euclaise/mathqa_programs huggingface dataset:
Problem: the difference of the areas of two squares drawn on two line segments of different lengths is 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm .
Options: a ) 6 cm , b ) 7 cm , c ) 9 cm , d ) 11 cm , e ) none
Rationale: "solution let the lengths of the line segments be x cm and ( x + 2 ) cm . then ( x + 2 ) 2 - x 2 = 32 < = > x 2 + 4 x + 4 - x 2 = 32 < = > 4 x = 28 therefore x = 7 . length of longer line segment = ( 7 + 2 ) cm = 9 cm . answer c"
Answer: c
Python program:
a = 2 * 2
b = 32 - a
c = b / 4
Problem: a cube of edge 6 cm is cut into cubes each of edge 3 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 4 , b ) 1 : 25 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1 / 4 = 1 : 4 . answer a"
Answer: a
Python program:
a = 4 / 100
Problem: robert ate 7 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) 4 , b ) 7 , c ) 9 , d ) 5 , e ) 2
Rationale: 7 - 3 = 4 . answer is a
Answer: a
Python program:
a = 7 - 3
Problem: a car traveling at a certain constant speed takes 20 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 36 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "36 * t = 1 km = > t = 1 / 36 km / h v * ( t + 20 / 3600 ) = 1 v ( 1 / 36 + 20 / 3600 ) = 1 v ( 120 / 3600 ) = 1 v = 30 km / h the answer is d ."
Answer: d
Python program:
a = 1 / 36
b = 3600 * a
c = b + 20 
d = c / 3600
e = 1 / d
Problem: the product of x and y is a constant . if the value of x is increased by 50 % , by what percentage must the value of y be decreased ?
Options: a ) 50 % , b ) 40 % , c ) 33 1 ⁄ 3 % , d ) 25 % , e ) 12 1 ⁄ 2 %
Rationale: "product of x and y = xy if the value of x is increased by 50 % , value of y needs to be = xy / ( 1.5 x ) = 2 / 3 y decrease in value of y = y - 2 / 3 y = 1 / 3 y % decrease in value of y = ( 1 / 3 y ) / y * 100 % = 33 1 ⁄ 3 % answer c"
Answer: c
Python program:
a = 100 + 50 
b = 100 / a
c = 1 - b
d = c * 100
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 sq . cm , what is the width of the rectangle ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 150 3 w ^ 2 / 2 = 150 w ^ 2 = 100 w = 10 the answer is a ."
Answer: a
Python program:
a = 150 / 10
Problem: working at a constant rate , p can finish a job in 3 hours . q , also working at a constant rate , can finish the same job in 15 hours . if they work together for 2 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 45 , e ) 48
Rationale: each hour they complete 1 / 3 + 1 / 15 = 2 / 5 of the job . in 2 hours , they complete 2 ( 2 / 5 ) = 4 / 5 of the job . the time for p to finish is ( 1 / 5 ) / ( 1 / 3 ) = ( 3 / 5 ) hour = 36 minutes the answer is b .
Answer: b
Python program:
a = 1/(3)
b = 1/(15)
c = a + b 
d = c * 2
e = 1 - d
f = 1/(3)
g = e / f
h = g * const_60
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 54 )
Options: a ) 251 , b ) 261 , c ) 262 , d ) 269 , e ) 278
Rationale: "there are 31 digits in 10 ^ 30 when we subtract 54 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 54 = 9999999 . . . . ( 30 times ) + 1 - 54 = 9999999 . . . . ( 30 times ) - 53 consider the last 2 digits , 99 - 53 = 46 the last 2 digits will be 46 . and our number would be 99999 . . . . . . 99946 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 46 the sum of the digits will be ( 28 * 9 ) + 4 + 6 = 262 answer : - c"
Answer: c
Python program:
a = 10 - 1
b = 30 - 2
c = a * b
d = c + 10
Problem: a room of 6 m 20 cm long and 5 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 88900 , b ) 87700 , c ) 88970 , d ) 88000 , e ) 89000
Rationale: "explanation : area of the room = 620 * 574 sq cm size of largest square tile = h . c . f of 620 cm and 574 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 620 * 574 ) / ( 2 * 2 ) = 88970 answer : c ) 88970"
Answer: c
Python program:
a = 6 * 100
b = a + 20 
c = 5 * 100
d = c + 74 
e = b * d
f = 6 * 100
g = f + 20 
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is ?
