euclaise/mathqa_programs huggingface dataset:
Problem: if the product of two numbers is 17820 and their h . c . f . is 12 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1485 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 17820 , because we know product of two numbers = product of hcf and lcm lcm = 17820 / 12 = 1485 option c"
Answer: c
Python program:
a = 17820 / 12
Problem: thabo owns exactly 160 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 25 , c ) 35 , d ) 46 , e ) 50
Rationale: i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 160 3 x + 60 + x = 160 x = 25 answer ( b . )
Answer: b
Python program:
a = 160 + 20 
b = a / 4
c = b - 20
Problem: if x + y = 2 x - 2 z , x - 2 y = 4 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4.5 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 2.5 .
Rationale: given : x + y = 2 x - 2 z , - - > eq 1 x - 2 y = 4 z - - > eq 2 x + y + z = 21 - - > eq 3 . now we are asked to find the value of y / z . now let choose some option randomly , take c , which is 3 , i randomly chose this value as it is positive : ) y / z = 3 , this is the value we need to get . then y = 3 z - - eq 4 sub this in eq 1 . x + 3 z = 2 x - 2 z = > x = 5 z - - > eq 5 . sub x and y value in eq 3 . 5 z + 3 z + z = 21 = > z = 21 / 9 . now sub this value to get y , we get y = 21 / 3 . then y / z = 21 / 3 / 21 / 9 = we get 3 again . so this option is correct . answer : option c is correct .
Answer: c
Python program:
a = 21 * 2
Problem: evaluate 100 / . 25
Options: a ) 400 , b ) 510 , c ) 500 , d ) none of these , e ) 506
Rationale: explanation : 100 / . 25 = 10000 / 25 = 400 option a
Answer: a
Python program:
a = 25 / 100
b = 100 / a
Problem: the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously ?
Options: a ) 5 kg , b ) 12,5 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 10 kg . as the price falls by 20 % , new price for 10 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 10 = rs . 8 per kg . rice can bought now at = 100 / 8 = 12,5 kg . answer : option b"
Answer: b
Python program:
a = 100 - 20
b = a / 10
c = 100 / b
Problem: what is the smallest integer that is the sum of 2 distinct prime integers , each greater than 70 ?
Options: a ) 147 , b ) 142 , c ) 173 , d ) 144 , e ) 186
Rationale: a prime number ( or a prime ) is a natural number greater than 1 that has no positive divisors other than 1 and itself . here are the first few prime numbers : 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197 , 199 , etc . immediate two prime numbers after 70 are - 71 and 73 sum = 71 + 73 = 144 answer - d
Answer: d
Python program:
a = 70 + 1 
b = 70 + 3 
c = a + b
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 940 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 24 , b ) 22 , c ) 16 , d ) 18 , e ) 20
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 940 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest noall factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( opps / / it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which haslength of integeris 9 . now , since x = 512 , x + 3 y < 940 so , 3 y < 428 = = > y < 428 / 3 so , y can take any value which is less than 428 / 3 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . c"
Answer: c
Python program:
a = 4 + 3 
b = 4 + 4 
c = b + 1 
d = a + c
Problem: how many 7 in between 1 to 100 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 , 87,97 20 7 ' s between 1 to 100 answer : b"
Answer: b
Python program:
a = 7 * 3
b = 100 / a
Problem: the perimeter of a semi circle is 162 cm then the radius is ?
Options: a ) 31.5 , b ) 28 , c ) 98 , d ) 37 , e ) 13
Rationale: "36 / 7 r = 162 = > r = 31.5 answer : a"
Answer: a
Python program:
a = 2 + math.pi 
b = 162 / a
Problem: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours r would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job r in 44 hours . answer : c ."
