euclaise/mathqa_programs huggingface dataset:
Problem: a man can swim in still water at 5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.78 , b ) 1.667 , c ) 1.15 , d ) 1.5 , e ) 1.2
Rationale: m = 5 s = x ds = 5 + x us = 5 - x 5 + x = ( 5 - x ) 2 5 + x = 10 - 2 x 3 x = 5 x = 1.667 answer : b
Answer: b
Python program:
a = 5 / 3
Problem: in an office , 10 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 16 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 10 / 100 ) * workers = x + 16 = > x = 16 answer a"
Answer: a
Python program:
a = 10 / 100
b = 16 / a
c = b * 90
d = c / 100
e = 10 / 100
f = 16 / e
g = 1 / 2
h = f * g
i = d - h
j = 2 * 4
k = i / j
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 11 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 80 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 200 days
Rationale: rate of both = 1 / 20 together they do = 1 / 20 * 11 = 11 / 20 left work = 1 - 11 / 20 = 9 / 20 adam completes 9 / 20 work in 10 day so he took 10 * 20 / 9 = 200 / 9 days to complete the left work alone . thus the rate of adam is 9 / 200 rate of micheal = 1 / 20 - 9 / 200 = 1 / 200 thus micheal takes 200 days to complete the whole work . ans . e .
Answer: e
Python program:
a = 1/(20)
b = 1/(20)
c = b * 11
d = 1 - c
e = 1/(d)
f = e * 10
g = 1/(f)
h = a - g
i = 1/(h)
Problem: a train crosses a platform of 250 m in 20 sec , same train crosses another platform of length 640 m in 40 sec . then find the length of the train ?
Options: a ) 150 m , b ) 180 m , c ) 152 m , d ) 140 m , e ) 160 m
Rationale: "length of the train be ‘ x ’ x + 250 / 20 = x + 640 / 40 2 x + 500 = x + 640 x = 140 m answer : d"
Answer: d
Python program:
a = 20 / 3
b = 20 / a
c = 640 * b
d = 20 / 3
e = 40 / d
f = 250 * e
g = c - f
Problem: the difference between the ages of two persons is 11 years . ten years ago , the elder one was twice as old as the younger one . the present age of the elder person is
Options: a ) 18 , b ) 19 , c ) 20 , d ) 17 , e ) 16
Rationale: "let their ages of x years and ( x + 11 ) years respectively . then , ( x + 11 ) - 10 = 2 ( x - 10 ) ⇔ x + 1 = 2 x - 20 ⇔ 3 x = 21 . ∴ present age of the elder person = ( 7 + 11 ) = 18 years . answer : 18 years"
Answer: a
Python program:
a = 3 + 2 
b = 11 - a
c = 11 - b
d = 3 + 2 
e = 11 - d
f = e * 2
g = c + f
Problem: a walks at 10 kmph and 3 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 60 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 3 hours . x / 10 - x / 20 = 3 x = 60 km answer is c"
Answer: c
Python program:
a = 3 * 20
Problem: a goods train runs at the speed of 72 km / hr and crosses a 80 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 440 , c ) 278 , d ) 270 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 80 ) / 26 = 20 x = 440 m . answer : b"
Answer: b
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 80
Problem: what is the total cost of 2 sandwiches at $ 1.49 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.46 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 11.85
Rationale: answer = b 2 * 1.49 + 4 * 0.87 = 2 ( 1.50 - 0.01 ) + 4 ( 1.00 - 0.13 ) = 3 + 4 - 0.02 - 0.52 = 7 - 0.54 = 6.46
Answer: b
Python program:
a = 2 * 1
b = 4 * 0
c = a + b
Problem: population of a city in 20004 was 1500000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 3251625 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 3251625 / 2 e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1500000 * h
Problem: how many prime numbers between 1 and 100 are factors of 7,150 ?
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: "make prime factorization of 7,150 - - > 7,150 = 2 ∗ 5 ^ 2 ∗ 11 ∗ 13 so , 4 prime numbers between 1 and 100 ( namely 2 , 5 , 11 , and 13 ) are factors of 7,150 . answer : d ."
