euclaise/mathqa_programs huggingface dataset:
Problem: 300 × ? + ( 12 + 4 ) × 1 / 8 = 602
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 5 , d ) d ) 2 , e ) e ) 8
Rationale: explanation : = > 300 × ? + ( 12 + 4 ) × 1 / 8 = 602 = > 300 × ? = 602 - ( 12 + 4 ) × 1 / 8 = > 300 × ? = 602 - 2 = 600 = > ? = 600 / 300 = 2 answer : option d
Answer: d
Python program:
a = 12 + 4 
b = 1 / 8
c = a * b
d = 602 - c
e = d / 300
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 36 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 6
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 36 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 37 incorrect c . 2 / 2 = 2 / 3 + 2 / 38 incorrect d . 2 / 3 = 2 / 4 + 2 / 39 incorrect e . 2 / 4 = 2 / 5 + 2 / 40 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Python program:
a = 2 + 2 
b = a + 1 
c = 36 / b
Problem: girl and boy together can complete a piece of work in 35 days while girl alone can complete the same work in 60 days . boy alone will be able to complete the same working in :
Options: a ) 72 , b ) 75 , c ) 84 , d ) 88 , e ) 90
Rationale: subtraction of fraction ab − cd = ad − cbbd girl and boy finish one work with company = 35 days ( girl + boy ) ′ s one day ’ s work = 135 girl alone finish the same work = 60 days girl ′ s one day ’ s work = 160 b ′ s one day ’ s work = ( a + b ) ′ s one day ’ s work - a ′ s one day ’ s work 135 − 160 = 184 hence b alone can complete the work in 84 days
Answer: b
Python program:
a = 1/(35)
b = 1/(60)
c = a - b
d = 1/(c)
e = d - 10
Problem: what is 15 percent of 34
Options: a ) 5.1 , b ) 4.1 , c ) 3.1 , d ) 2.1 , e ) none of these
Rationale: "explanation : it will be 15 % of 34 = ( 15 / 100 ) * 34 = 5.10 answer : option a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 15 * n
p = o / 100
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
Options: a ) 2288 , b ) 27669 , c ) 1766 , d ) 1000 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 140 x = 1000 answer : d"
Answer: d
Python program:
a = 6 * 2500
b = a / 100
c = 140 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
Problem: the difference between the local value and the face value of 7 in the numeral 32675149 is ?
Options: a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of these
Rationale: "( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 d )"
Answer: d
Python program:
a = 7 * 1000
b = a - 7
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 42 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 42 , it is 26 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 42 is already 26 more than 16 and hence we only have 29 - 26 = 3 extra to distribute between r and s . since s must be greater than r , r can be 16 + 1 = 17 and s can be 16 + 2 = 18 . so r is 17 . answer ( a )
Answer: a
Python program:
a = 16 * 5
b = a - 42
c = b / 2
d = c - 2
Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 231 trial and error : 20 * 10 = 200 ( too low ) 21 * 11 = 231 the length is 21 meters . the answer is a ."
Answer: a
Python program:
a = 231 / 10
b = a / 2
c = const_0_33 + b 
d = const_0_25 + c 
e = 10 + d
Problem: a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 20 , c ) 90 , d ) 80 , e ) 11
Rationale: "600 - - - - 180 100 - - - - ? = > 80 % answer : d"
Answer: d
Python program:
a = 1080 - 600
b = a / 600
c = b * 100
Problem: how many integers are between 3 and 86 / 7 , inclusive ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "86 / 7 = 12 . xx we are not concerned about the exact value of 86 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 3 and 86 / 7 would be 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 total number of integers = 10 option c if we need to find the number of integers between two numbers n and m , where m > n the number of integers = m - n + 1 in the given question , the number of integers = 12 - 3 + 1 = 10 answer : c"
Answer: c
Python program:
a = 86 / 7
b = a - 3
c = b + 1
Problem: a man goes downstream at 15 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 3.5 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 15 - 8 ) kmph = 3.5 kmph . correct option : b"
Answer: b
Python program:
a = 15 - 8
b = a / 2
Problem: if 12 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 9.00 , e ) $ 20.00
Rationale: d for me 11 people with 1 $ each - > maximum = 9
Answer: d
Python program:
a = 12 - 1
b = a * 1
c = 20 - b
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 76,875 , how much profit did the business make ?
