euclaise/mathqa_programs huggingface dataset:
Problem: a can do a piece of work in 5 days and b can do it in 7 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 11 , c ) 7 / 12 , d ) 9 / 12 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 7 ( a + b ) ’ s one day work = 1 / 5 + 1 / 7 = 12 / 35 = > time = 35 / 12 = 2 9 / 12 days answer : option d"
Answer: d
Python program:
a = 1 / 5
b = 1 / 7
c = a + b 
d = 1 / c
Problem: find the value of m 72519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Python program:
a = 9999 - 4
b = a * 72519
Problem: sandy buys an old scooter for $ 800 and spends $ 200 on its repairs . if sandy sells the scooter for $ 1200 , what is the gain percent ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 25 %
Rationale: selling price / total cost = 1200 / 1000 = 1.2 the gain percent is 20 % . the answer is c .
Answer: c
Python program:
a = 200 + 800 
b = 1200 - a
c = 200 + 800 
d = b / c
e = d * 100
Problem: a certain bacteria colony doubles in size every day for 21 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 20 , d ) 15 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 21 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 20 times . answer : c . similar questions to practice : hope it helps ."
Answer: c
Python program:
a = 21 / 21
b = 21 - a
Problem: a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 6000 , b ) 9000 , c ) 9500 , d ) 12000 , e ) none
Rationale: "sol . let b ’ s capital be rs . x . then , 3500 * 12 / 7 x = 2 / 3 ⇔ 14 x = 126000 ⇔ x = 9000 . answer b"
Answer: b
Python program:
a = 3500 * 12
b = a * 3
c = 12 - 5
d = c * 2
e = b / d
Problem: how many consecutive zeros are there at the end of 100 ! ( 100 factorial ) ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: number of zeros will be 24 reason 100 / 5 = 20 20 / 5 = 4 so the total number of 5 will be 20 + 4 = 24 answer : d
Answer: d
Python program:
a = 4 + 1 
b = 100 / a
c = 4 + 1 
d = 4 + 1 
e = c * d
f = 100 / e
g = b + f
Problem: the ratio of spinsters to cats is 2 to 7 . if there are 55 more cats than spinsters , how many spinsters are there ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 55 x = 11 and the number of spinsters is 2 ( 11 ) = 22 . the answer is c ."
Answer: c
Python program:
a = 7 - 2
b = 55 / a
c = b * 2
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 4000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 500 , d ) s . 800 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 4000 ) = rs . 500 answer = c"
Answer: c
Python program:
a = 1/(3)
b = 1/(8)
c = 1/(6)
d = b + c 
e = a - d
f = e * 4000
g = f * 3
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 20 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 64 , b ) 130 , c ) 140 , d ) 160 , e ) 120
Rationale: "white : yellow = x : ( x + 20 ) = 8 : 13 - - > 13 x = 8 x + 160 - - > x = 32 . the total # of balls originally x + x = 32 + 32 = 64 . answer : a ."
Answer: a
Python program:
a = 8 * 20
b = 13 - 8
c = a / b
d = c * 2
Problem: ramu bought an old car for rs . 42000 . he spent rs . 10000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 17 % , b ) 19 % , c ) 24.8 % , d ) 14 % , e ) 16 %
Rationale: "total cp = rs . 42000 + rs . 10000 = rs . 52000 and sp = rs . 64900 profit ( % ) = ( 64900 - 52000 ) / 52000 * 100 = 24.8 % answer : c"
Answer: c
Python program:
a = 42000 + 10000 
b = 64900 - a
c = 42000 + 10000 
d = b / c
e = d * 100
Problem: find the average of all numbers between 5 and 45 which are divisible by 6
Options: a ) 26 , b ) 24 , c ) 28 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 6 + 12 + 18 + 24 + 30 + 36 + 42 / 6 ) = 168 / 6 = 28 option c"
Answer: c
Python program:
a = 6 * 3
b = 6 * 2
c = 6 + b 
d = a + c 
e = 6 * 4
f = d + e 
g = 4 + 1 
h = g * 6
i = f + h 
j = i / 6
Problem: a group of men decided to do a work in 40 days , but 5 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 60 , b ) 15 , c ) 40 , d ) 10 , e ) 25
Rationale: "original number of men = 5 * 60 / ( 60 - 40 ) = 15 answer is b"
Answer: b
Python program:
a = 5 * 60
b = 60 - 40
c = a / b
Problem: if an object travels at nine feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 1800 , e ) 32400
Rationale: "speed = 9 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 9 = 32400 answer e"
Answer: e
Python program:
a = 3 * const_60
b = a * const_60
Problem: the youngest of 4 children has siblings who are 3 , 6 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 30 , what is the age of the youngest sibling ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "x + ( x + 3 ) + ( x + 6 ) + ( x + 7 ) = 120 4 x + 16 = 120 4 x = 104 x = 26 the answer is e ."