Answer: c
Python program:
a = 1 / 4
b = 1 / 11
c = a + b 
d = c / 15
e = 1 / d
Problem: the cricket team of 11 members is 28 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 28 + 31 ) = 9 ( x - 1 ) = > 11 x - 9 x = 50 = > 2 x = 50 = > x = 25 . so , average age of the team is 25 years . d"
Answer: d
Python program:
a = 28 + 3 
b = a + 28 
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 400 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 5000 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 400 b capital = 30000 * 1 / 6 = 5000 . answer : d"
Answer: d
Python program:
a = 400 * 100
b = a / 2
Problem: a reduction of 30 % in the price of apples would enable a man to obtain 54 more for rs . 30 , what is reduced price per dozen ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 7 , e ) 10
Rationale: "b 30 * ( 30 / 100 ) = 9 - - - 54 ? - - - 12 = > rs . 2"
Answer: b
Python program:
a = 30 * 30
b = a / 100
c = b / 54
d = c * 12
Problem: a certain psychologist charges $ 35 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 350 , what is the total charge to a patient who receives only 2 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 161 , d ) $ 165 , e ) $ 192
Rationale: "let the charge for first hour = x + 35 then charge for each additional hour = x x + 35 + 4 x = 350 = > 5 x = 315 = > x = 63 total charge for patient for 3 hours of therapy = x + 35 + x = 2 x + 35 = 161 $ answer c"
Answer: c
Python program:
a = 350 - 35
b = a / 5
c = b * 2
d = c + 35
Problem: the average length of 6 ropes is 80 cm . if the average length of one third of the ropes measure to 70 cm , what is the average of the other ropes ?
Options: a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .
Rationale: edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third ropes is 70 . that means out 6 / 3 = 2 ropes . let the avg length of two ropes be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining ropes . imo correct option is b .
Answer: b
Python program:
a = 70 * 2
b = a / 6
c = 80 - b
d = 6 / 4
e = c * d
Problem: x and y are two towns . ganesh covers the distance from x to y at an average speed of 44 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 39.6 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 44 * 36 / 44 + 36 = 39.6 answer : a"
Answer: a
Python program:
a = 44 - 10
b = a + 100 
c = 44 - 10
d = c + 100 
e = b + d 
f = 44 - 10
g = f + 100 
h = g / 44
i = 44 - 10
j = i + 100 
k = j / 36
l = h + k 
m = e / l
Problem: if the cost price is 95 % of selling price then what is the profit percentage .
Options: a ) 5.26 , b ) 5.16 , c ) 5.61 , d ) 5.52 , e ) 5
Rationale: "selling price = rs 100 : then cost price = rs 95 : profit = rs 5 . profit = { ( 5 / 95 ) * 100 } % = 5.26 % answer is a ."
Answer: a
Python program:
a = 100 - 95
b = a / 95
c = b * 100
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 20 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 65 % , b ) 50 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.20 - - > x = 0.5 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.20 - - > x = 0.5 . answer : b ."
Answer: b
Python program:
a = 20 / 100
b = 100 * a
c = 1 / 4
d = c * 100
e = 100 - d
f = 10 / 100
g = e * f
h = b - g
i = 1 / 4
j = i * 100
k = h / j
l = k * 100
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 20 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 44 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 4.8 , so radius is 2.4 new area = 5.76 π increase in area is 1.76 π % increase in area = 1.76 / 4 * 100 so , % increase is 44 % answer will be ( d )"
Answer: d
Python program:
a = 20 * 2
b = a / 1000
c = b + 3 
d = c ** 2
e = d - 4
f = e / 4
g = f * 100
Problem: what is the perimeter of a square field whose diagonal is 8 √ 2 ?
Options: a ) 82 m , b ) 32 m , c ) 27 m , d ) 26 m , e ) 76 m
Rationale: "4 a = 32 m answer : b"
Answer: b
Python program:
a = 8 ** 2
b = 2 ** 2
c = a - b
d = math.sqrt(c)
e = d + 2 
f = 8 ** 2
g = 2 ** 2
h = f - g
i = math.sqrt(h)
j = i + 2 
k = e + j 
l = k / 2
Problem: in a division sum , the quotient is 120 , the divisor 456 and the remainder 333 , find the dividend ?
Options: a ) 55287 , b ) 29887 , c ) 27768 , d ) 55053 , e ) 17191
Rationale: "explanation : 120 * 456 + 333 = 55053 answer : d"
Answer: d
Python program:
a = 120 * 456
b = a + 333
Problem: what is the probability that a number selected from number 1 to 30 is prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 30 , b ) 20 / 30 , c ) 1 , d ) 5 / 30 , e ) 15 / 30
Rationale: x = { 2,3 , 5,7 , 11,13 , 17,19 , 23,29 } n ( x ) = 10 n ( s ) = 30 hence required probability = n ( x ) / n ( s ) = 10 / 30 option a is answer
Answer: a
Python program:
a = 5 * 2
b = a / 30
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 8.00 ?
