euclaise/mathqa_programs huggingface dataset:
Problem: a cuban cigar would cost 3 dollar less than 1.5 times a french cigar , had the french cigar cost 0.7 dollar less than it does now . an arabian cigar costs 50 cents more than 1.5 times the cuban cigar . the 3 cigars together cost 74.7 dollars . what is the price of the french cigar ?
Options: a ) 19.7 $ . , b ) 23 $ . , c ) 14.7 $ . , d ) 35 $ . , e ) 37.4 $ .
Rationale: the three cigars together cost 74.7 dollars . if each cost the same , they would have cost a little less than 25 dollars each . from the given data we know french cigar < cuban cigar < arabic cigar and each is more expensive 1.5 times . therefore eliminate options a , d , e straightaway . since french cigar is at least 1.5 times cheaper we know b can not be the answer . therefore c is the answer .
Answer: c
Python program:
a = 1 * 5
b = a + 3 
c = 1 * 5
d = c + 3 
e = 1 * 5
f = 50 / 100
g = e - f
h = b + g 
i = 74 - 7
j = 1 * 5
k = 1 + 5 
l = k + 1 
m = i / l
n = m + 0
Problem: the salary of a worker is first increased by 15 % and afterwards reduced by 15 % . what is the net change in the worker ' s salary ?
Options: a ) 5.25 % increase , b ) 5.25 % decrease , c ) 2.25 % increase , d ) 2.25 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.85 ( 1.15 x ) = 0.9775 x the answer is d ."
Answer: d
Python program:
a = 15 + 100 
b = 15 + 100 
c = b * 15
d = c / 100
e = a - d
f = 100 - e
Problem: a company decreased the price of its main product by 25 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 2.0 , b ) 4.0 , c ) 5.0 , d ) 6.0 , e ) 8.0
Rationale: "for the total revenue to remain the same when the price is one fourth , the number of products sold must four times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 25 % = 4.0 answer : b"
Answer: b
Python program:
a = 100 / 25
Problem: a firm is comprised of partners and associates in a ratio of 2 : 63 . if 35 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 7 of the increase in 35 associates . the ratio changed from 14 : 441 to 14 : 476 . thus the number of partners is 14 . the answer is b ."
Answer: b
Python program:
a = 34 * 2
b = a - 63
c = 35 / b
d = c * 2
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 9 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "area of first rectangle is 12 * 15 = 180 hence area of second would be 9 x = 180 x x = 20 answer is d"
Answer: d
Python program:
a = rectangle_area / (
Problem: x starts a business with rs . 45000 . y joins in the business after 6 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 1 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 30000 × 6 = 45 × 12 : 30 × 6 = 3 × 12 : 2 × 6 = 3 : 1 answer is c"
Answer: c
Python program:
a = 45000 * 12
b = 4 + 3 
c = 30000 * b
d = a / c
Problem: sam invested $ 1000 @ 20 % per annum for one year . if the interest is compounded half yearly , then the amount received by sam at the end of the year will be ?
Options: a ) $ 1542 , b ) $ 1145 , c ) $ 1210 , d ) $ 1642 , e ) $ 1020
Rationale: "p = $ 1000 r = 20 % p . a . = 10 % t = 2 half years amount = 1000 * ( 1 + 10 / 100 ) ^ 2 = 1000 * 11 / 10 * 11 / 10 = $ 1210 answer is c"
Answer: c
Python program:
a = 4 + 1 
b = a / 100
c = b + 1 
d = c * 1000
e = 4 + 1 
f = e / 100
g = f + 1 
h = d * g
Problem: solve below question 3 x - 5 = - 20
Options: a ) - 8 , b ) - 9 , c ) - 5 , d ) - 4 , e ) 1
Rationale: 1 . subtract 1 from both sides : 3 x - 5 + 5 = - 20 + 5 2 . simplify both sides : 3 x = - 15 3 . divide both sides by 3 : 4 . simplify both sides : x = - 5 c
Answer: c
Python program:
a = 20 + 5 
b = negate / (
Problem: the average of runs of a cricket player of 10 innings was 30 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 74 , c ) 10 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 34 required number of runs = ( 34 * 11 ) - ( 30 * 10 ) = 374 - 300 = 74 . answer : b"
Answer: b
Python program:
a = 10 + 1 
b = 4 + 30 
c = a * b
d = 10 * 30
e = c - d
Problem: if 30 % of a number is equal to one - fourth of another number , what is the ratio of first number to the second number ?