Options: a ) $ 98,000 , b ) $ 106,000 , c ) $ 112,000 , d ) $ 118,000 , e ) $ 123,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 76,875 p = $ 123,000 the answer is e ."
Answer: e
Python program:
a = 1 + 4 
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i 
k = c / j
Problem: a and b can do a piece of work in 40 days and 40 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 40 + 1 / 40 ] = 10 [ 1 + 1 / 40 ] = 1 / 2 a complete remaining work in 1 / 2 * 40 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Python program:
a = 10 / 40
b = 10 / 40
c = a + b 
d = 10 - c
e = 10 / 40
f = d / e
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 20 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 5 , e ) 12.5
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 20 run rate needed = 250 / 20 = 12.5 answer : option e"
Answer: e
Python program:
a = 10 * 3
b = 282 - a
c = b / 20
Problem: a car dealership has 40 cars on the lot , 30 % of which are silver . if the dealership receives a new shipment of 80 cars , 40 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 35 % , b ) 37.5 % , c ) 45 % , d ) 47.5 % , e ) 50 %
Rationale: "number of silver cars before shipment = 30 % of 40 = 12 number of silver cars after shipment = 60 % of 80 = 48 total number of silver cars out of 120 = 48 + 12 = 60 , which is 50 % e is my answer ."
Answer: e
Python program:
a = 30 / 100
b = 40 * a
c = 40 / 100
d = 80 * c
e = b + d 
f = 40 + 80 
g = e / f
h = g * 100
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 12 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 1.25 , b ) 1.75 , c ) 2.25 , d ) 2.75 , e ) 3.25
Rationale: "time = 6 / 4 + 6 / 8 = 18 / 8 = 2.25 hours the answer is c ."
Answer: c
Python program:
a = 12 / 2
b = a / 4
c = 12 / 2
d = c / 8
e = b + d
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 5 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 54
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 5 th year = 50 , 6 th year = 50 - 5 = 45 . the correct answer is c ."
Answer: c
Python program:
a = 5 - 1
b = a - 1
c = 5 - 1
d = 50 + c 
e = b + d 
f = e / 3
g = f + 3
Problem: in what ratio must rice of rs . 32 per kg be mixed with rice of rs . 42 per kg so that cost of mixture is rs . 20 per kg ?
Options: a ) 13 : 6 , b ) 13 : 5 , c ) 11 : 6 , d ) 11 : 5 , e ) 12 : 5
Rationale: "( 20 - 42 ) / ( 32 - 20 ) = 22 / 12 = 11 : 6 answer : c"
Answer: c
Python program:
a = 20 - 42
b = 32 - 42
c = a / b
d = 20 - 42
e = 32 - 42
f = d / e
g = 1 - f
h = c / g
Problem: in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 5 , d ) 1 / 7 , e ) 3 / 5
Rationale: "total draws = prizes + blanks = 10 + 25 = 35 probability of getting a prize = 10 / 35 = 2 / 7 correct option is b"
Answer: b
Python program:
a = 10 + 25 
b = 25 / a
Problem: if the number is divided by 3 , it reduced by 48 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 72 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 48 = > 2 x / 3 = 48 = > x = 72 answer : option d"
Answer: d
Python program:
a = 48 * 3
b = 3 - 1
c = a / b
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 80 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 480 cm
Rationale: "we have 80 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues . so we have 80 , 40,20 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 80 / 1 - ( 1 / 2 ) = 160 equilateral triangle perimeter is 3 a = 3 * 160 = 480 . so option e ."
Answer: e
Python program:
a = triangle_perimeter + (
Problem: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 , then n =
Options: a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 25
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 = > 4 x 2 ^ 2 n = 4 ^ 26 = 2 ^ 52 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 52 = > 2 ^ ( 2 n + 2 ) = 2 ^ 52 = > 2 n + 2 = 52 = > n = 25 so . answer will be e"
Answer: e
Python program:
a = 26 * 2
b = a - 2
c = b / 2
Problem: if a - b = 5 and a 2 + b 2 = 34 , find the value of ab .
Options: a ) a ) 4.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 34 - 25 = 9 ab = 4.5 . answer : a"
Answer: a
Python program:
a = 5 ** 2
b = 34 - a
c = b / 2
Problem: john makes $ 60 a week from his job . he earns a raise and now makes $ 110 a week . what is the % increase ?