Answer: e
Python program:
a = 4 * 30
b = 4 + 6 
c = b + 7 
d = a - c
e = d / 4
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 126 grams of water ?
Options: a ) 110 , b ) 112 , c ) 114 , d ) 116 , e ) 118
Rationale: "( 16 / 18 ) * 126 = 112 grams the answer is b ."
Answer: b
Python program:
a = 2 + 16 
b = 126 / a
c = 2 * b
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 6 : 1 be mixed with another mixture q of milk and water in the ratio 3 : 4 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 3 : 4
Rationale: "( 6 / 7 ) * p + ( 3 / 7 ) * q = ( 1 / 7 ) * p + ( 4 / 7 ) * q 5 p = q p / q = 1 / 5 the answer is c ."
Answer: c
Python program:
a = 1 + 4 
b = 6 + 3 
c = a - b
d = c + 1
Problem: sum of two numbers prime to each other is 8 and their l . c . m . is 15 . what are the numbers ?
Options: a ) 3 and 5 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 10 , e ) 6 and 8
Rationale: "as two numbers are prime , only options satisfy ie option a and b and c but option d will not make the product of numbers i . e 15 answer : a"
Answer: a
Python program:
a = 15 + 8
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 120 , b ) $ 180 , c ) $ 310 , d ) $ 450 , e ) $ 640
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 × $ 0.4 = $ 180 the answer is b ."
Answer: b
Python program:
a = 1000 * 1000
b = 2 * 16
c = 20 * 20
d = c * 12
e = b / d
f = e * 0
Problem: the sector of a circle has radius of 21 cm and central angle 90 o . find its perimeter ?
Options: a ) 91.5 , b ) 75 , c ) 93 , d ) 94 , e ) 95
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 90 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 75 cm answer : option b"
Answer: b
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21
Problem: in what ratio should a variety of rice costing rs . 5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 1 / 2 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6
Rationale: let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5 ) = 1 / 2 answer : a
Answer: a
Python program:
a = 8 - 75
b = 8 - 75
c = a / b
d = 8 - 75
e = 8 - 75
f = d / e
g = 1 - f
h = c / g
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 160 kg then find the average weight of all the 7 rounds ?
Options: a ) 91.4 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 160 / 7 = 91.4 kgs answer : a
Answer: a
Python program:
a = 1 + 3 
b = a * 160
c = b / 7
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 30 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 9 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 630 secs . his sis ' time = 576 secs . percent increase needed = ( 630 - 576 / 630 ) * 100 = 54 / 640 * 100 = 9 % . ans ( c ) ."
Answer: c
Python program:
a = 10 * 10
b = 9 * const_60
c = b + 36 
d = 10 * const_60
e = d + 30 
f = c / e
g = 1 - f
h = a * g
Problem: sum of two numbers is 20 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 20 2 x – 3 y = 5 x = 13 y = 7 d )"
Answer: d
Python program:
a = 5 / 2
b = 20 - a
c = b / 2
d = 20 - c
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity e of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters .
