euclaise/mathqa_programs huggingface dataset:
Problem: the average of 45 results is 12 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 12 * 45 - 15 * 22 + 20 * 22 = 540 - 330 + 440 = 650 answer is d"
Answer: d
Python program:
a = 45 * 12
b = 22 * 20
c = a - b
d = 22 * 15
e = c - d
Problem: how many digits are in ( 8 × 10 ^ 8 ) ( 10 × 10 ^ 10 ) ?
Options: a ) 20 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "the question simplfies to ( 8 × 10 ^ 8 ) ( 10 ^ 11 ) = > 8 * 10 ^ 19 = > will contain 19 zeros + 1 digit 8 = > 20 ans a"
Answer: a
Python program:
a = 3 + 4 
b = 10 + a
Problem: the water level in a rectangular swimming pool measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 1200 , e ) 4687.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 50 * 25 * 1 / 2 = 625 feet ^ 3 of water must be removed , which equals to 625 * 7.5 = 4687.5 gallons . answer : e ."
Answer: e
Python program:
a = 10 + 2 
b = 6 / a
c = volume_rectangular_prism * (
Problem: if 34 men do a work in 40 days , in how many days will 20 men do it ?
Options: a ) 65 , b ) 68 , c ) 61 , d ) 55 , e ) 74
Rationale: "34 * 40 = 20 * x x = 68 days answer : b"
Answer: b
Python program:
a = 34 * 40
b = a / 20
Problem: susan finds that she spends her free time during summer vacation between swimming , reading , and hanging out with friends in a ratio of 1 : 4 : 10 . how many hours did she spend reading if she hung out with her friends for 20 hours ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 10
Rationale: the ratio is 1 hour swimming : 4 hours reading : 10 hours hanging out with friends . divide 20 by 10 to find 1 ` ` part ' ' of the ratio . 20 / 10 = 2 multiply this by 4 to find the hours spent reading . 2 * 4 = 8 the answer is d .
Answer: d
Python program:
a = 1 + 4 
b = a + 10 
c = 20 * b
d = c / 10
e = d * 4
f = 1 + 4 
g = f + 10 
h = e / g
Problem: 3 ltr of water is added with 11 ltr of a solution containing 42 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 23 % , b ) 35 % , c ) 33 % , d ) 40 % , e ) 45 %
Rationale: "we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 × 42 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 × 42 / 100 14 × 100 = 11 × 4210014 × 100 = 11 × 3 / 100 = 33 % c"
Answer: c
Python program:
a = 42 / 100
b = a * 11
c = 3 + 11 
d = b / c
e = 100 * d
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 30 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 255 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 30 ) = 21 + 234 = > 255 hence answer will be ( b )"
Answer: b
Python program:
a = 0 * 65
b = a * 12
Problem: when positive integer x is divided by positive integer y , the remainder is 1.44 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 1.44 - - > x = qy + 1.44 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 1.44 - - > y = 12 . answer : e ."
Answer: e
Python program:
a = math.floor(96, 12)
b = 96 - 12
c = 1 / 44
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many e hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in e = 3 hours ) solving these 2 equations we can find b as 12 so , d
Answer: d
Python program:
a = 1 / 3
b = 1 / 4
c = a - b
d = 1/(c)
Problem: sophia finished 23 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?
Options: a ) 180 , b ) 200 , c ) 250 , d ) 270 , e ) 300
Rationale: "let x be the total number of pages in the book , then she finished 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ x pages left . 23 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 90 x = 270 . so answer is d ."
Answer: d
Python program:
a = 2 / 3
b = 2 / 3
c = 1 - b
d = a - c
e = 90 / d
Problem: on dividing a n by 9 , remainder is 8 . the quotient obtained when divided by 11 , leaves remainder 9 . now the quotient when divided by 13 , leaves remainder 8 . find the remainder when when the n is divided by 1287
Options: a ) 871 , b ) 881 , c ) 891 , d ) 904 , e ) 987
Rationale: take from the last step division suppose no . is n which is divided by 13 and remainder 8 = 13 n + 8 now 13 n + 8 will be the no . which is divided by 11 and remainder is 9 = [ 11 * ( 13 n + 8 ) ] + 9 now this no . is used for the very first step which is divider is 9 and remainder is 8 = { 9 * [ 11 * ( 13 n + 8 ) ] + 9 } + 8 solve and ans is 881 answer : b
Answer: b
Python program:
a = 9 * 9
b = a * 11
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 50 extra yellow balls and making ratio of white balls to yellow balls 7 / 11 . how many tennis balls did the retailer order originally .
