euclaise/mathqa_programs huggingface dataset:
Problem: there were totally 100 men . 82 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 82 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 18 - 25 - 15 - 30 = 100 - 88 = 12 answer : b"
Answer: b
Python program:
a = 100 - 82
b = 100 - 75
c = a + b 
d = 100 - 85
e = c + d 
f = 100 - 70
g = e + f 
h = 100 - g
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 900 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 .
b ) 40 .
c ) 42 .
d ) 44 .
e ) 45 .
Rationale: let the width = x x * 4 x = 900 x ^ 2 = 225 x = 15 length = 4 * 15 = 60 difference = 60 - 15 = 45 e is the answer
Answer: e
Python program:
a = 900 / 4
b = math.sqrt(a)
c = b * 4
d = 900 / 4
e = math.sqrt(d)
f = c - e
Problem: sachin is younger than rahul by 18 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.5 , b ) 63 , c ) 65 , d ) 36 , e ) 24.19
Rationale: "explanation : if rahul age is x , then sachin age is x - 18 , so , 9 x - 162 = 7 x 2 x = 162 x = 81 so sachin age is 81 - 18 = 63 answer : b ) 63"
Answer: b
Python program:
a = 9 - 7
b = 18 / a
c = b * 7
Problem: average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 590 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 1170 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 590 x 3 rs . = 1170 rs . correct option : c"
Answer: c
Python program:
a = 735 * 4
b = 4 - 1
c = 590 * b
d = a - c
Problem: two numbers are less than third number by 32 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 14 %
Rationale: "let the third number is x . then first number = ( 100 - 32 ) % of x = 68 % of x second number is ( 63 x / 100 ) difference = 68 x / 100 - 63 x / 100 = x / 20 so required percentage is , difference is what percent of first number ( x / 20 * 100 / 68 x * 100 ) % = 14 % answer : e"
Answer: e
Python program:
a = 37 - 32
b = 100 - 32
c = a / b
d = c * 100
e = d - 10
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 100 at the end of 2 years and further to $ 200 at the end of another 4 years . what was the rate of interest in which he invested his sum ?
Options: a ) 50 % , b ) 25 % , c ) 10 % , d ) 30 % , e ) 18 %
Rationale: "explanatory answer initial amount invested = $ x amount at the end of year 2 = $ 100 amount at the end of year 6 ( another 4 years ) = $ 200 therefore , the interest earned for the 4 year period between the 2 rd year and 6 th year = $ 200 - $ 100 = $ 100 as the simple interest earned for a period of 4 years is $ 100 , interest earned per year = $ 25 . therefore , interest earned for 2 years = 2 * 25 = $ 50 . hence , initial amount invested x = amount after 2 years - interest for 2 years = 100 - 50 = $ 50 . rate of interest = ( interest per year / principal ) * 100 = 25 / 50 * 100 = 50 % correct choice is a"
Answer: a
Python program:
a = 200 - 100
b = a / 4
c = 200 - 100
d = c / 4
e = d * 2
f = 100 - e
g = b / f
h = g * 100
Problem: two nascar stock cars take off from the starting line at the exact same time , heading in opposite directions . the budweiser car travels at 145 miles per hour , while the stella artois car travels at 150 miles per hour . at this rate , and ignoring other variable , how long will the cars have to drive in order to be 500 miles , in total , from each other ?
Options: a ) 1.5 hours , b ) 1.27 hours , c ) 1.73 hours , d ) 2 hours , e ) 1.69 hours
Rationale: the cars travel ( 145 + 150 = 295 ) miles in one hour . 500 miles / 295 miles / hour = 1.69 hours answer is e
Answer: e
Python program:
a = 145 + 150 
b = 500 / a
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 2 / 3 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 8
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 2 x / 3 ) ( 3 y / 4 ) = xy / 2 the total number of boxes is xy + xy / 2 = 3 xy / 2 the fraction loaded by the day crew is xy / ( 3 xy / 2 ) = 2 / 3 the answer is b ."