Options: a ) 287 , b ) 278 , c ) 698 , d ) 279 , e ) 275
Rationale: "s . i . for 1 year = ( 854 - 815 ) = rs . 39 s . i . for 3 years = 39 * 3 = rs . 117 principal = ( 815 - 117 ) = rs . 698 . answer : c"
Answer: c
Python program:
a = 854 - 815
b = a * 3
c = b / 4
d = 815 - c
Problem: a football team lost 5 yards and then gained 7 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: for lost , use negative . for gain , use positive . progress = - 5 + 7 = 2 yards a
Answer: a
Python program:
a = 7 - 5
Problem: the sum of four consecutive numbers is 102 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27
Rationale: "let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e"
Answer: e
Python program:
a = 102 + 1 
b = a / 2
Problem: what is the least common multiple of 12 , 18 , and 24 ?
Options: a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 12 = 2 ^ 2 * 3 ^ 1 18 = 2 ^ 1 * 3 ^ 2 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"
Answer: a
Python program:
a = 10 + 2 
b = 3 * 10
c = b - 3
d = math.lcm(a, c)
e = math.lcm(d, 18)
Problem: a batsman makes a score of 90 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 90 = 11 x x = 90 - 50 = 40 answer is a"
Answer: a
Python program:
a = 11 * 5
b = 90 - a
c = b + 5
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 72 , then how old is b ?
Options: a ) 28 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 72 5 x = 70 = > x = 14 hence , b ' s age = 2 x = 28 years . answer : a"
Answer: a
Python program:
a = 72 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 14,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 4634 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 14000 . t = 3 years and r = 10 % p . a . c . i . = rs . 14000 x 1 + 10 3 - 1 100 = rs . 14000 x 331 1000 = 4634 . b"
Answer: b
Python program:
a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 60 / 6
g = f / 100
h = 1 + g 
i = 60 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: dick and jane each saved $ 1,000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %
Rationale: 1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d
Answer: d
Python program:
a = 15 / 100
b = a + 1 
c = 2 - b
d = 1 - c
e = d * 100
Problem: worker a takes 10 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 40 / 9 days , c ) 39 / 9 days , d ) 6 days , e ) 60 / 9 days
Rationale: "a ' s one hour work = 1 / 10 . b ' s one hour work = 1 / 15 . ( a + b ) ' s one hour work = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 . both a & b can finish the work in 6 days d"
Answer: d
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / c
Problem: how many seconds will a 620 metre long train take to cross a man running with a speed of 8 km / hr in the direction of the moving train if the speed of the train is 80 km / hr ?
Options: a ) 25 , b ) 30 , c ) 31 , d ) 45 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 80 - 8 ) km / hr = 72 km / hr = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken to pass the man = ( 620 / 20 ) sec = 31 sec . answer : c"
Answer: c
Python program:
a = 80 - 8
b = const_0_2778 * a
c = 620 / b
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1040 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1040 20 x / 100 = 1040 x = 1040 * 100 / 20 = 5200 answer is b"
Answer: b
Python program:
a = 100 - 60
b = 60 - a
c = b / 100
d = 1040 / c
Problem: a person is traveling at 40 km / hr and reached his destiny in 6 hr then find the distance ?
Options: a ) 260 km , b ) 240 km , c ) 280 km , d ) 340 km , e ) 350 km
Rationale: "t = 6 hrs d = t * s = 40 * 6 = 240 km answer is b"
Answer: b
Python program:
a = 40 * 6
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.07 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.86 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.07 2 nd day fine - 0.07 * 2 = 0.14 ( as doubling gives lower value ) 3 rd day fine - 0.14 * 2 = 0.28 ( as doubling gives lower value ) 4 rd day fine - 0.28 * 2 = 0.56 ( as doubling gives lower value ) 5 th day fine - 0.56 + 0.3 = 0.86 ( as doubling gives higher value we add 0.3 this time ) answer : c ."