Options: a ) 40 , b ) 60 , c ) 96 , d ) 120 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 8 ( 1 / 12 ) * x = 8 x = 96 answer : c"
Answer: c
Python program:
a = 1 / 0
b = 0 / 50
c = a - b
d = 8 / 0
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 53 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 22 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 53 ounces of a substance has a volume of ( 48 / 112 ) * 53 = 22 cubic inches answer d"
Answer: d
Python program:
a = 48 / 112
b = a * 53
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 22 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 1 , b ) 3 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 22 s = ( 27 x + 17 y ) / ( x + y ) = 22 = ( 27 x + 17 y ) / = 22 ( x + y ) = 5 x = 5 y = x / y = 5 / 5 = 1 / 1 i . e 1 : 1 answer : a
Answer: a
Python program:
a = 27 - 22
b = 22 - 17
c = a / b
Problem: roses can be purchased individually for $ 5.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 317 , d ) 324 , e ) 325
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 5.3 = ~ 5 roses for that amount . total = 312 + 5 = 317 . answer : c ."
Answer: c
Python program:
a = 680 / 50
b = math.floor(a)
c = 12 * 2
d = b * c
e = 680 / 50
f = math.floor(e)
g = f * 50
h = 680 - g
i = h / 5
j = math.floor(i)
k = d + j
Problem: the salaries of a and b together is rs . 14000 . a spend 80 % of his salary and b spends 85 % of his salary . what is the salary of b if their savings are equal ?
Options: a ) rs . 6000 , b ) rs . 8000 , c ) rs . 7500 , d ) rs . 6500 , e ) rs . 8500
Rationale: let the salaries of a and b are x and y respectively x + y = 14000 savings of a = 20 x / 100 = savings of b = 15 y / 100 x = ¾ y 3 / 4 y + y = 14000 , 7 y / 4 = 14000 , y = 8000 answer : b
Answer: b
Python program:
a = 80 / 100
b = 14000 * a
c = 14000 - b
d = 1 + 1 
e = 80 / 100
f = d - e
g = 85 / 100
h = f - g
i = c / h
Problem: how many of the positive divisors q of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . q = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Python program:
a = 120 / 4
b = a / 2
c = b / 3
Problem: how many integers between 323,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,349
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 323,700 and 458,600 is 458,600 - 323,700 = 134,900 - one number per each hundred gives 134,900 / 100 = 1,349 numbers . answer : e ."
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 458 - 600
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 6 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 12 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 6 ) = l cx = 6 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 6 l = 1 / 12 answer will be b"
Answer: b
Python program:
a = 1 / 6
b = 2 / 3
c = 1 - b
d = 2 / 3
e = c / d
f = a * e
Problem: 11 + 12 + 13 + . . . 51 + 52 + 53 = ?
Options: a ) 1361 , b ) 1376 , c ) 1363 , d ) 1364 , e ) 1365
Rationale: "sum = 11 + 12 + 13 + . . . 51 + 52 + 53 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 53 positive integers = 53 * 54 / 2 sum of first 10 positive integers = 11 * 10 / 2 sum = 11 + 12 + 13 + . . . 51 + 52 + 53 = 53 * 54 / 2 - 11 * 10 / 2 = 1376 answer : b"
Answer: b
Python program:
a = 51 + 11 
b = 51 * a
c = b / 12
Problem: a man buys 52 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 11.32 % , d ) 11.91 % , e ) 7.8 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 52 pens = rs . 46 s . p . of 52 pens = 99 % of rs . 52 = rs . 51.48 profit % = ( profit / c . p . ) x 100 profit % = ( 5.48 / 46 ) x 100 = 11.91 % answer : d"
Answer: d
Python program:
a = 100 - 1
b = 52 * a
c = 46 * 100
d = b - c
e = 46 * 100
f = d / e
g = 100 * f
Problem: express 50 mps in kmph ?
Options: a ) 172 , b ) 160 , c ) 150 , d ) 180 , e ) 120
Rationale: "25 * 18 / 5 = 180 kmph answer : d"
Answer: d
Python program:
a = 50 / 1000
b = a * 3600
Problem: the total price of a kilogram each of shimla apples and red delicious apples is 250 rupees more than the total price of a kilogram each of red delicious apples and fuji apples . fuji apples is how much cheaper than shimla apples ?