Answer: b
Python program:
a = 3 * 4
b = 3 * 4
c = 3 * 2
d = b + c 
e = a / d
Problem: convert 400 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 643736
Rationale: "1 mile = 1609.34 meters 400 mile = 400 * 1609.34 = 643736 meters answer is e"
Answer: e
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 400
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: find the average of all numbers between 6 and 36 which are divisible by 7
Options: a ) 20 , b ) 15 , c ) 25 , d ) 30 , e ) 35
Rationale: explanation : average = ( 7 + 14 + 21 + 28 + 35 ) / 7 = 105 / 7 = 15 option b
Answer: b
Python program:
a = 7 * 3
b = 7 * 2
c = 7 + b 
d = a + c 
e = 7 * 4
f = d + e 
g = 4 + 1 
h = g * 7
i = f + h 
j = i / 7
Problem: in how many ways 3 boys and 3 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 36 , d ) 256 , e ) none
Rationale: "solution : let the arrangement be , b g b g b g b 34 boys can be seated in 3 ! ways . girl can be seated in 3 ! ways . required number of ways , = 3 ! * 3 ! = 36 . answer : option c"
Answer: c
Python program:
a = math.factorial(3)
b = math.factorial(3)
c = a * b
Problem: if you multiply all the numbers on your mobile phone except 0 , what is the answer ?
Options: a ) 256485 , b ) 362880 , c ) 125425 , d ) 0 , e ) 125826
Rationale: "we have to multiply 1 to 9 to find the answer . therefore 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 = 362880 answer is b"
Answer: b
Python program:
a = 1 - 1
b = 1 * a
Problem: a straight line in the xy - plane has slope 4 . on this line the x - coordinate of the point is 50 and y - coordinate is 300 then what is the y intercept of the plane ?
Options: a ) 150 , b ) 110 , c ) 100 , d ) 200 , e ) 50
Rationale: eq of line = y = mx + c m = 4 x = 50 y = 50 * 4 + c , substitute y by 300 as given in question . 300 = 200 + c , c = 100 correct option is c
Answer: c
Python program:
a = 50 * 4
b = 300 - a
Problem: what two - digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 13 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 13 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 99 thus the answer is b
Answer: b
Python program:
a = 13 - 5
b = a + 1 
c = 10 * b
d = c + 5
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area q of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Python program:
a = 4 * math.pi
b = 3 / math.pi
c = a * b
d = c / 2
e = 3 / math.pi
f = math.pi * e
g = d + f
Problem: a and b invests rs . 10000 each , a investing for 8 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 25000 , find their shares ?
Options: a ) 22277 , b ) 26782 , c ) 22882 , d ) 15000 , e ) 28761
Rationale: "the ratio of their profits a : b = 8 : 12 = 2 : 3 share of a in the total profit = 2 / 5 * 25000 = rs . 10000 share of a in the total profit = 3 / 5 * 25000 = rs . 15000 answer : d"
Answer: d
Python program:
a = 10000 * 1
b = a / 3
Problem: a river 3 m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 2678 , c ) 3600 , d ) 3400 , e ) 2500
Rationale: "( 2000 * 3 * 36 ) / 60 = 3600 m 3 answer : c"
Answer: c
Python program:
a = 3 * 36
b = 2 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 20 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 1777 meters , d ) 200 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 20 seconds distance = speed * time 36000 * 20 / 3600 = 200 meters . d is the answer ."
Answer: d
Python program:
a = 100 - 64
b = a * const_0_2778
c = b * 20
Problem: how many seconds will a 900 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 23 sec , b ) 30 sec , c ) 49 sec , d ) 54 sec , e ) 59 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 900 * 3 / 50 = 54 sec . answer : d"
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 900 / b
Problem: two airplanes take off from one airfield at noon . one flies due east at 201 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 166 , b ) 332 , c ) 400 , d ) 402 , e ) 566
Rationale: "d in two hours : the plane flying east will be 402 miles away from airport . the other plane will be 566 miles away from airport . 566 / 402 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 402 miles apart . d"
Answer: d
Python program:
a = 283 * 2
b = a ** 2
c = 201 * 2
d = c ** 2
e = b - d
f = math.sqrt(e)
Problem: what is the sum of all the multiples of 10 between 0 and 120 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 780
Rationale: "the multiples of 10 between 0 and 120 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 , 110 and 120 . if these are all added together , the result is 780 . final answer : e"
Answer: e
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 10 
t = 2 + 4 
u = s + t
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 11,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 100,000
Rationale: answer equals c in 48 years . i thought by 50 th year it would reach 95,500 . options should have been separated more widely for clarity .
Answer: c
Python program:
a = 2 + 3 
b = a * 1000
c = b * 12
d = c / 2
Problem: the ratio 4 : 20 expressed as percent equals to
Options: a ) 20 % , b ) 25 % , c ) 55 % , d ) 65 % , e ) none of above
Rationale: explanation : actually it means 4 is what percent of 20 , which can be calculated as , ( 4 / 20 ) * 100 = 4 * 5 = 20 answer : option a
Answer: a
Python program:
a = 4 / 20
b = a * 100
Problem: jack takes a loan of $ 120000 with 12 % annual interest : the interest is paid once , at the end of the year . jill takes a loan of $ 120000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to jack ' s loan interest , approximately how much more does jill have to repay ?