Answer: c
Python program:
a = 0 * 7
b = a * 2
c = b * 2
d = c + 0
Problem: 7 , 26 , 63 , 124 , ( . . . . )
Options: a ) 342 , b ) 125 , c ) 289 , d ) 564 , e ) 36
Rationale: "explanation : numbers are 2 ^ 3 - 1 = 7 3 ^ 3 - 1 = 26 4 ^ 3 - 1 = 63 5 ^ 3 - 1 = 124 6 ^ 3 - 1 = 342 answer : a"
Answer: a
Python program:
a = negate - (
Problem: by selling 100 pens , a trader gains the cost of 40 pens . find his gain percentage ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 30 %
Rationale: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 40 pens = rs . 40 profit % = 40 / 100 * 100 = 40 % answer : a"
Answer: a
Python program:
a = 40 / 100
b = a * 100
Problem: a sum of rs . 1870 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 330 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1870 = > 17 x / 12 = 1870 = > 1870 x 12 / 17 = rs . 1320 hence , b ’ s share = rs . ( 1320 / 4 ) = rs . 330 . answer d"
Answer: d
Python program:
a = 1870 / 10
b = a * 2
c = b - 12
d = c - 12
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 30 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 69 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 5.2 , so radius is 2.6 new area = 6.76 π increase in area is 2.76 π % increase in area = 2.76 / 4 * 100 so , % increase is 69 % answer will be ( c )"
Answer: c
Python program:
a = 30 * 2
b = a / 1000
c = b + 3 
d = c ** 2
e = d - 4
f = e / 4
g = f * 100
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 15000 and b rs . 25000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4200 , e ) 7291
Rationale: "15 : 25 = > 3 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 3 / 8 = 3240 + 960 = 4200 answer : d"
Answer: d
Python program:
a = 10 / 100
b = 1 - a
c = 9600 * b
d = 15000 + 25000 
e = 25000 / d
f = c * e
g = 9600 - f
Problem: how many numbers from 19 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 12
Rationale: "19 / 11 = 1 and 79 / 11 = 7 = = > 7 - 1 = 6 numbers answer : b"
Answer: b
Python program:
a = 79 / 11
b = math.floor(a)
c = b * 11
d = 19 / 11
e = math.floor(d)
f = e + 1 
g = f * 11
h = c - g
i = h / 11
j = i + 1
Problem: two pipes can fill a tank in 10 minutes and 15 minutes . an outlet pipe can empty the tank in 30 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 ) 7.0 , b ) 7.5 , c ) 8.0 , d ) 8.5 , e ) 9.0
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 10 + v / 15 - v / 30 = 2 v / 15 per minute the tank will be filled in 15 / 2 = 7.5 minutes . the answer is b ."
Answer: b
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / 30
e = c - d
Problem: exactly 20 % of the reporters for a certain wire service cover local politics in country x . if 20 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 75 % , e ) 84 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 20 % of reporters who cover politics do not cover local politics so 80 % do cover local politics . reporters covering local politics = 80 % of reporters covering politics = 20 % ofall reporters reporters covering politics / all reporters = 20 / 80 = 1 / 4 reporters not covering politics / all reporters = 3 / 4 = 75 % = d"
Answer: d
Python program:
a = 100 - 20
b = 20 / a
c = 1 - b
d = c * 100
Problem: we had $ 840 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 1000 , b ) $ 1050 , c ) $ 1100 , d ) $ 1150 , e ) $ 1200
Rationale: let x be the amount of money we started with . 0.7 x = 840 x = 1200 the answer is e .
Answer: e
Python program:
a = 30 / 100
b = 1 - a
c = 840 / b
Problem: if the sum and difference of two numbers are 10 and 8 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 80
Rationale: "let the numbers be x and y . then , x + y = 10 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 10 * 8 = 80 . answer : e"
Answer: e
Python program:
a = 10 + 8 
b = a / 2
c = b ** 2
d = 10 + 8 
e = d / 2
f = 10 - e
g = f ** 2
h = c - g
Problem: how many times will the digit 5 be written when listing the integers from 1 to 1000 ?
Options: a ) 300 , b ) 380 , c ) 180 , d ) 415 , e ) 264
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 5 ) 3000 / 10 = 300 times . answer : a ."
Answer: a
Python program:
a = 1 * 10
b = a * 10
c = b * 3
Problem: the average of first six prime numbers which are between 30 and 70 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 67
Rationale: "explanation : first six prime numbers which are between 30 and 70 = 31 , 37 , 41 , 43 , 47 , 53 average = ( 31 + 37 + 41 + 43 + 47 + 53 ) / 6 = 42 answer : b"
Answer: b
Python program:
a = 30 + 1
Problem: what is the units digit of ( 3 ^ 11 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 13 = 3 ^ 4 * 3 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 13 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Python program:
a = 4 + 3 
b = a + 2
Problem: the distance from steve ' s house to work is 30 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 30 km = > speed = 15 kmph answer : d"
Answer: d
Python program:
a = 30 / 2
b = 30 + a 
c = b / 6
d = c * 2
Problem: the sector of a circle has radius of 21 cm and central angle 270 o . find its perimeter ?
Options: a ) 145 cm , b ) 135 cm , c ) 121 cm , d ) 141 cm , e ) 151 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 270 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 99 + 42 = 141 cm answer : d"
Answer: d
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21
Problem: how many times in a day the hands of a clock are straight ?
Options: a ) 21 , b ) 27 , c ) 24 , d ) 22 , e ) 25
Rationale: "in 12 hours , the hands coincide or are in oppesite direction 22 times . in 24 hours , they are at right angles 22 times . answer is d ."