Options: a ) 17.5 , b ) 130 , c ) 175 , d ) 195 , e ) 220
Rationale: "white : yellow = x : ( x + 50 ) = 7 : 11 - - > 11 x = 7 x + 350 - - > x = 87.5 . the total # of balls originally x + x = 87.5 + 87.5 = 175 . answer : c ."
Answer: c
Python program:
a = 7 * 50
b = 11 - 7
c = a / b
d = c * 2
Problem: two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 10 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.5 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option b 20 + 10 t = 50 t t = 0.5"
Answer: b
Python program:
a = 50 - 10
b = 20 / a
Problem: an equilateral triangle and three squares are combined as shown above , forming a shape of area 48 + 4 √ 3 . what is the perimeter of the shape formed by the triangle and squares ?
Options: a ) 18
b ) 27
c ) 36
d ) 48
e ) 64
Rationale: triangle area = root ( 3 ) s ^ 2 / 4 area of 3 squares together = 3 s ^ 2 root ( 3 ) s ^ 2 / 4 + 3 s ^ 2 = 48 + 4 root ( 3 ) root ( 3 ) / 4 s ^ 2 = 4 root ( 3 ) s ^ 2 = 16 = > s = 4 there are 3 sides of each square = 3 ( 4 ) ( 3 ) = 36 option c
Answer: c
Python program:
a = 3 ** 2
b = a * 4
Problem: if 10 litres of an oil of rs . 54 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 58 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "54 * 10 = 540 66 * 5 = 330 870 / 15 = 58 answer : b"
Answer: b
Python program:
a = 10 * 54
b = 5 * 66
c = a + b 
d = 10 + 5 
e = c / d
Problem: a tank is filled by 3 pipes a , b , c in 10 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 20 hr , b ) 52 hr , c ) 70 hr , d ) 66 hr , e ) 48 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 10 7 / x = 1 / 10 x = 70 hours answer is c"
Answer: c
Python program:
a = 2 * 2
b = a + 2 
c = b + 1 
d = c * 10
Problem: the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is
Options: a ) 4 / 5 , b ) 7 / 11 , c ) 7 / 13 , d ) 7 / 15 , e ) 8 / 11
Rationale: let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 a )
Answer: a
Python program:
a = 9 - 4
b = 4 / a
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 2250 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 900
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 2250 * 2 / 5 = $ 900 answer is e"
Answer: e
Python program:
a = 3 + 2 
b = 2 / a
c = b * 2250
Problem: a can complete the job in 3 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: 1 / 6 = a
Answer: a
Python program:
a = 3 - 1
b = a - 3
c = 3 * 3
d = b / c
Problem: hcf and lcm two numbers are 20 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 220
Rationale: 20 * 396 = 36 * x x = 220 answer : e
Answer: e
Python program:
a = 20 * 396
b = a / 36
Problem: a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 , is
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none of these
Rationale: "x / 5 + 5 = x / 4 - 5 = > x / 5 - x / 4 = 10 x / 20 = 10 = > x = 200 answer : c ."
Answer: c
Python program:
a = 5 + 5 
b = 1 / 5
c = 1 + 5 
d = 1 / c
e = b - d
f = a / e
Problem: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 250 m , c ) 876 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 15 ) m = 250 m . answer : b"
Answer: b
Python program:
a = 60 * 1000
b = a / 3600
c = b * 15
Problem: what is the least number which should be added to 2982 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 14 , b ) 18 , c ) 22 , d ) 26 , e ) 30
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2982 by 60 , the remainder is 42 . the number to be added = 60 - 42 = 18 . the answer is b ."
Answer: b
Python program:
a = 5 * 2
b = 5 + a 
c = 6 + b 
d = 4 + c 
e = 3 + d
Problem: the ratio of toddlers to infants at a day care center is 7 to 3 . if 12 more infants join the day care to change the ratio to 7 to 5 , how many toddlers are there at this day care center ?
