euclaise/mathqa_programs huggingface dataset:
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 36 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 36 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 36 lets say x machines are used to attain the desired rate , thus x / 36 + x / 36 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + x ) / 36 = 1 / 2 2 x / 36 = 1 / 2 x = 9 . qa = 9 ( answer d )"
Answer: d
Python program:
a = 1 / 36
b = 1 / 2
c = a + b 
d = 36 * c
e = 1 / d
Problem: ? x 24 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 1730 , e ) 534
Rationale: "let y x 24 = 173 x 240 then y = ( 173 x 240 ) / 24 = 173 x 10 = 1730 answer : d"
Answer: d
Python program:
a = 173 * 240
b = a / 24
Problem: in how many no . between 10 and 20 exactly two of the digits is 1 ?
Options: a ) 25 , b ) 35 , c ) 10 , d ) 1 , e ) 15
Rationale: "it ' s simple can be solved by elimination of answer choices . option a and b are too large , not possible . even ce are large to have correct choice . ans : d"
Answer: d
Python program:
a = 20 / 10
b = a / 1
Problem: a man sells a car to his friend at 11 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 25561.80 , b ) rs . 37500.80 , c ) rs . 50561.80 , d ) rs . 60000 , e ) none of these
Rationale: explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 11 % . now s . p = rs . 45000 and loss = 11 % c . p . rs . [ 100 / 89 ã — 45000 ] = rs . 50561.80 . correct option : c
Answer: c
Python program:
a = 54000 * 100
b = 100 + 20 
c = a / b
d = c * 100
e = 100 - 11
f = d / e
Problem: given that 268 x 74 = 19532 , find the value of 2.68 x . 74 .
Options: a ) 1.9532 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9532 answer a"
Answer: a
Python program:
a = 268 / 100
b = 74 / 100
c = a * b
Problem: if a = { 1 , 3 , 5 } , b = { 3 , 5 , 6 } . find a ∪ b
Options: a ) { 1,5 } , b ) { 1,3 , 5,6 } , c ) { 2,6 } , d ) { 8,9 } , e ) { 4,12 }
Rationale: "a = { 1 , 3,5 } b = { 3 , 5,6 } therefore , correct answer : a ∪ b = { 1 , 3 , 5 , 6 } b"
Answer: b
Python program:
a = 1 + 3 
b = a + 5 
c = b + 3 
d = c + 5 
e = 4 + 1 
f = d / e
g = f + 5
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 3 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 64
Rationale: "let the numbers be 1 x and 3 x . then , their l . c . m = 3 x . so , 3 x = 48 or x = 16 . the numbers are 16 and 48 . hence , required sum = ( 16 + 48 ) = 64 . answer : e"
Answer: e
Python program:
a = 1 * 48
b = a / 3
Problem: after a storm deposits 115 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 245 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 115 billion gallons , volume of water in the reservoir = 245 + 115 = 360 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 360 / 0.8 = 450 billion gallons therefore percentage of reservoir that was full before the storm = ( 245 / 450 ) * 100 = 54.4 % option c"
Answer: c
Python program:
a = 115 + 245 
b = 80 / 100
c = a / b
d = 245 / c
e = d * 100
Problem: the sum of the ages of 5 children born at the intervals of 2 years each is 50 years . what is the age of the youngest child ?
Options: a ) 6 , b ) 18 , c ) 10 , d ) 99 , e ) 38
Rationale: let x = the youngest child . each of the other four children will then be x + 2 , x + 4 , x + 6 , x + 8 . we know that the sum of their ages is 50 . so , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 therefore the youngest child is 6 years old answer : a
Answer: a
Python program:
a = 5 / 2
b = 50 / a
c = 5 - 1
d = c * 2
e = b - d
f = e / 2
Problem: an inspector rejects 0.08 % of the meters as defective , how many meters he examine to reject 2 meteres
Options: a ) 1200 , b ) 2400 , c ) 1400 , d ) 2500 , e ) none of these
Rationale: explanation : it means that 0.08 % of x = 2 = > ( 8 / 100 × 100 × x ) = 2 = > x = 2 × 100 × 100 / 8 = > x = 2500 option d
Answer: d
Python program:
a = 2 * 100
b = a / 0
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 36 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 7 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 36 / 49 = ( 6 / 7 ) * ( 6 / 7 ) therefore probability that the next one she draws is pink = 1 / 7 option ( a )"
Answer: a
Python program:
a = 36 / 49
b = math.sqrt(a)
c = 1 - b
Problem: increasing the original price of a certain item by 30 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 69.0
Rationale: "we ' re told that the original price of an item is increased by 30 % and then that price is increased by 30 % . . . . if . . . . starting value = $ 100 + 30 % = 100 + . 30 ( 100 ) = 130 + 30 % = 130 + . 30 ( 130 ) = 130 + 39 = 169 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 59 / 100 = 69 % final answer : e"
Answer: e
Python program:
a = 30 / 100
b = a + 1 
c = 30 / 100
d = c + 1 
e = b * d
f = e - 1
g = f * 100
Problem: the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 15 , what is the perimeter of the garden , in feet ?