Answer: d
Python program:
a = 4 * 1
Problem: a firm is comprised of partners and associates in a ratio of 2 : 61 . if 60 more associates were hired , the ratio of partners to associates would be 4 : 137 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 2 : 61 = 4 : 122 so the ratio changed from 4 : 122 to 4 : 137 . 137 - 122 = 15 which is 1 / 4 of the increase in 60 associates . the ratio changed from 16 : 488 to 16 : 548 . thus the number of partners is 16 . the answer is c ."
Answer: c
Python program:
a = 137 * 2
b = a - 61
c = 60 / b
d = c * 2
Problem: 5 , 7 , 11 , 18 , 33 , ( . . . )
Options: a ) 22 , b ) 35 , c ) 27 , d ) 63 , e ) 25
Rationale: "explanation : 5 5 × 2 - 3 = 7 7 × 2 - 3 = 11 11 × 2 - 3 = 18 18 × 2 - 3 = 33 33 × 2 - 3 = 63 answer : option d"
Answer: d
Python program:
a = negate - (
Problem: if the radius of a circle that centers at the origin is 5 , how many w points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : w = c"
Answer: c
Python program:
a = 5 * 5
b = 5 + 4 
c = a - b
d = 2 ** 2
e = c - d
Problem: how many multiples of 7 are there between 14 and 252 ?
Options: a ) 33 , b ) 46 , c ) 59 , d ) 66 , e ) 80
Rationale: "it should be mentioned whether 14 and 252 are inclusive . if 14 and 252 are inclusive , then the answer is ( 252 - 14 ) / 7 + 1 = 35 . if 14 and 252 are not inclusive , then the answer is ( 245 - 21 ) / 7 + 1 = 33 . since oa is a , then we have not inclusive case ."
Answer: a
Python program:
a = 252 - 14
b = a / 7
c = b + 1
Problem: solve x 2 â € “ 3 x â € “ 4 = 0 .
Options: a ) 14 , b ) - 14 , c ) 23 , d ) 2 , - 3 , e ) 34
Rationale: this one factors easily : x 2 â € “ 3 x â € “ 4 = 0 ( x + 1 ) ( x â € “ 4 ) = 0 x + 1 = 0 or x â € “ 4 = 0 x = â € “ 1 or x = 4 the solution is x = â € “ 1 , 4 answer b
Answer: b
Python program:
a = 4 * 2
Problem: the height of two right circular cones are in the ratio 1 : 2 and their perimeters of their bases are in the ratio 3 : 4 , the ratio of their volume is ?
Options: a ) 9 : 38
b ) 9 : 31
c ) 9 : 32
d ) 9 : 39
e ) 9 : 35
Rationale: 9 : 32 answer : c
Answer: c
Python program:
a = 1 / 2
b = 3 / 4
c = b ** 2
d = a * c
Problem: ? % of 360 = 93.6
Options: a ) 277 , b ) 36 , c ) 26 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 93.6 or , ? = 93.6 × 100 / 360 = 26 answer c"
Answer: c
Python program:
a = 93 * 6
b = a / 360
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 450 , what were her original savings ?
Options: a ) $ 1500 , b ) $ 1600 , c ) $ 1700 , d ) $ 1800 , e ) $ 1900
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 450 . so 1 / 4 of her savings is $ 450 . so her original savings are 4 times $ 450 = $ 1800 correct answer d"
Answer: d
Python program:
a = 3 / 4
b = 1 - a
c = 450 / b
Problem: a man purchased 1 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 650
Rationale: "10 * 150 = 1500 1 * 100 + 5 * 150 = 850 1500 – 850 = 650 answer : e"
Answer: e
Python program:
a = 10 * 150
b = 1 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: rice weighing 29 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 21 , b ) 25 , c ) 29 , d ) 33 , e ) 37
Rationale: "29 / 4 ÷ 4 = 29 / 16 pounds in each container 29 / 16 pounds * 16 ounces / pound = 29 ounces in each container the answer is c ."