Options: a ) zero , b ) $ 81.90 , c ) $ 8190.03 , d ) $ 819.00 , e ) $ 8.19
Rationale: jack ' s interest = $ 120,000 * 0.12 = $ 14400 or $ 1,200 each month . jills ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 120,000 * 0.01 = $ 1,200 ; for the 2 nd month = $ 1,200 + 1 % of 1,200 = $ 1,212 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1,212 + 1 % of 1,212 = ~ $ 1,224 ; for the 4 th month = $ 1,224 + 1 % of 1,224 = ~ $ 1,236 ; . . . for the 12 th month = $ 1,320 + 1 % of 1,320 = ~ $ 1,332 . the difference between jack ' s interest and jill ’ s interest = ~ ( 12 + 24 + . . . + 132 ) = $ 792 . answer : d .
Answer: d
Python program:
a = 12 * 100
b = 12 / a
c = 1 + b 
d = c ** 12
e = 120000 * d
f = e - 120000
g = 120000 * 12
h = g / 100
i = f - h
Problem: the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 2.5 , d ) 7 / 3 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 4 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 4 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 4 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 7 / 3 answer : d"
Answer: d
Python program:
a = 8 / 2
b = 4 * a
c = b - 12
d = 32 - c
e = d / 12
Problem: evaluate 45 / . 05
Options: a ) 700 , b ) 900 , c ) 705 , d ) none of these , e ) 506
Rationale: "explanation : 45 / . 05 = 4500 / 5 = 900 option b"
Answer: b
Python program:
a = 5 / 45
b = 100 / 0
Problem: how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 1 ?
Options: a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495
Rationale: 510 , 512 , 514 , 516 , and 518 , so total 5 . hence option a .
Answer: a
Python program:
a = 3 + 1 
b = a + 1
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 150 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 * 150 = 300 meters . since second time ( when they run full circumference ) brenda runs 300 meters and sally runs 200 meters , thus the circumference is 300 + 200 = 500 meters . answer : e .
Answer: e
Python program:
a = 2 * 150
b = a + 200
Problem: a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 400 bolts ?
Options: a ) 36 , b ) 72 , c ) 96 , d ) 144 , e ) 180
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 400 bolts 400 * 6 / 25 = 96 mins ans c"
Answer: c
Python program:
a = 100 / const_60
b = 150 / const_60
c = a + b 
d = 400 / c
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 110
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 40 . thus , 3434 ( 90 + x ) = 40 + x or 270 + 3 x = 160 + 4 x or x = 110 answer : e"
Answer: e
Python program:
a = 90 - 40
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 600 m , b ) 300 m , c ) 400 m , d ) 700 m , e ) 500 m
Rationale: "a 600 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1600 ) = 600 m"
Answer: a
Python program:
a = 1 * 6
b = 18 * a
c = b / 48
Problem: a train passes a station platform in 50 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 240 m , c ) 168 m , d ) 300 m , e ) 691 m
Rationale: speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 50 = 15 = > x = 300 m answer : d
Answer: d
Python program:
a = 54 * const_0_2778
b = 20 * a
Problem: the lowest number which should be added to 8247 so that the sum is exactly divisible by 5 , 6 , 7 , 8 and 9 is :
Options: a ) 1833 , b ) 1853 , c ) 1733 , d ) 1233 , e ) 1832
Rationale: "l . c . m . of 5 , 6 , 7 , 8 and 9 = 2520 . on dividing 8247 by 2520 , the remainder is 687 . number to be added = ( 2520 - 687 ) = 1833 . answer : option ' a '"
Answer: a
Python program:
a = 8247 / 6
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 3 cm , and the point of contact is 5 cm above the ground , what is the radius of the other ball ?
Options: a ) 3 cm , b ) 9 cm , c ) 12 cm , d ) 15 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 3 = 3 / r - 3 giving r = 15 . answer : d"
Answer: d
Python program:
a = 3 + 5 
b = a + 3
Problem: in a class there are a total of 8 rows of desks and each desk can seat one student . there are 10 desks in the first row . in each subsequent row there are 2 more desks than in the previous row . find the maximum number of students seated in the class ?
Options: a ) 112 , b ) 144 , c ) 136 , d ) 132 , e ) 118
Rationale: the 8 rows form an arithmetic progression with first term 10 and last 24 . avg is 17 . so 17 * 8 = 136 answer is c .