Options: a ) 28 , b ) 36 , c ) 40 , d ) 56 , e ) 64
Rationale: "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 15 ( p ^ 2 ) / 16 = 2 p + 15 p ^ 2 = 32 p + 240 p ^ 2 - 32 p - 240 = 0 p ^ 2 - 40 p + 6 p - 240 = 0 p ( p - 40 ) + 6 ( p + 40 ) = 0 ( p - 40 ) ( p + 6 ) = 0 p = 40 or - 6 discarding negative value , p = 40 answer is c"
Answer: c
Python program:
a = 15 * 2
b = 10 + a 
c = b - const_0_25
d = c - const_0_25
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 370 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 740 , e ) 720
Rationale: explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 370 ) = 2 + 2 ( extra ) = > 2 x - 740 = x = > x = 740 . answer : d
Answer: d
Python program:
a = 370 * 2
Problem: if the perimeter of a rectangular garden is 900 m , its length when its breadth is 190 m is ?
Options: a ) 338 m , b ) 778 m , c ) 200 m , d ) 260 m , e ) 971 m
Rationale: "2 ( l + 190 ) = 900 = > l = 260 m answer : d"
Answer: d
Python program:
a = 900 / 2
b = a - 190
Problem: two pipes can fill a tank in 20 minutes and 15 minutes . an outlet pipe can empty the tank in 10 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 20 + v / 15 - v / 10 = v / 60 per minute the tank will be filled in 60 minutes . the answer is e ."
Answer: e
Python program:
a = 1 / 20
b = 1 / 15
c = a + b 
d = 1 / 10
e = c - d
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 200 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 200 meters , thus the circumference is 200 + 200 = 400 meters . answer : d ."
Answer: d
Python program:
a = 2 * 100
b = a + 200
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 11 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 11 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 11 hence x = 13 . answer is c"
Answer: c
Python program:
a = 11 + 2
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 2 ) and ( 9 , 2 ) 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 ) 5 , b ) 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 8
Rationale: if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 1 ) is 1 / 5 . the answer is d .
Answer: d
Python program:
a = 9 - 1
b = a + 2 
c = b / 2
d = 1 / c
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - third of his earnings to charity . if the worker ' s charitable contributions totaled one - eighth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 33 / 25 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 3 = 1 / 8 ( 11 x + nx ) ; 11 / 10 + n / 3 = 1 / 8 ( 11 + n ) 33 + 10 n / 30 = 11 + n / 8 = > 264 + 80 n = 330 + 30 n = > 50 n = 66 n = 66 / 50 = 33 / 25 answer : d ."
Answer: d
Python program:
a = 12 - 1
b = 12 - 3
c = 1/(b)
d = 1/(10)
e = c - d
f = a * e
g = 1 + 4 
h = 1/(g)
i = 12 - 3
j = 1/(i)
k = h - j
l = f / k
Problem: what is the units digit of ( 5 ! * 4 ! + 6 ! * 5 ! ) / 3 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 1
Rationale: "( 5 ! * 4 ! + 6 ! * 5 ! ) / 3 = 5 ! ( 4 ! + 6 ! ) / 3 = 120 ( 24 + 720 ) / 3 = ( 120 * 744 ) / 3 = 120 * 248 units digit of the above product will be equal to 0 answer d"
Answer: d
Python program:
a = math.factorial(5)
b = math.factorial(4)
c = a * b
d = math.factorial(5)
e = math.factorial(5)
f = d * e
g = c + f 
h = g / 5
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 3 parts , respectively . this will give us in the final mixture ( 5 + 3 ) : ( 3 + 3 ) , which means 4 : 3 answer d .
Answer: d
Python program:
a = 4 * 5
b = 5 + 3 
c = b / 2
d = 3 * c
e = a + d 
f = 4 * 3
g = 5 + 3 
h = g / 2
i = 3 * h
j = f + i 
k = e / j
Problem: if x is 11 percent greater than 70 , then x =
Options: a ) 77.7 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 70 = ( 70 * 0.11 ) = 7.7 11 % greater than 70 = 70 + 7.7 = 77.7 answer is clearly a ."
Answer: a
Python program:
a = 11 / 100
b = a * 70
c = 70 + b
Problem: if an examination 63 % of the candidates in english , 65 % passed in mathematics , and 27 % failed in both subjects . what is the pass percentage ?
Options: a ) 55 % , b ) 60 % , c ) 65 % , d ) 75 % , e ) none .