Options: a ) 24 , b ) 36 , c ) 42 , d ) 72 , e ) 120
Rationale: 5 x - 3 x = 12 so , 2 x = 6 hence no of toddlers is 6 * 7 = 42 answer will be ( c ) 42
Answer: c
Python program:
a = 7 * 7
b = 5 * 3
c = a - b
d = c + 12 
e = d - 4
Problem: without stoppages , a train travels certain distance with an average speed of 400 km / h , and with stoppages , it covers the same distance with an average speed of 360 km / h . how many minutes per hour the train stops ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "due to stoppages , it covers 40 km less . time taken to cover 40 km = 40 â  „ 400 h = 1 â  „ 10 h = 1 â  „ 10 ã — 60 min = 6 min answer d"
Answer: d
Python program:
a = 360 / 400
b = a * const_60
c = const_60 - b
Problem: express a speed of 18 kmph in meters per second ?
Options: a ) 10 mps , b ) 06 mps , c ) 09 mps , d ) 05 mps , e ) 11 mps
Rationale: d 5 mps 18 * 5 / 18 = 5 mps
Answer: d
Python program:
a = const_0_2778 * 18
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 16 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 8 hours , d ) 16 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 16 = 8 hours answer is c"
Answer: c
Python program:
a = 12 - 10
b = a / 16
Problem: each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 20 , e ) 24
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 6 . we need to remove 18 of the 20 - pound boxes . the answer is c ."
Answer: c
Python program:
a = 20 * 30
b = 30 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 30
h = 30 * 18
i = g - h
j = 20 - 10
k = i / j
l = 30 - k
m = 20 * l
n = f + m 
o = 30 * 15
p = n - o
q = 20 - 15
r = p / q
Problem: a train 280 m long , running with a speed of 72 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 280 * 1 / 20 = 14 sec answer : d"
Answer: d
Python program:
a = 72 * 1000
b = 280 / a
c = b * 3600
Problem: in a coconut grove , ( x + 4 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 4 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) none of the above
Rationale: ( x + 4 ) × 60 + x × 120 + ( x − 4 ) × 180 / ( x + 4 ) + x + ( x − 4 ) = 100 ⇒ 360 x − 480 / 3 x = 100 ⇒ 60 x = 480 ⇒ x = 8 answer c
Answer: c
Python program:
a = 180 * 4
b = 60 * 4
c = a - b
d = 60 + 120 
e = d + 180 
f = 100 * 3
g = e - f
h = c / g
Problem: what is the sum of the greatest common factor and the lowest common multiple of 12 and 36 ?
Options: a ) 48 , b ) 22 , c ) 32 , d ) 36 , e ) 38
Rationale: "prime factorization of 12 = 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 36 sum = 48 . answer a ."
Answer: a
Python program:
a = 12 * 36
b = a / 4
Problem: what is the sum of all the prime numbers greater than 30 but less than 50 ?
Options: a ) 126 , b ) 199 , c ) 198 , d ) 188 , e ) 122
Rationale: "required sum = ( 31 + 37 + 41 + 43 + 47 ) = 199 note : 1 is not a prime number answer b"
Answer: b
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 + 30 
t = 2 + 4 
u = s + t
Problem: in one hour , a boat goes 16 km along the stream and 6 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 11 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 16 + 6 ) kmph . = 11 kmph . answer b"
Answer: b
Python program:
a = 16 + 6 
b = a / 2
Problem: what is the sum of the integers from - 150 to 155 , inclusive ?
Options: a ) 865 , b ) 955 , c ) 1050 , d ) 765 , e ) 750
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 155 , a = - 150 , d = 1 hence , 155 = - 150 + ( n - 1 ) or n = 306 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 306 * ( - 150 + 155 ) / 2 sn = 306 * 5 / 2 = 765 answer : d"
Answer: d
Python program:
a = 150 * 155
b = a / 4
Problem: how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 150 m length ?
Options: a ) 12.7 sec , b ) 13.9 sec , c ) 18.1 sec , d ) 17.1 sec , e ) 19.7 sec
Rationale: "speed = 70 * 5 / 18 = 19.4 m / sec total distance covered = 120 + 150 = 270 m . required time = 270 / 19.4 ' = 13.9 sec . answer : b"
Answer: b
Python program:
a = 120 + 150 
b = 70 * const_0_2778
c = a / b
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of two metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 2 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 2 + 2 = 26 meter answer is c ."
Answer: c
Python program:
a = 12 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: a palindrome is a number that reads the same forward and backward , such as 121 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500
Rationale: first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 90 = 50 answer : c
Answer: c
Python program:
a = 4 / 2
b = 10 ** a
c = b / 2
Problem: in an aquarium there is 14 purple fish , 8 orange fish , 12 pink fish , 3 golden fish . how many fish are there in an aquarium ?