Answer: d
Python program:
a = 48 / const_60
b = 4 + 1 
c = a * b
d = const_60 * c
e = 50 * d
Problem: if p # q denotes the least common multiple of p and q , then t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Python program:
a = 18 * 24
b = 12 * 16
c = a - b
d = c / 2
e = d + 24
Problem: how many seconds will it take for a car that is traveling at a constant rate of 90 miles per hour to travel a distance of 22 yards ? ( 1 mile = 1,160 yards )
Options: a ) 0.8 , b ) 0.5 , c ) 1.0 , d ) 1.1 , e ) 1.2
Rationale: speed = 90 miles / hr = 44 yard / s distance = 22 yards time = distance / speed = 22 / 44 = 0.5 sec ans - b
Answer: b
Python program:
a = 90 / 3600
b = 90 + 90 
c = b - 4
d = c * 10
e = a * d
f = 22 / e
Problem: if 4 men and 1 boy working together , can do two times as much work per hour as a man and a boy together . find the ratio of the work done by a man and that of a boy for a given time ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 3 : 3 , d ) 1 : 2 , e ) 6 : 1
Rationale: 4 m + 1 b = 2 ( 1 m + 1 b ) 4 m + 1 b = 2 m + 2 b 2 m = 1 b the required ratio of work done by a man and a boy = 1 : 2 d
Answer: d
Python program:
a = 2 - 1
b = 4 - 2
c = a / b
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 54 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.15 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : b"
Answer: b
Python program:
a = 1 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 15
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 5 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.2 . , d ) 8 . , e ) 6.4
Rationale: w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 5 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 5 = 8 desks d is the correct answer .
Answer: d
Python program:
a = 5 / 2
b = 2 / a
c = b / 2
d = c * 4
e = d * 5
Problem: a retailer buys 60 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 40 , b ) 65 , c ) 72 , d ) 78 , e ) 20
Rationale: let the market price of each pen be $ 1 then , cost price of 60 pens = $ 36 selling price of 60 pens = 99 % of $ 60 = $ 59.40 profit % = ( ( 23.40 * 100 ) / 36 ) % = 65 % answer b
Answer: b
Python program:
a = 1 / 100
b = 1 - a
c = 36 / 60
d = b - c
e = 36 / 60
f = d / e
g = 100 * f
Problem: if 65 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
Rationale: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 15 % = 40 % . the answer is b ."
Answer: b
Python program:
a = 65 + 55 
b = a + 20 
c = b - 100
Problem: a person starts walking at a speed of 5 km / hr through half the distance , rest of the distance he covers with aspeed 4 km / hr . total time of travel is 6 hours . what is the maximum distance he can cover ?
Options: a ) 20 km , b ) 40 km , c ) 60 km , d ) 80 km , e ) 26.6 km
Rationale: t = d / s , so 6 = x / 2 * 1 / 5 + x / 2 * 1 / 4 ( because half distance with 5 km / ph , and remaining half with 4 km / hr ) 6 = x ( 18 / 80 ) x = 26.6 km answer : e
Answer: e
Python program:
a = 5 * 2
b = 4 * 2
c = a * b
d = c * 6
e = 5 * 2
f = 4 * 2
g = e + f 
h = d / g
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 1 year ?
Options: a ) 12300 , b ) 12350 , c ) 12000 , d ) 12500 , e ) 12600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 120 / 100 = 12000 c"
Answer: c
Python program:
a = 10000 * 20
b = a / 100
c = b * 1
d = 10000 + c
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 95 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 50 , b ) 43 , c ) 45 , d ) 55 , e ) 60
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 93 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 / 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 95 - 45 = 50 option a"
Answer: a
Python program:
a = 4 + 1 
b = 95 / a
c = math.floor(b)
d = 95 / 4
e = math.floor(d)
f = c + e 
g = 4 + 1 
h = 10 + g 
i = 95 / h
j = math.floor(i)
k = f - j
l = 95 - k
Problem: what percent is 10 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 3 %
Rationale: "1 kg = 1000 gm 10 / 1000 × 100 = 1000 / 1000 = 1 % b )"
Answer: b
Python program:
a = 10 / 1
b = a * 100
Problem: 7 people went to a restaurant for dinner . 6 of them spent $ 11 each on their meals and the seventh person spent $ 6 more than the average expenditure of all 7 people . what was the total amount of money that the 7 people spent ?
Options: a ) $ 80 , b ) $ 81 , c ) $ 82 , d ) $ 83 , e ) $ 84
Rationale: let t be the total amount of money spent . 6 * 11 + ( t / 7 + 6 ) = t 72 = 6 t / 7 t = ( 7 * 72 ) / 6 = 84 the answer is e .