Options: a ) 4 : 7 , b ) 6 : 5 , c ) 1 : 2 , d ) 2 : 3 , e ) 5 : 6
Rationale: let 30 % of a = 1 / 4 b . then , 30 a / 100 = 1 b / 4 = > 3 a / 10 = 1 b / 4 a / b = ( 1 / 4 * 10 / 3 ) = 5 / 6 a : b = 5 : 6 . answer : e
Answer: e
Python program:
a = 1 / 4
b = 30 / 100
c = a / b
Problem: a cistern is two - third full of water . pipe a can fill the remaining part in 12 minutes and pipe b in 8 minutes . once the cistern is emptied , how much time will they take to fill it together completely ?
Options: a ) 12 minutes , b ) 12.5 min , c ) 14.4 min , d ) 10.2 min , e ) 14.66 min
Rationale: as pipe a takes 12 min . to fill remaining one - third it takes 36 min . to fill completely . similarly pipe b takes 24 min . to fill completely so , total time taken by both together is reciprocal of : ( 1 / 36 ) + ( 1 / 24 ) = 5 / 72 ans : 14.4 min . answer : c
Answer: c
Python program:
a = 12 * 3
b = 8 * 3
c = a * b
d = 12 * 3
e = 8 * 3
f = d + e 
g = c / f
Problem: what should be added to 5021 so that it may become a perfect square ?
Options: a ) 20 , b ) 23 , c ) 26 , d ) 27 , e ) 29
Rationale: "71 x 71 = 5041 5041 - 5021 = 20 if added to 20 get perfect square answer = a"
Answer: a
Python program:
a = 10 + 10 
b = 10 + 10 
c = a + b 
d = 10 + 10 
e = c + d 
f = 4 + 3 
g = e + f 
h = 10 + 10 
i = 10 + 10 
j = h + i 
k = 10 + 10 
l = j + k 
m = 4 + 3 
n = l + m 
o = g * n
p = o - 5021
Problem: when a student joe , weighing 44 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5.5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 7 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 44 + 30 = 74 so , the average the two persons = 37 that gives the answer 44 - 37 = 7 answer e"
Answer: e
Python program:
a = 30 + 1 
b = 44 - a
c = 30 * b
d = c + 44 
e = 30 + 1 
f = 44 - e
g = f - 1
h = g * 30
i = d - h
j = i / 2
k = 44 - j
Problem: 70 is what percent of 125 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 56 %
Rationale: 70 / 125 × 100 = 56 % answer : e
Answer: e
Python program:
a = 70 / 125
b = a * 100
Problem: ( 525 + 275 ) ã — 4 ã — ( 3 + 2 ) = ?
Options: a ) 12000 , b ) 24000 , c ) 16000 , d ) 14000 , e ) 16200
Rationale: "( 525 + 275 ) ã — 4 ã — ( 3 + 2 ) = ? or , ? = 800 ã — 4 ã — 5 = 16000 answer c"
Answer: c
Python program:
a = 525 + 275 
b = a / 4
Problem: if a 2 - b 2 = 8 and a * b = 2 , find a 4 + b 4 .
Options: a ) 62 , b ) 72 , c ) 82 , d ) 92 , e ) 62
Rationale: "a 2 - b 2 = 8 : given a 4 + b 4 - 2 a 2 b 2 = 82 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 82 : substitute a 4 + b 4 = 72 correct answer b"
Answer: b
Python program:
a = 8 ** 2
b = 2 ** 2
c = b * 2
d = a + c
Problem: when positive integer x is divided by positive integer y , the remainder is 5.76 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 5.76 - - > x = qy + 5.76 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 5.76 - - > y = 48 . answer : c ."