Options: a ) 27 , b ) 37 , c ) 17 , d ) 47 , e ) 07
Rationale: 14 + 8 + 12 + 3 = 37 . answer is b
Answer: b
Python program:
a = 3 * 12
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 100 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 500 , b ) 1500 , c ) 2500 , d ) 2000 , e ) 1000
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 100 accidents as 2 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 100 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 100 x = 20 * 100 = 2000 answer : d"
Answer: d
Python program:
a = 2 * 10
b = 100 * a
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 40 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 40 hours , c ) 8 hours , d ) 20 hours , e ) 30 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 40 = 20 hours answer is d"
Answer: d
Python program:
a = 12 - 10
b = a / 40
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128000 locusts ?
Options: a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16
Rationale: - 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d
Answer: d
Python program:
a = 10 / 2
b = a * 2
Problem: an error 2 % in excess ismade while measuring the side ofa square . the % of error in the calculated area of the square is ?
Options: a ) 4.00 %
b ) 4.04 %
c ) 4.16 %
d ) 4.30 %
e ) 5 %
Rationale: 100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b
Answer: b
Python program:
a = 100 + 2 
b = 100 + 2 
c = a * b
d = 100 * 100
e = c - d
f = e / 100
Problem: if x is the product of the positive integers from 1 to 9 , inclusive , and if i , k , m , and p are positive integers such that x = 2 i 3 k 5 m 7 px = 2 i 3 k 5 m 7 p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 13
Rationale: "x = 9 ! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = ( 3 ^ 2 ) * ( 2 ^ 3 ) * 7 * ( 2 * 3 ) * 5 * 2 ^ 2 * 3 * 2 * 1 = 2 ^ 7 * 3 ^ 4 * 5 * 7 = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p i + k + m + p = 7 + 4 + 1 + 1 = 13 answer e"
Answer: e
Python program:
a = 7 + 2 
b = 5 / 5
c = a + b 
d = 3 / 3
e = c + d
Problem: of the diplomats attending a summit conference , 22 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 100 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 22 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 100 . answer : c ."
Answer: c
Python program:
a = 32 - 22
b = 20 / 100
c = 10 / 100
d = b - c
e = a / d
Problem: a football team lost 5 yards and then gained 10 . 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 + 10 = 5 yards c"
Answer: c
Python program:
a = 10 - 5
Problem: find the sum of first 20 natural numbers
Options: a ) 470 , b ) 210 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 20 ( 20 + 1 ) / 2 = 20 ( 21 ) / 2 = 210 answer : option b"
Answer: b
Python program:
a = 20 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 20 / e
g = f / 2
h = 20 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 20 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: weights of two friends ram and shyam are in the ratio 2 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 17 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 2 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 2 / 5 or , x = 17 % . answer : option a"
Answer: a
Python program:
a = 15 - 10
b = 2 / 5
c = a * b
d = 15 + c
Problem: what is the tens digit of 36 ^ 12 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 24 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 24 ( dont actually calculate full values ) and answer is e : 9"
Answer: e
Python program:
a = 4 + 1 
b = 36 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: the smallest number which when diminished by 8 , is divisible 8 , 16 , 24 , 32 and 40 is :
Options: a ) 1008 , b ) 1015 , c ) 488 , d ) 490 , e ) 590
Rationale: "required number = ( l . c . m . of 8 , 16 , 24 , 32 , 40 ) + 8 = 480 + 8 = 488 answer : option c"
Answer: c
Python program:
a = 3 ** 8
b = 8 ** 4
c = a * b
d = 3 + 4 
e = c * d
f = e + 8
Problem: how many numbers from 2 to 15 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 15 / 2 = 7 7 - 1 = 6 6 + 1 = 7 numbers . answer : d"
Answer: d
Python program:
a = 15 / 2
b = math.floor(a)
c = b * 2
d = 2 / 2
e = math.floor(d)
f = e + 1 
g = f * 2
h = c - g
i = h / 2
j = i + 1
Problem: calculate 469160 x 9999 = ?
Options: a ) 4691130840 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none
Rationale: "answer 469160 x 9999 = 469160 x ( 10000 - 1 ) = 4691600000 - 469160 = 4691130840 . option : a"
Answer: a
Python program:
a = 469160 * 9999