Answer: c
Python program:
a = 29 / 4
b = a * 16
c = b / 4
Problem: the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 90 meters ?
Options: a ) 12 , b ) 16 , c ) 17 , d ) 18 , e ) 20
Rationale: "the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 90 meters = 90 / 5 = 18 seconds . the answer is d ."
Answer: d
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 90 / b
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 9 ] * [ 10 ] equivalent to ?
Options: a ) [ 25 ] , b ) [ 135 ] , c ) [ 30 ] , d ) [ 90 ] , e ) [ 45 ]
Rationale: [ 9 ] * [ 10 ] = 27 * 5 = 135 = 3 * 45 = [ 45 ] the answer is e .
Answer: e
Python program:
a = 10 / 2
b = 3 * 9
c = a * b
d = c / 3
Problem: a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability q that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes q = 15 / 36 . answer : c ."
Answer: c
Python program:
a = 12 + 3 
b = 1 / 6
c = b ** 2
d = a * c
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 20 % profit ?
Options: a ) 15.12 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 120 % of rs . 630 = 120 / 100 * 630 = rs . 756 s . p . per kg = 756 / 50 = rs . 15.12 answer : a"
Answer: a
Python program:
a = 30 * 11
b = 20 * 14
c = a + b 
d = 30 * 11
e = 20 * 14
f = d + e 
g = f / 100
h = g * 20
i = c + h 
j = 30 + 20 
k = i / j
Problem: double of quarter of 2 percent written as a decimal is :
Options: a ) 0.01 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 2 % = 2 * ( 1 / 4 * 2 / 100 ) = 0.01 . answer : a"
Answer: a
Python program:
a = 2 / 100
b = a / 2
c = b * 2
Problem: a boat covers a certain distance downstream in 1 hour , while it comes back in 11 ⁄ 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 14 kmph , b ) 15 kmph , c ) 13 kmph , d ) 12 kmph , e ) none of these
Rationale: "explanation : let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x - 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 ⁄ 2 hour . ie , distance travelled downstream in 1 hour = distance travelled upstream in 11 ⁄ 2 hour since distance = speed × time , we have ( x + 3 ) × 1 = ( x − 3 ) ( 3 / 2 ) = > 2 ( x + 3 ) = 3 ( x - 3 ) = > 2 x + 6 = 3 x - 9 = > x = 6 + 9 = 15 kmph . answer : option b"
Answer: b
Python program:
a = 3 / 2
b = a * 3
c = b + 2 
d = 3 / 2
e = d - 1
f = c / e
Problem: a certain bag contains 100 balls â € ” 50 white , 30 green , 8 yellow , 9 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.88 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 8 ) / 100 = 88 / 100 = 0.88 . answer is d"
Answer: d
Python program:
a = 9 + 3 
b = 100 - a
c = b / 100
Problem: if the wheel is 9 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 26 , c ) 14 , d ) 18.7 , e ) 91
Rationale: "2 * 22 / 7 * 9 * x = 1056 = > x = 18.7 answer : d"
Answer: d
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 9
h = 1056 / g
Problem: kanul spent $ 80000 in buying raw materials , $ 30000 in buying machinery and 20 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 135656 , b ) $ 137500 , c ) $ 134446 , d ) $ 123265 , e ) $ 124564
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 80000 + 30000 80 % of x = 110000 80 x / 100 = 110000 x = $ 1100000 / 8 x = $ 137500 answer is b"
Answer: b
Python program:
a = 80000 + 30000 
b = 20 / 100
c = 1 - b
d = a / c
Problem: the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 185 , e ) none
Rationale: "explanation let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer c"
Answer: c
Python program:
a = 2 * 4107
b = 37 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 4107
f = d + e 
g = math.sqrt(f)
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 3 ø 1 ) ø 2 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "3 ø 1 = 2 ^ 3 / 2 ^ 1 = 4 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 the answer is b ."