Options: a ) 16 % , b ) 83.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 50 / 60 ) * 100 = ( 5 / 6 ) * 100 = 83.33 % . b"
Answer: b
Python program:
a = 110 - 60
b = a / 60
c = b * 100
Problem: a certain number of workers can do a work in 35 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 35 - 10 ) / 10 = 25 answer is a"
Answer: a
Python program:
a = 35 - 10
b = a * 10
c = 35 - 10
d = 35 - c
e = b / d
Problem: in the formula a = ( 2 r ) ^ 3 , if r is halved , then a is multiplied by ?
Options: a ) 64 , b ) 1 / 8 , c ) 1 , d ) 8 , e ) 1 / 64
Rationale: say r = 2 = > a 1 = 64 when r = 1 ; v 2 = 8 v 2 = 1 / 8 * v 1 . answer : b
Answer: b
Python program:
a = 2 ** 3
b = 1 / a
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 22,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 118000 , d ) 277768 , e ) 188871
Rationale: the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 22,000 is made = 96,000 + 24,000 = rs . 1 , 18,000 answer : c
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 20 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: a cycle is bought for rs . 900 and sold for rs . 1180 , find the gain percent ?
Options: a ) 11 , b ) 31 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 280 100 - - - - ? = > 31 % answer : b"
Answer: b
Python program:
a = 1180 - 900
b = a / 900
c = b * 100
Problem: all the students of class are told to sit in circle shape . here the boy at the 8 th position is exactly opposite to 33 th boy . total number of boys in the class ?
Options: a ) 40 , b ) 50 , c ) 28 , d ) 38 , e ) 48
Rationale: "as half the circle shape consist of 33 - 8 = 25 boys , so total number of boys in full circle = 2 * 25 = 50 answer : b"
Answer: b
Python program:
a = 33 - 8
b = a * 2
Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be not a couple ?
Options: a ) 17 / 2900 , b ) 2683 / 2700 , c ) 2496 / 2700 , d ) 2369 / 2700 , e ) 198 / 270
Rationale: in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . probability of there will not be a couple = 1 - ( 17 / 2700 ) = 2683 / 2700 ans - b
Answer: b
Python program:
a = math.comb(45, 1)
b = math.comb(60, 1)
c = a * b
d = math.comb(17, 1)
e = c - d
f = math.comb(45, 1)
g = math.comb(60, 1)
h = f * g
i = e / h
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 11 / 15 find p ( a | b )
Options: a ) 11 / 4 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a â ˆ ª b ) / p ( b ) p ( a | b ) = ( 11 / 15 ) / ( 4 / 15 ) = 11 / 4 . a"
Answer: a
Python program:
a = 11 / 15
b = 2 / 15
c = a / b
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 134 m length ?
Options: a ) 82.1 sec . , b ) 12.2 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 + 134 = 244 m . required time = 244 / 20 = 12.2 sec . answer : b"
Answer: b
Python program:
a = 110 + 134 
b = 72 * const_0_2778
c = a / b
Problem: what percent is 70 of 280 ?
Options: a ) 12 % , b ) 25 % , c ) 26 % , d ) 27 % , e ) 28 %
Rationale: "70 / 280 = 1 / 4 1 / 4 × 100 = 25 % b"
Answer: b
Python program:
a = 70 / 280
b = a * 100
Problem: ifaequals the sum of the even integers from 2 to 40 , inclusive , andbequals the sum of the odd integers from 1 to 39 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 20 , e ) 21
Rationale: this is a solution from beatthegmat : even numbers : ( 40 - 2 ) / 2 + 1 = 20 even integers . ( 40 + 2 ) / 2 = 21 is the average of the even set . sum = avg * ( # of elements ) = 21 * 20 = 420 = a odd numbers : ( 39 - 1 ) / 2 + 1 = 20 odd integers . ( 39 + 1 ) / 2 = 20 is the average of the odd set . sum = avg * ( # of elements ) = 20 * 20 = 400 = b a - b = 420 - 400 = 20 . answer : d
Answer: d
Python program:
a = 40 / 2
b = 40 / 2
c = b + 1 
d = a * c
e = 39 + 1 
f = e / 2
g = 39 - 1
h = g / 2
i = h + 1 
j = f * i
k = d - j
Problem: a train running at the speed of 90 km / hr crosses a pole in 12 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 300
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 75 / 3 m / sec length of train ( distance ) = speed * time ( 75 / 3 ) * 12 = 300 meter answer : e"
Answer: e
Python program:
a = 90 * 1000
b = a / 3600
c = b * 12
Problem: two cars , car 1 and car 2 move towards each other from e and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach e starting from y ?