Rationale: fail in english = 100 - 63 = 37 % fail in maths = 100 - 65 = 35 % so pass % = 100 - ( 37 + 35 - 27 ) = 55 % answer : a
Answer: a
Python program:
a = 100 - 63
b = 100 - 65
c = a + b 
d = c - 27
e = 100 - d
Problem: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train ?
Options: a ) 250 meter , b ) 876 meter , c ) 167 meter , d ) 719 meter , e ) 169 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 15
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 1 strokes ?
Options: a ) 1 / 2 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 so removed = 1 - 1 / 2 = 1 / 2"
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = b / 2
d = a + c 
e = 1 / 2
f = e / 2
g = f / 2
h = d + g 
i = 1 / 2
j = i / 2
k = j / 2
l = k / 2
m = h + l 
n = 1 / 2
o = n / 2
p = o / 2
q = p / 2
r = q / 2
s = m + r
Problem: fred and sam are standing 40 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 4 miles per hour and sam walks at a constant speed of 4 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 20 , d ) 30 , e ) 45
Rationale: "relative distance = 40 miles relative speed = 4 + 4 = 8 miles per hour time taken = 40 / 8 = 5 hours distance travelled by sam = 4 * 5 = 20 miles = c"
Answer: c
Python program:
a = 4 + 4 
b = 40 / a
c = 4 * b
Problem: the average of first seven multiples of 5 is :
Options: a ) 20 , b ) 16 , c ) 15 , d ) 8 , e ) 10
Rationale: "explanation : ( 5 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 5 x 28 / 7 = 20 answer : a"
Answer: a
Python program:
a = 5 + 1
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot at the rate of 26.50 per metre is 5,300 , what is the length of the plot ( in metres ) ?
Options: a ) 40 , b ) 120 , c ) 50 , d ) data inadequate , e ) none of these
Rationale: "perimeter of the rectangular plot = [ ( b + 20 ) + b ] × 2 = 5300 / 26.5 = 200 = 200 ∴ ( 2 b + 20 ) 2 = 200 ⇒ b = 40 ⇒ l = 40 + 20 = 60 m answer e"
Answer: e
Python program:
a = 5 / 300
b = a / 2
c = 2 * 20
d = b - c
Problem: a , b and c are entered into a partnership . a invested rs . 6500 for 6 months , b invested rs . 8400 for 5 months and c invested for rs . 10000 for 3 months . a is a working partner and gets 5 % of the total profit for the same . find the share of c in a total profit of rs . 7400 ?
Options: a ) 2998 , b ) 1900 , c ) 2788 , d ) 2662 , e ) 1122
Rationale: 65 * 6 : 84 * 5 : 100 * 3 26 : 28 : 20 c share = 74000 * 95 / 100 = 7030 * 20 / 74 = > 1900 answer : b
Answer: b
Python program:
a = 5 * 7400
b = a / 100
c = 7400 - b
d = 10000 * 3
e = c * d
f = 6500 * 6
g = 8400 * 5
h = f + g 
i = 10000 * 3
j = h + i 
k = e / j
Problem: if 25 men do a work in 96 days , in how many days will 40 men do it ?
Options: a ) 66 , b ) 53 , c ) 55 , d ) 60 , e ) 61
Rationale: "25 * 96 = 40 * x x = 60 days answer : d"
Answer: d
Python program:
a = 25 * 96
b = a / 40
Problem: there are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 8 and for second = 7 so total methods = 8 * 7 = 56 answer : d"
Answer: d
Python program:
a = math.comb(8, 2)
b = math.comb(8, 2)
c = a + b
Problem: the expression ( 12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 ) will be a perfect square for p equal to
Options: a ) 0.28 , b ) 0.26 , c ) 1 , d ) 0 , e ) 2
Rationale: explanation : 12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 = ( 12.86 ) 2 + 12.86 × p + ( 0.14 ) 2 this can be written as ( 12.86 + 0.14 ) 2 = 132 , if 12.86 × p = 2 × 12.86 × 0.14 i . e . , if p = 2 × 0.14 = 0.28 hence , p = 0.28 . answer : option a
Answer: a
Python program:
a = 0 * 14
Problem: if the sample interest on a sum of money 20 % per annum for 2 years is $ 400 , find the compound interest on the same sum for the same period at the same rate ?