Answer: d
Python program:
a = 2 * 12
b = 2 * a
c = b - 4
d = c / 2
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 9 / 16 , e ) 15 / 16
Rationale: "p ( missing all 3 ) = ( 1 / 2 ) ^ 3 = 1 / 8 p ( success on at least one attempt ) = 1 - 1 / 8 = 7 / 8 the answer is c ."
Answer: c
Python program:
a = 1 / 2
b = a ** 3
c = 1 - b
Problem: twelve machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 12 = 18 so we need 18 - 12 = 6 more machines . answer : d
Answer: d
Python program:
a = 8 / 12
b = 1/(a)
c = 12 * b
d = c - 12
Problem: if 49 ( 7 ^ x ) = 1 then x =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "7 ^ x = 1 / 49 7 ^ x = 1 / 7 ^ 2 7 ^ x = 7 ^ - 2 x = - 2 a"
Answer: a
Python program:
a = 1 / 49
b = math.log(a)
c = math.log(7)
d = b / c
Problem: a cab driver 5 days income was $ 200 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 420 , b ) $ 410 , c ) $ 400 , d ) $ 390 , e ) $ 380
Rationale: "avg = sum of observations / number of observations avg income = ( 200 + 150 + 750 + 400 + 500 ) / 5 = 400 answer is c"
Answer: c
Python program:
a = 200 + 150 
b = a + 750 
c = b + 400 
d = c + 500 
e = d / 5
Problem: x is able to do a piece of work in 14 days and y can do the same work in 20 days . if they can work together for 5 days , what is the fraction of work completed ?
Options: a ) 15 / 28 , b ) 17 / 28 , c ) 13 / 28 , d ) 19 / 28 , e ) 11 / 28
Rationale: explanation : amount of work x can do in 1 day = 1 / 14 amount of work y can do in 1 day = 1 / 20 amount of work x and y can do in 1 day = 1 / 14 + 1 / 20 = 17 / 140 amount of work x and y can together do in 5 days = 5 × ( 17 / 140 ) = 17 / 28 answer : option b
Answer: b
Python program:
a = 14 * 20
b = 14 + 20 
c = a / b
d = 5 / c
Problem: a football field is 9600 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards ?
Options: a ) 450
b ) 600
c ) 700
d ) 2400
e ) 3200
Rationale: answer c ) 9600 yards need 1200 lbs 1 yard will need 1200 / 9600 = 1 / 8 lbs 3600 yards will need 1 / 8 * 5600 yards = 700 lbs
Answer: c
Python program:
a = 1200 / 9600
b = 5600 * a
Problem: if a man buys 1 liter of milk for 12 rs . and mixes it with 20 % water and sells it for 15 rs then what is the % age of gain . . .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: quantity after adding 20 % water = 1.2 liter sp of 1.2 lit . @ 15 rs . / liter = 15 * 1.2 = 18 rs cp = 12 rs / lit . % profit = 100 * ( 18 - 12 ) / 12 = 50 answer : c
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b * 15
d = c - 12
e = d / 12
f = e * 100
Problem: a tightrope approximately 320 m long is suspended between two poles . during a performance , a break occurs in the line . assume that the line has an equal chance of breaking anywhere along its length . what is the probability that the break happened in the first 50 meters of the rope ?
Options: a ) 27 / 32 , b ) 1 / 2 , c ) 5 / 32 , d ) 5 / 27 , e ) . 2 / 3
Rationale: simly 50 / 320 = 5 / 32 answer will be ( c )
Answer: c
Python program:
a = 50 / 320
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 18 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 18 more transactions than cal . jade = 66 + 18 = 84 jade handled = 84 transactions . answer : e"
Answer: e
Python program:
a = 90 / 100
b = 10 + 100 
c = a * b
d = c * 2
e = d / 3
f = e + 18
Problem: while working alone at their constant rates , computer x can process 240 files in 4 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 2 , b ) 2.2 , c ) 2.4 , d ) 2.6 , e ) 2.8
Rationale: both computers together process files at a rate of 240 / 4 + 240 / 6 = 60 + 40 = 100 files per hour . the time required to process 240 files is 240 / 100 = 2.4 hours the answer is c .
Answer: c
Python program:
a = 240 / 4
b = 240 / 6
c = a + b 
d = 240 / c
Problem: $ 2,000 is deposited in a savings account that pays 4 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 2125.15 , b ) $ 2083.12 , c ) $ 2184.22 , d ) $ 2150.84 , e ) $ 2080.80
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 4 / 2 = 2 % now , ca = 2000 ( 1 + 2 / 100 ) ^ 2 = $ 2080.80 hence answer is e"
Answer: e
Python program:
a = 100 * 100