Options: a ) 250 , b ) 125 , c ) 500 , d ) 100 , e ) 80
Rationale: ( shimla + red delicious ) - ( red delicious + fuji ) = 250 shimla - fuji = 250 answer : a
Answer: a
Python program:
a = 250 * 1
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 138 m length ?
Options: a ) 82.1 sec . , b ) 12.4 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 138 = 248 m . required time = 248 / 20 = 12.4 sec . answer : b
Answer: b
Python program:
a = 110 + 138 
b = 72 * const_0_2778
c = a / b
Problem: what is the 25 th digit to the right of the decimal point in the decimal form of 6 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : to determine the greatest possible number of members , first recognize that each member had to contribute the lowest amount given . build an inequality for the individual contributions and the total amount collected , with n = the number of members in the club , and solve for n . 12 n ≤ 599 n ≤ 49 11 / 12 since n represents individual people it must be a whole number . thus the greatest number of people is 49 . answer : option c"
Answer: c
Python program:
a = 6 / 11
Problem: a sum of money lent out at s . i . amounts to a total of $ 590 after 2 years and to $ 815 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 490 , b ) $ 500 , c ) $ 510 , d ) $ 520 , e ) $ 530
Rationale: "s . i for 5 years = $ 815 - $ 590 = $ 225 the s . i . is $ 45 / year s . i . for 2 years = $ 90 principal = $ 590 - $ 90 = $ 500 the answer is b ."
Answer: b
Python program:
a = 815 - 590
b = 2 / 5
c = a * b
d = 590 - c
Problem: if 5 < x < 9 and y = x + 7 , what is the greatest possible integer value of x + y ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "x + y = x + x + 7 = 2 x + 7 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 8.5 then x + y = 8.5 + 15.5 = 24 . the answer is d ."
Answer: d
Python program:
a = 7 + 10 
b = a + 10
Problem: there are 8 students . 4 of them are men and 4 of them are women . if 4 students are selected from the 8 students . what is the probability that the number of men is equal to that of women ?
Options: a ) 18 / 35 , b ) 16 / 35 , c ) 14 / 35 , d ) 13 / 35 , e ) 12 / 35
Rationale: men = women means 2 men 2 women total such combinations = 4 c 2 * 4 c 2 = 4 ! / 2 ! . 2 ! * 4 ! / 2 ! . 2 ! = 6 * 6 total combinations = 8 c 4 = 8 * 7 * 6 * 5 / 4 * 3 * 2 * 1 = 70 so probability = 36 / 70 = 18 / 35 hence a
Answer: a
Python program:
a = 4 / 2
b = math.comb(4, a)
c = 4 / 2
d = math.comb(4, c)
e = b * d
f = math.comb(8, 4)
g = e / f
Problem: how many seconds will a train 200 meters long running at the rate of 36 kmph take to pass a certain telegraph post ?
Options: a ) 10 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 35 sec
Rationale: distance = length of train = 200 meters speed = 36 kmph = 36 * 5 / 18 = 10 m / s required time = 200 / 10 = 20 sec answer is b
Answer: b
Python program:
a = const_0_2778 * 36
b = 200 / a
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 40 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 96 , c ) 100 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 5.6 , so radius is 2.8 new area = 7.84 π increase in area is 3.84 π % increase in area = 3.84 / 4 * 100 so , % increase is 96 % answer will be ( b )"
Answer: b
Python program:
a = 40 * 2
b = a / 1000
c = b + 3 
d = c ** 2
e = d - 4
f = e / 4
g = f * 100
Problem: a , b and c enter into a partnership by investing $ 11000 , $ 15000 and $ 23000 respectively . at the end of 8 months , b receives $ 3315 as his share . find the share of a .
Options: a ) $ 1865 , b ) $ 2087 , c ) $ 2217 , d ) $ 2431 , e ) $ 2662
Rationale: the ratio of capital of a , b and c = 11000 : 15000 : 23000 = 11 : 15 : 23 a ' s share = ( 11 / 15 ) * 3315 = $ 2431 the answer is d .
Answer: d
Python program:
a = 15000 * 8
b = a / 100
c = 3315 / b
d = 11000 * c
e = d * 8
f = e / 100
Problem: a reduction of 35 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: 800 * ( 35 / 100 ) = 280 - - - - 5 ? - - - - 1 = > rs . 56 answer : c
Answer: c
Python program:
a = 800 * 35
b = a / 100
c = b / 5