Answer: b
Python program:
a = 2 ** 3
b = 2 ** 2
c = a / b
d = 2 ** c
e = 2 ** 2
f = d / e
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 63 , what is the value of x ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 61 , e ) 66
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 63 x = 61 answer : d"
Answer: d
Python program:
a = 4 * 2
b = 2 * 2
c = a - b
Problem: a movie buff owns movies on dvd and on blu - ray in a ratio of 9 : 2 . if she buys 2 more blu - ray movies , that ratio would change to 17 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 187
Rationale: "if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 9 x and b ( d ) = 2 x now from the next line the new eqn becomes 9 x / ( 2 x + 2 ) = 17 / 4 solving it 36 x = 34 x + 34 x = 17 which means m ( d ) = 153 and b ( d ) = 34 so total initially is m ( d ) + b ( d ) = 187 e"
Answer: e
Python program:
a = 2 + 1 
b = 17 * a
c = 4 * 9
d = 17 * 2
e = c - d
f = b / e
g = 9 + 2 
h = f * g
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 5 strokes ?
Options: a ) 31 / 32 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 left after 4 th stroke = 1 / 2 * 1 / 8 = 1 / 16 left after 5 th stroke = 1 / 2 * 1 / 16 = 1 / 32 so removed = 1 - 1 / 32 = 31 / 32
Answer: a
Python program:
a = 1 / 2
b = 1 / 2
c = b / 2
d = a + c 
e = 1 / 2
f = e / 2
g = f / 2
h = d + g 
i = 1 / 2
j = i / 2
k = j / 2
l = k / 2
m = h + l 
n = 1 / 2
o = n / 2
p = o / 2
q = p / 2
r = q / 2
s = m + r
Problem: the average weight of 9 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 78.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 9 × 1.5 = 13.5 kg so the weight of new person = 65 + 13.5 = 78.5 kg answer c"
Answer: c
Python program:
a = 9 * 1
b = 65 + a
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1344 ?
Options: a ) 1000 , b ) 2217 , c ) 1200 , d ) 2777 , e ) 2991
Rationale: "1344 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1200 answer : c"
Answer: c
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 1344 / f
Problem: there are 100 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of manager to 98 % ?
Options: a ) 1 , b ) 2 , c ) 50 , d ) 49 , e ) 97
Rationale: "we have 99 managers and 1 director . that 1 director to compose 2 % of the total number of people , there must be 50 people in the room , hence 50 managers must leave . answer : c ."
Answer: c
Python program:
a = 99 / 100
b = 100 * a
c = 98 / 100
d = 100 * c
e = b - d
f = 98 / 100
g = 1 - f
h = e / g
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , b receives :
Options: a ) s . 11,000 , b ) s . 11,300 , c ) s . 11,500 , d ) s . 11,700 , e ) s . 11,900
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 35000 x 17 / 50 ) = rs . 11,900 . e"
Answer: e
Python program:
a = 10 * 5000
b = a - 5000
c = 4000 + 5000 
d = b - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 10 * 5000
i = g / h
j = 3 + 4 
k = j * 5000
l = i * k
m = l / 1000
n = math.floor(m)
o = n - 1
Problem: how many 3 digit positive integers e exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Python program:
a = 100 * 10
b = a - 1
c = 10 + 4 
d = c * 7
e = d + 5 
f = b - e
g = f / 7
Problem: 6.2 is what percent of 1000 ?
Options: a ) 62 % , b ) 6.2 % , c ) 0.62 % , d ) 0.062 % , e ) 0.0062 %
Rationale: "10 % of 1000 is 100 . 6.2 is way less than 100 ( 10 % of 1000 ) . so it can not be 62 % of 1000 . eliminate option a 1 % of 1000 is 10 . 6.2 is less than 10 . so it cant be 6.2 % . eliminate option b ( 0.5 % ) i . e . half of 1 % of 1000 is 5 . but 6.2 is greater than 5 . . so it has to be greater than 0.5 % . . . hence answer is 0.62 % , answer : c"
Answer: c
Python program:
a = 6 / 2
b = a * 100
Problem: a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 12 cm . what is the length of the wire ?