Answer: e
Python program:
a = 6 * 11
b = a + 6 
c = 7 - 1
d = b / c
e = d + 6 
f = 6 * 11
g = e + f
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 32 ) = 32 hence answer will be ( d )"
Answer: d
Python program:
a = 10 - 1
b = a * 4
Problem: there are 15 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 272 , b ) 167 , c ) 157 , d ) 352 , e ) 380
Rationale: "the total number of stations = 17 from 17 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 17 p ₂ ways . 17 p ₂ = 17 * 16 = 272 . answer : a"
Answer: a
Python program:
a = 15 + 1 
b = 15 + 1 
c = b + 1 
d = a * c
Problem: how long will it take a train travelling at 68 kmph to pass an electric pole if the train is 170 m long
Options: a ) 6.99 , b ) 5.99 , c ) 8.99 , d ) 4.99 , e ) 9.99
Rationale: "sol . speed = [ 68 x 5 / 18 ] m / sec = 18.9 m / sec . time taken = ( 170 / 18.9 ) sec = 8.99 sec . answer c"
Answer: c
Python program:
a = 170 / 1000
b = a / 68
c = b * 3600
Problem: a , b and c rents a pasture for rs . 1073 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 267 , d ) 255 , e ) 333
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 1073 = 333 answer : e"
Answer: e
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 1073 / e
g = 16 * 9
h = f * g
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 15 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 160 %
Rationale: "kim purchased 20 gallons of gas . she paid for 15 + 0.9 * 5 = 19.5 gallons , so the overall discount she got was 0.5 / 20 = 0.025 . isabella purchased 25 gallons of gas . she paid for 15 + 0.9 * 10 = 24 gallons , so the overall discount she got was 1 / 25 = 0.04 . 4 / 2.5 * 100 = 160 % answer : e ."
Answer: e
Python program:
a = 10 - 1
b = 10 + a 
c = 100 - 10
d = b * c
e = d / 100
f = e + 15 
g = f / 25
h = 1 - g
i = h * 100
j = 10 + 4 
k = 100 - 10
l = j * k
m = l / 100
n = 15 + m 
o = n / 20
p = 1 - o
q = p * 100
r = i / q
s = r * 100
Problem: a batsman makes a score of 100 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 ) + 100 = 11 x x = 100 - 50 = 50 answer is b"
Answer: b
Python program:
a = 11 * 5
b = 100 - a
c = b + 5
Problem: sam wrote 7 letters on tuesday and 3 letters on wednesday . how many letters did he write on average per day ?
Options: a ) 10 , b ) 4 , c ) 21 , d ) 3 , e ) 5
Rationale: ( 7 + 3 ) / 2 = 5 the correct answer is e
Answer: e
Python program:
a = 7 + 3 
b = a / 2
Problem: the mean of 20 observations was 36 . it was found later that an observation 25 was wrongly taken as 40 . the corrected new mean is
Options: a ) 30 , b ) 25.4 , c ) 40 , d ) 35.25 , e ) 26.55
Rationale: "explanation : correct sum = ( 36 * 20 + 25 - 40 ) = 705 correct mean = = 705 / 20 = 35.25 answer : d"
Answer: d
Python program:
a = 36 * 20
b = 20 - 2
c = b - 40
d = a + c 
e = d / 20
Problem: an outlet pipe can empty 2 / 3 of a cistern in 12 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 2 / 7 , d ) 2 / 9 , e ) 3 / 10
Rationale: "4 / 12 * 2 / 3 = 2 / 9 the answer is d ."
Answer: d
Python program:
a = 2 / 3
b = 4 * a
c = b / 12
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 30 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 55 , d ) d . 68 , e ) e . 60
Rationale: "30 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 75 thus , more men needed to finish the task = 75 - 30 = 45 hence answer is b"
Answer: b
Python program:
a = 15 - 2
b = 30 * a
c = b * 100
d = 300 - 100
e = 2 * 5
f = c / e
g = f - 30
Problem: how many of the positive factors of 24 are not factors of 26
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 6
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 26 - 1 , 2 , 13 , 26 comparing both , we have 6 factors of 24 which are not factors of 26 - 3 , 4 , 6 , 8 , 12,24 answer : e"
Answer: e
Python program:
a = 26 / 24
Problem: he average weight of 6 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 80 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : d"
Answer: d
Python program:
a = 2 * 5
b = a + 65