Answer: c
Python program:
a = math.floor(96, 12)
b = 96 - 12
c = 5 / 76
Problem: timothy leaves home for school , riding his bicycle at a rate of 6 miles per hour . fifteen minutes after he leaves , his mother sees timothy ’ s math homework lying on his bed and immediately leaves home to bring it to him . if his mother drives at 36 miles per hour , how far ( in terms of miles ) must she drive before she reaches timothy ? i think is a 700 level problem but i tag it as 600 / 700 , let me know . either way i hope in an explanationthanks
Options: a ) 1 / 3 , b ) 9 / 5 , c ) 4 , d ) 9 , e ) 12
Rationale: in 15 mins , timothy travels = 6 / 4 miles . now , let his mother takes x hours to reach him , traveling at 36 mph . so , 36 x = 6 x + 6 / 4 x = 1 / 20 hrs . thus , the distance traveled by his mother to reach = 36 * 1 / 20 = 9 / 5 miles . ans b
Answer: b
Python program:
a = 36 - 6
b = 4 * a
c = 6 / b
d = c * 36
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 ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 20 2 x = 20 x = 10 . answer : d"
Answer: d
Python program:
a = 20 - 4
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 55 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 13 sec , d ) 67 sec , e ) 11 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 55 d = 55 * 100 / 18 = 2750 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2750 / 9 * 18 / 500 = 11 sec answer : e"
Answer: e
Python program:
a = 60 - 40
b = const_0_2778 * a
c = b * 55
d = 60 + 40 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: the instructions state that cheryl needs 5 / 9 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 24 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 5 / 9 , e ) 2 1 / 9
Rationale: "total bought = 5 / 9 + 1 / 3 left part 8 / 24 - - - > 1 / 3 so used part 5 / 9 + 1 / 3 - 1 / 3 = 5 / 9 answer : d"
Answer: d
Python program:
a = 5 / 9
b = 1 / 3
c = a + b 
d = 8 / 24
e = c - d
Problem: what is the value of n if the sum of the consecutive odd intergers q from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Python program:
a = math.sqrt(169)
b = a * 2
c = 2 * 1
d = b - c
e = d + 1
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 30 % solution ?
Options: a ) a ) 6.7 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 28.6
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 30 / 100 100 + 10 x = 300 + 3 x 7 x = 200 x = 28.6 answer is e"
Answer: e
Python program:
a = 30 - 10
b = 30 / 100
c = 1 - b
d = a / c
Problem: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 3600 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2299 , b ) 2699 , c ) 3000 , d ) 6725 , e ) 2601
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 3600 ( 100 / 120 ) = rs . 3000 answer : c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 3600 / b
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 11 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 13.5 , c ) 14 , d ) 14.5 , e ) 15.3
Rationale: "ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 12 ) + ( x / 11 ) ) = 15.3 ( formula avg speed = total distance / total time )"
Answer: b
Python program:
a = 11 * 10
b = 11 * 10
c = b / 2
d = a + c 
e = 11 * 10
f = e / 12
g = 11 * 10
h = g / 2
i = h / 11
j = f + i 
k = d / j
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 30 % on his income , while mindy pays a rate of only 20 % on hers . if mindy earned 3 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 22.5 %
Rationale: say morks income is - 100 so tax paid will be 30 say mindys income is 3 * 100 = 300 so tax paid is 20 % * 300 = 60 total tax paid = 30 + 60 = 90 . combined tax % will be 90 / 100 + 300 = 22.5 %
Answer: e
Python program:
a = 30 / 100
b = 20 / 100
c = 3 * b
d = a + c 
e = 1 + 3 
f = d / e
g = 100 * f
Problem: sahil purchased a machine at rs 9000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22500 , b ) rs . 24500 , c ) rs . 26500 , d ) rs . 28500 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 9000 + 5000 + 1000 = 15000 150 % of 15000 = 150 / 100 * 15000 = 22500 option a"
Answer: a
Python program:
a = 9000 + 5000 
b = a + 1000 
c = 9000 + 5000 
d = c + 1000 
e = d / 100
f = e * 50
g = b + f
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 15 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 525 , b ) 500 , c ) 510 , d ) 530 , e ) 550
Rationale: "( 3500 * 5 * 3 ) / 100 = > 525 answer : a"
Answer: a
Python program:
a = 3500 * 15
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: two twins sisters sita and geeta were standing back to back and suddenly they started running in opposite directions for 10 km each . then they turned left and ran for another 7.5 km . what is the distance ( in kilometers ) between the the two twins when they stop ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 30
Rationale: the distance between them is the hypotenuse of a right angle triangle with sides 15 km and 20 km . the hypotenuse = sqrt ( 15 ^ 2 + 20 ^ 2 ) = 25 the answer is c .
Answer: c
Python program:
a = 7 * 5
b = a ** 2
c = 10 * 2
d = c ** 2
e = b + d 
f = math.sqrt(e)
Problem: a train running at the speed of 30 km / hr crosses a pole in 6 sec . what is the length of the train ?