Options: a ) 6 cm , b ) 14 cm , c ) 16 cm , d ) 23 cm , e ) 29 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 12 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 16 cm answer : c"
Answer: c
Python program:
a = 12 ** 3
b = 12 ** 2
c = a / b
d = 4 * c
e = d / 3
Problem: a van takes 6 hours to cover a distance of 252 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 28 kmph , b ) 60 kmph , c ) 70 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 252 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 252 / 9 = 28 kmph a"
Answer: a
Python program:
a = 3 / 2
b = a * 6
c = 252 / b
Problem: the ages of two persons differ by 28 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 40,12 , b ) 20,10 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 28 ) years . 5 ( x - 5 ) = ( x + 28 - 5 ) or 4 x = 48 or x = 12 . their present ages are 40 years and 12 years option a"
Answer: a
Python program:
a = 28 * 5
b = 5 - 1
c = a / b
d = c + 5 
e = d - 28
Problem: 3 x + y = 21 , and x + 3 y = 1 . find the value of 2 x + 2 y
Options: a ) 20 , b ) 18 , c ) 16 , d ) 11 , e ) 5
Rationale: "add these two equations 4 x + 4 y = 22 divide by 2 ( to get 2 x + 2 y ) answer will be d . 11"
Answer: d
Python program:
a = 21 + 1 
b = a / 2
Problem: x can finish a work in 20 days . y can finish the same work in 15 days . yworked for 9 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 20 work done by y in 1 day = 1 / 15 work done by y in 9 days = 9 / 15 = 3 / 5 remaining work = 1 – 3 / 5 = 2 / 5 number of days in which x can finish the remaining work = ( 2 / 5 ) / ( 1 / 20 ) = 8 d"
Answer: d
Python program:
a = 1 / 15
b = 9 * a
c = 1 - b
d = 1 / 20
e = c / d
Problem: thomas worked in the factory @ 4550 / - per week . owner told him to give the amount after one month . then how much amount will be paid to thomas ?
Options: a ) 9500 , b ) 17500 , c ) 18200 , d ) 19500 , e ) 6750
Rationale: total salary paid to thomas in one week : 4550 / - salary for one day : 4550 / 7 = 650 / - total for one month = 650 / - * 30 days = 19500 / - answer is option ( d )
Answer: d
Python program:
a = 100 * 10
b = a * 10
c = 4550 * 2
d = b + c 
e = 100 * 4
f = d + e
Problem: in the first 10 overs of a cricket game , the run rate was only 3.6 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.15 , d ) 7 , e ) 8
Rationale: "10 overs - run rate = 3.6 runs scored in first 10 overs = 36 remaining overs 40 total runs to be scored = 282 32 runs already scored 282 - 36 = 246 246 runs to be scored in 40 overs let required runrate be x 40 * x = 246 x = 246 / 40 x = 6.15 the required runrate is 6.15 answer : c"
Answer: c
Python program:
a = 10 * 3
b = 282 - a
c = b / 40
Problem: in a tree , 3 / 5 of the birds are parrots while the rest are toucans . if 1 / 3 of the parrots are female and 3 / 4 of the toucans are female , what fraction of the birds in the tree are male ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 3 / 10 , e ) 7 / 10
Rationale: the fraction of birds that are male parrots is ( 2 / 3 ) ( 3 / 5 ) = 2 / 5 . the fraction of birds that are male toucans is ( 1 / 4 ) ( 2 / 5 ) = 1 / 10 . the total fraction of male birds is 2 / 5 + 1 / 10 = 1 / 2 . the answer is a .
Answer: a
Python program:
a = 3 / 5
b = 1 / 3
c = 1 - b
d = a * c
e = 2 / 5
f = 3 / 4
g = 1 - f
h = e * g
i = d + h