Answer: c
Python program:
a = 8 * 2
b = 8 + 10 
c = a + b 
d = c / 2
e = d * 8
Problem: what is the smallest positive integer nn such that 6,480 ∗ n √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
Rationale: "sol : let ' s factorize 6480 and we get 6480 = 3 ^ 4 * 2 ^ 4 * 5 now we need to see for what minimum value of n √ n * 6480 = a ^ 3 where a is an integer so from 6480 we already have 2 ^ 4 * 3 ^ 4 * 5 * n √ n = ( 2 ^ 2 ) ^ 3 * ( 3 ^ 2 ) ^ 3 * ( 5 ) ^ 3 why cause a is an integer which will need to be have the same factors which are in lhs solving for n √ n = ( 2 ^ 6 * 3 ^ 6 * 5 ^ 3 ) / 2 ^ 4 * 3 ^ 4 * 5 and we get n √ n = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 or n = 2 ^ 4 * 3 ^ 4 * 5 ^ 4 or 30 ^ 4 ans is e"
Answer: e
Python program:
a = 3 + 4
Problem: a candidate who gets 20 % of the marks fails by 40 marks . but another candidate who gets 30 % marks gets 20 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 160 marks , e ) 827 marks
Rationale: "20 % - - - - - - - - - - - - 40 30 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - - - - - - 60 20 % - - - - - - - - - - - - - - 120 120 + 40 = 160 marks answer : d"
Answer: d
Python program:
a = 40 + 20 
b = 30 / 100
c = 20 / 100
d = b - c
e = a / d
f = 20 / 100
g = e * f
h = g + 40
Problem: 10 women can complete a work in 8 days and 10 children take 12 days to complete the work . how many days will 6 women and 3 children together take to complete the work ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 9 , e ) 11
Rationale: "explanation : 1 women ’ s 1 day ’ s work = 1 / 8 / 10 = 1 / 80 1 child ’ s 1 day ’ s work = 1 / 12 / 10 = 1 / 120 6 women ’ s 1 day ’ s work = 1 / 80 × 6 = 3 / 40 3 children ’ s 1 day ’ s work = 1 / 120 × 3 = 1 / 40 6 women ’ s + 3 children ’ s 1 day ’ s work = 3 / 40 + 1 / 40 = 1 / 10 therefore , they will finish the whole work in 10 days . answer : option b"
Answer: b
Python program:
a = 10 * 8
b = 6 / a
c = 3 * 12
d = 10 / c
e = b + d 
f = 1/(e)
Problem: solve for x and check : - 200 x = 1600
Options: a ) 2000 , b ) 2573 , c ) 1600 , d ) 2950 , e ) none of these
Rationale: "solution : dividing each side by - 200 , we obtain ( - 200 x / - 200 ) = ( 1600 / - 200 ) therefore : x = - 8 check : - 200 x = 1600 ( - 200 * - 8 ) = 1600 1600 = 1600 answer : c"
Answer: c
Python program:
a = 1600 / 200
b = 200 * a
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 140 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 17.5 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 140 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 140 units is ' 7 times ' 20 , we need ' 7 times ' more time . ( 2.5 hours ) ( 7 times ) = 17.5 hours final answer : [ reveal ] spoiler : c"
Answer: c
Python program:
a = 20 / 10
b = a / 5
c = b * 20
d = 140 / c
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 1 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.8 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.10 i ( last year ) = 1.1 i ( last year ) 1 = 1.1 x i ( last year ) i ( last year ) = 1 / 1.1 = 10 / 11 = 0.90909 . . . or i ( last year ) = 0.91 % answer : c"
Answer: c
Python program:
a = 1 * 100
b = 1 + 100 
c = a / b
Problem: there are 450 birds at a small zoo . the number of birds is 5 times the number of all the other animals combined . how many more birds are there than non bird animals at the zoo ?
Options: a ) 400 , b ) 360 , c ) 270 , d ) 180 , e ) 90
Rationale: total birds = 450 = 5 * other animals ( x ) or x = 90 . so , difference in birds and x = 450 - 90 = 360 . answer is b .
Answer: b
Python program:
a = 450 / 5
b = 450 - a
Problem: a man can row downstream at 20 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 15,2 , b ) 15 , 4 , c ) 15 , 8 , d ) 15 , 5 , e ) 15,7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 30 = > x = 15 , y = 5 . answer : d"
Answer: d
Python program:
a = 20 + 10 
b = a / 2
c = b / 2