54 * ( 5 / 18 ) m / sec = 15 m / sec length of train ( distance ) = speed * time = 15 * 7 = 105 meter option b"
Answer: b
Python program:
a = 54 * 1000
b = a / 3600
c = b * 7
Problem: what will be the fraction of 25 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 25 * 1 / 100 = 1 / 4 option a"
Answer: a
Python program:
a = 25 / 2
b = circle_area / (
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 4
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 12 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 4 = 1.25 so biggest is 5 / 4 and smallest is 2 / 3 their difference is 5 / 4 - 2 / 3 = 7 / 12 option c"
Answer: c
Python program:
a = 4 / 5
b = 2 / 3
c = a - b
Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 5 : 8
b ) 3 : 2
c ) 6 : 1
d ) 8 : 7
e ) 5 : 6
Rationale: let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 4 y and y . 2 ( 3 x + 2 x ) = 2 ( 4 y + y ) 5 x = 5 y x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 4 y * y = 6 x ^ 2 : 4 y ^ 2 = 6 x ^ 2 : 4 x ^ 2 = 6 : 4 = 3 : 2 the answer is b .
Answer: b
Python program:
a = rectangle_area / (
Problem: if the sides of a triangle are 26 cm , 24 cm and 20 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 288 , d ) 266 , e ) 240
Rationale: "the triangle with sides 26 cm , 24 cm and 20 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 20 = 240 cm 2 answer : e"
Answer: e
Python program:
a = 24 * 20
b = a / 2
Problem: it takes 40 identical printing presses 9 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "40 printing presses can do 1 / 9 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 9 = 1 / 12 of the job each hour . the answer is d ."
Answer: d
Python program:
a = 1000 / 2
b = a * 1000
c = 1000 / 2
d = c * 1000
e = d / 40
f = e / 9
g = f * 30
h = b / g
Problem: the average age of 15 students of a class is 16 years . out of these , the average age of 6 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 10 years , b ) 11 years , c ) 12 years , d ) 13 years , e ) 14 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 6 + 16 * 9 ) ] = ( 240 - 228 ) = 12 years . answer : c"
Answer: c
Python program:
a = 15 * 15
b = 6 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 6 inches wide on each side , the total area would have been ( m + 200 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 12 ) ( y + 12 ) = m and so ( 2 ) xy + 12 x + 12 y + 144 = m + 200 let ' s subtract equation ( 1 ) from equation ( 2 ) . 10 x + 10 y + 140 = 200 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b
Python program:
a = 6 * 2
b = a ** 2
c = 1 * 2
d = c ** 2
e = b - d
f = 200 - e
g = f / 2
Problem: how many numbers between 100 and 600 are divisible by 2 , 3 , and 7 together ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 600 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 600 : 600 / 42 = 14.28 hence , 42 * 14 = 588 is the last number divisible by 42 within 600 hence , total numbers divisible by 2 , 3 , 7 together are ( 14 – 2 ) = 12 answer : b"
Answer: b
Python program:
a = 2 * 3
b = a * 7
c = 600 / b
d = 2 * 3
e = d * 7
f = 100 / e
g = c - f
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 5 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 22 hr , d ) 24 hr , e ) 26 hr
Rationale: work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 5 ) = 1 / 22 leak will empty the tank in 22 hrs . answer : c
Answer: c
Python program:
a = 1 / 2
b = 2 * 5
c = b + 1 
d = c / 5
e = 1/(d)
f = a - e
g = 1/(f)
Problem: the salary of a labourer increase consistently by 40 % per year . if his present salary is rs . 3000 then what will his salary be after 3 years ?
Options: a ) 8232 , b ) 3282 , c ) 4282 , d ) 8242 , e ) 2382
Rationale: explanation : salary = 3000 x 1.4 x 1.4 x 1.4 = 8232 answer : option a
Answer: a
Python program:
a = 40 / 100
b = 1 + a 
c = b ** 3
d = 3000 * c
Problem: in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 30 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 35 % , b ) 48 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 3 x not job of choice w / o diploma = . 7 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 30 % of 60 % = 18 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 10 % = 30 % ) . 30 % + 18 % = 48 % . therefore 48 % of the people in country z have a diploma . ans b
Answer: b
Python program:
a = 100 - 40
b = 30 * a
c = b / 100
d = 40 - 10
e = c + d
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 50 per square m ?
Options: a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 47500
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 50 * 950 = rs . 47500 e"
Answer: e
Python program:
a = 20 * 15
b = a * 2
c = b * 50
d = 20 * 5
e = d * 2
f = e * 50
g = c + f 
h = 15 * 5
i = h * 2
j = i * 50
k = g + j
Problem: there is a 55 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 55 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: only the prime numbers greater than 10 and less than 55 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , and 53 . the total is 12 . the answer is e .
Answer: e
Python program:
a = 10 + 2