Options: a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec
Rationale: e - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance ey = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d
Answer: d
Python program:
a = 20 + 15 
b = 20 * 10
c = b / 15
d = a * c
e = d / 15
Problem: the radius of a semicircular plot is 25 . what is the approximate perimeter of the plot ?
Options: a ) 114
b ) 150
c ) 129
d ) 25
e ) 57
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 25 + 2 * 25 = 128.50 approximately 129 answer c
Answer: c
Python program:
a = circumface / (
b = 25 + a
Problem: how many two - digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4 ? options :
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: numbers giving remainder 3 when divided by 10 = 13,23 , 33,43 , 53,63 , 73,83 , 93 numbers giving remainder 3 when divided by 4 = alternate numbers ( coloured in red ) = 4 correct option : d
Answer: d
Python program:
a = math.lcm(10, 4)
b = 3 + 2 
c = a / b
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number t of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "t = 7 is the correct answer . good solution buneul . b"
Answer: b
Python program:
a = 25 / 5
b = a + 2
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 30 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 117 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 30 % = 90 * 1.3 = 117 thus ratio = 117 / 100 = 1.17 ( in % terms = 117 % ) . thus b is the correct answer ."
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = 100 * b
d = 100 - 25
e = d / 100
f = c * e
g = 100 + 30 
h = g / 100
i = f * h
Problem: a rectangular tiled patio is composed of 40 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 40 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "r * c = 70 and ( 6 + 4 ) ( c - 2 ) = 70 - - > r = 6 and c = 6 . answer : b ."
Answer: b
Python program:
a = negate + ( 
b = 4 ** 2
c = 40 * 2
d = 4 * c
e = b + d 
f = math.sqrt(e)
g = a / f
h = 40 / g
Problem: set s consists of integers { 6 , 7 , 10 , 12 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 40 % . what is the value of integer n ?
Options: a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 40 % , the new mean is 14 . thus , on average , 5 numbers increase by 4 . therefore n = 14 + 20 = 34 the answer is c ."
Answer: c
Python program:
a = 10 + 12 
b = a + 12
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1224 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1224 or 9 x = 1224 or x = 136 . required number = 136 . answer : d"
Answer: d
Python program:
a = 43 - 34
b = 1224 / a
Problem: what will be the difference between simple and compound interest @ 20 % per annum on a sum of $ 500 after 2 years ?
Options: a ) $ 10 , b ) $ 20 , c ) $ 25 , d ) $ 30 , e ) $ 40
Rationale: "s . i . = 500 * 20 * 2 / 100 = $ 200 c . i . = 500 * ( 1 + 20 / 100 ) ^ 2 - 500 = $ 220 difference = 220 - 200 = $ 20 answer is b"
Answer: b
Python program:
a = 20 / 100
b = a + 1 
c = b ** 2
d = 500 * c
e = d - 500
f = 20 / 100
g = 500 * f
h = g * 2
i = e - h
Problem: martins made a part payment of $ 650 toward buying a brand new washing machine , which represents 15 % of the total cost of the washing machine , how much remains to be paid ?
Options: a ) $ 1116.3 , b ) $ 3583.3 , c ) $ 3283.3 , d ) $ 3683.3 , e ) $ 2683.3
Rationale: explanation : let ' s start with what the total price of the washing machine would be . if 15 % is equal to $ 650 then 100 % equals $ x . we just have to multiply $ 650 by 6.67 to get total amount = $ 4333.3 . out of this amount we then need to deduct the amount already paid which was $ 650 so we have $ 4333.3 - $ 650 = $ 3683.3 answer : option d
Answer: d
Python program:
a = 15 / 100
b = 650 / a
c = b - 650
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet . what is its area , in square feet ?
Options: a ) 43,200 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 300 , you can deduce the following a = 180 b = 240 180 x 240 = 43,200 a is the answer ."
Answer: a
Python program:
a = 2 + 3 
b = 300 / a
c = b * 3
d = 2 + 3 
e = 300 / d
f = e * 4
g = c * f