Options: a ) $ 460 , b ) $ 510 , c ) $ 440 , d ) $ 500 , e ) $ 550
Rationale: "rate = 20 % time = 2 years s . i . = $ 400 principal = 100 * 400 / 20 * 2 = $ 1000 amount = 1000 ( 1 + 20 / 100 ) ^ 2 = $ 1440 c . i . = 1440 - 1000 = $ 440 answer is c"
Answer: c
Python program:
a = 400 * 100
b = 20 * 2
c = a / b
d = 400 * 100
e = 20 * 2
f = d / e
g = f * 20
h = g / 100
i = c + h 
j = i * 20
k = j / 100
l = 400 * 100
m = 20 * 2
n = l / m
o = 400 * 100
p = 20 * 2
q = o / p
r = q * 20
s = r / 100
t = n + s 
u = k + t 
v = 400 * 100
w = 20 * 2
x = v / w
y = u - x
Problem: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is
Options: a ) 36 , b ) 40 , c ) 99 , d ) 13 , e ) 12
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b"
Answer: b
Python program:
a = 83 - 63
b = a * 2
Problem: a man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km per hour . find the distance travelled on foot .
Options: a ) 26 km , b ) 32 km , c ) 30 km , d ) 28 km , e ) none
Rationale: total time = 7 hrs let the distance travelled by foot @ 8 kmph be x kms ? distance travlled by bicycle @ 16 kmph be ( 80 - x ) kms atq . 7 hr = x / 8 + ( 80 - x ) / 16 ? 7 = ( 2 x + 80 - x ) / 16 ? x = 32 kms answer : b .
Answer: b
Python program:
a = 16 * 7
b = a - 80
Problem: after decreasing 24 % in the price of an article costs rs . 820 . find the actual cost of an article ?
Options: a ) 1400 , b ) 1079 , c ) 1200 , d ) 1023 , e ) 1523
Rationale: "cp * ( 76 / 100 ) = 820 cp = 10.78 * 100 = > cp = 1079 answer : b"
Answer: b
Python program:
a = 24 / 100
b = 1 - a
c = 820 / b
Problem: if x ^ 2 – x = 2 , then one possible value of x – 4 =
Options: a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 5
Rationale: x ^ 2 – x = 2 i . e . x ^ 2 – x - 2 = 0 i . e . x ^ 2 + x - 2 x - 2 = 0 i . e . ( x - 2 ) ( x + 1 ) = 0 i . e . x = 2 or - 1 i . e . x - 4 = 2 - 4 or - 1 - 4 i . e . x - 4 = - 2 or - 5 answer : option b
Answer: b
Python program:
a = 4 * 2
b = 1 + a 
c = math.sqrt(b)
d = 1 + c 
e = d / 2
f = e - 4
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 8 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.15 % , c ) 14.14 % , d ) 13.33 % , e ) 12.52 %
Rationale: ( 100 % + 8 % ) * ( 100 % - 19 % ) = 1.08 * . 81 = 0.8748 1 - 0.8748 = 12.52 % lost = - 12.52 % the answer is e the organization has lost 12.52 % of its total volunteers from fall to spring .
Answer: e
Python program:
a = 8 / 100
b = 1 + a 
c = 19 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: a train passes a platform in 25 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 75 , b ) 25 , c ) 26 , d ) 23 , e ) 22
Rationale: speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 20 = > 300 + l = 15 × 25 = 375 = > l = 375 - 300 = 75 meter answer is a .
Answer: a
Python program:
a = const_0_2778 * 54
b = 25 - 20
c = a * b
Problem: 5 + 8
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: b
Answer: b
Python program:
a = 5 / 8
b = a * 100
Problem: how many integers between 324,700 and 418,600 have tens digit 1 and units digit 3 ?
Options: a ) 652 , b ) 827 , c ) 939 , d ) 1045 , e ) 1136
Rationale: "the integers are : 324,713 324,813 etc . . . 418,513 the number of integers is 4186 - 3247 = 939 the answer is c ."
Answer: c
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 418 - 600
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 . 250 . find the total worth of the stock ?
Options: a ) 12500 , b ) 20000 , c ) 20289 , d ) 20027 , 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 = 250 = > x = 12500 answer : a"
Answer: a
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 = 250 / h
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 5 cm , and the point of contact is 7 cm above the ground , what is the radius of the other ball ?
Options: a ) 10 cm , b ) 25 / 2 cm , c ) 35 / 3 cm , d ) 15 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 5 = 5 / r - 5 giving r = 35 / 3 . answer : c"
Answer: c
Python program:
a = 5 + 7 
b = a + 5
Problem: a couple spent $ 158.40 in total while dining out and paid this amount using a credit card . the $ 158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 115 , b ) $ 120 , c ) $ 125 , d ) $ 130 , e ) $ 135
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 158.40 x = 120 the correct answer is b ."
Answer: b
Python program:
a = 158 * 40
b = 100 + 20 
c = a / b
d = c * 100
e = 100 + 10 
f = d / e
Problem: we have a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 120 inches and the width is 108 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 125
b ) b 120
c ) c 70
d ) d 40
e ) e 10
Rationale: l = 120 / 12 = 10 ft w = 108 / 12 = 9 ft area of paper = 90 area of cube = 10 * side ^ 2 side of cube = 5 v of cube = 125
Answer: a
Python program:
a = cube_edge_by_volume + (