Options: a ) 20 m , b ) 70 m , c ) 50 m , d ) can not be determined , e ) none of these
Rationale: "speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 6 = 50 m answer : c"
Answer: c
Python program:
a = 30 * 1000
b = a / 3600
c = b * 6
Problem: in how many ways can the integer 15 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: 15 = 3 * 5 since 15 is not a perfect square , no of ways = 2 answer e
Answer: e
Python program:
a = 15 / 1
b = a / 3
c = b - 3
Problem: if 5 x + 3 = 10 x – 17 , what is the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "solve for x : 5 x + 3 = 10 x - 17 20 = 5 x 4 = x correct answer d ) 4"
Answer: d
Python program:
a = 3 + 17 
b = 10 - 5
c = a / b
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.8 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 108 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.018 ) m 3 = 0.108 m 3 . mass of man = volume of water displaced × density of water = ( 0.108 × 1000 ) kg = 108 kg . answer c"
Answer: c
Python program:
a = 3 * 2
b = 1 / 8
c = a * b
d = c * 1000
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 36 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 766 min , b ) 656 min , c ) 144 min , d ) 877 min , e ) 555 min
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 36 4 / x = 1 / 36 = > x = 144 min . answer : c"
Answer: c
Python program:
a = 1 + 4 
b = a * 36
Problem: a batsman scored 150 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: "number of runs made by running = 150 - ( 3 x 4 + 8 x 6 ) = 150 - ( 60 ) = 90 now , we need to calculate 60 is what percent of 120 . = > 90 / 120 * 100 = 75 % e"
Answer: e
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 150 - c
e = d / 150
f = e * 100
Problem: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 50 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 60 % , b ) 70 % , c ) 100 % , d ) 90 % , e ) 80 %
Rationale: "anyway , in this question , there is no discount but the mark up is given as 50 % of the selling price . so it is not 50 % of $ 150 but instead , 50 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 50 % of s = s s = 300 profit = 150 which is calculated on cost price in % terms . so 150 / 150 * 100 = 100 % is profit . c"
Answer: c
Python program:
a = 50 / 100
b = 1 - a
c = 150 / b
d = c - 150
e = d * 100
f = e / 150
Problem: p and q started a business investing rs . 85,000 and rs . 15,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 1 , b ) 17 : 6 , c ) 17 : 9 , d ) 17 : 2 , e ) 17 : 3
Rationale: "p : q = 85000 : 15000 = 17 : 3 . answer : e"
Answer: e
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: 1 / 216 , 415 , 356 , _ ?
Options: a ) 28 / 3 , b ) 27 / 3 , c ) 26 / 3 , d ) 25 / 3 , e ) 24 / 3
Rationale: take alternative no . 1 / 2 , 43 16 / 4 = 4 15 / 5 = 3 56 / 6 = 28 / 3 hence ans is 28 / 3 answer : a
Answer: a
Python program:
a = 2 * 4
b = 10 * 2
c = a + b 
d = c / 3
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 368
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 16 ) . larger number = ( 23 x 16 ) = 368 . answer : option e"
Answer: e
Python program:
a = 23 * 16
Problem: two good train each 100 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 1.2 sec , b ) 2.4 sec , c ) 4.8 sec , d ) 9.6 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 100 + 100 ) m = 1000 m . required time = ( 200 x 6 / 125 ) sec = 9.6 sec . answer d"
Answer: d
Python program:
a = 45 + 30 
b = a * const_0_2778
c = 1/(b)
d = 100 * c
e = d * 2
Problem: what is the total number of positive integers that are less than 800 and that have no positive factor in common with 800 other than 1 ?
Options: a ) 200 , b ) 320 , c ) 480 , d ) 500 , e ) 600
Rationale: "since 800 = 2 ^ 5 * 5 ^ 2 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 400 odd numbers from 1 to 800 . we then need to eliminate the 80 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 795 . there are a total of 400 - 80 = 320 such numbers between 1 and 800 . the answer is b ."
Answer: b
Python program:
a = 800 - 1
b = 800 - 2
c = b - 2
d = c / 2
e = d + 1 
f = 800 / 100
g = 800 - f
h = 800 / 100
i = g - h
j = 800 / 100
k = i / j
l = k + 1 
m = e + l 
n = 800 - 10
o = n - 10
p = o / 10
q = p + 1 
r = m - q
s = a - r
Problem: the amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3 . if the project took 120 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 35 hours , b ) 40 hours , c ) 36 hours , d ) 38 hours , e ) 42 hours
Rationale: "let the persons be a , b , c . hours worked : a = 1 * 120 / 6 = 20 hours b = 2 * 120 / 6 = 40 hours c = 3 * 120 / 6 = 60 hours c is the hardest worker and a worked for the least number of hours . so the difference is 60 - 20 = 40 hours . answer : b"
Answer: b
Python program:
a = 1 + 2 
b = a + 3 
c = 120 / b
d = c * 3
e = 1 + 2 
f = e + 3 
g = 120 / f
h = g * 1
i = d - h