euclaise/mathqa_programs huggingface dataset:
Problem: robert ' s salary was decreased by 30 % and subsequently increased by 30 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 9 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 30 % = 100 - 100 x 30 / 100 = $ 70 salary after increasing 30 % on $ 70 = 70 + 70 x 30 / 100 = $ 91 percentage of loss = 100 - 91 = 9 % answer : b"
Answer: b
Python program:
a = 100 * 100
b = 100 - 30
c = 100 + 30 
d = b * c
e = a - d
f = 100 * 100
g = e / f
h = g * 100
Problem: 4 + 4
Options: a ) 8 , b ) 2 , c ) 1 , d ) 5 , e ) 2
Rationale: c
Answer: c
Python program:
a = 4 / 4
b = a * 100
Problem: the total age of a and b is 20 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 20 , b ) 12 , c ) 15 , d ) 16 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 20 a - c = 20 answer is a"
Answer: a
Python program:
a = 20 * 1
Problem: if 6 cats can kill 6 rats in 6 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 6 minutes
Rationale: "it will take 6 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 6 minutes , so 100 cats can kill 100 rats in 6 minutes answer e"
Answer: e
Python program:
a = 6 * 1
Problem: what is the smallest integer that is multiple of 5 , 7,20
Options: a ) 70 , b ) 35 , c ) 200 , d ) 280 , e ) 140
Rationale: "it is the lcm of 5 , 7 and 20 which is 140 . the answer is e ."
Answer: e
Python program:
a = 3 + 4
Problem: in the xy - coordinate system , what is the slope of the line that goes through the point ( 7 , 3 ) and is equidistant from the two points p = ( 5 , 5 ) and q = ( 13 , 7 ) ?
Options: a ) 0.5 , b ) 0.75 , c ) 1.0 , d ) 1.25 , e ) 1.5
Rationale: "first , get the middle coordinate between ( 5,5 ) and ( 13,7 ) . . . x = 5 + ( 13 - 5 ) / 2 = 9 y = 5 + ( 7 - 5 ) / 2 = 6 second , get the slope of ( 9,6 ) and ( 7,3 ) . m = 6 - 3 / 9 - 7 = 3 / 2 = 1.5 answer : e"
Answer: e
Python program:
a = 3 + 5 
b = a / 5
c = 7 + 3 
d = c / 5
e = b / d
Problem: if x is to be chosen at random from the integers between 1 to 7 , inclusive , and y is to be chosen at random from the integers between 8 and 12 , inclusive , what is the probability that x + y will be even ?
Options: a ) 2 / 5 , b ) 3 / 7 , c ) 5 / 7 , d ) 17 / 35 , e ) 24 / 35
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 7 * 3 / 5 = 9 / 35 p ( x and y are both odd ) = 4 / 7 * 2 / 5 = 8 / 35 p ( x + y is even ) = 9 / 35 + 8 / 35 = 17 / 35 the answer is d ."
Answer: d
Python program:
a = 2 * 2
b = 3 * 2
c = a + b 
d = 7 - 1
e = 7 * d
f = c / e
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of 1 hammers and three wrenches is one - third that of 8 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 5 / 4 , e ) 2
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 1 x + 3 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 1 x + 3 y ) = ( 8 x + 5 y ) 3 x + 9 y = 8 x + 5 y 4 y = 5 x y = 5 x / 4 ans - d"
Answer: d
Python program:
a = 3 * 2
b = 1 - a
c = 3 * 2
d = c - 8
e = b / d
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 175 kg then find the average weight of all the 7 rounds ?
Options: a ) 100 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 175 / 7 = 100 kgs answer : a"
Answer: a
Python program:
a = 1 + 3 
b = a * 175
c = b / 7
Problem: a jogger running at 9 km / hr along side a railway track is 360 m ahead of the engine of a 90 m long train running at 63 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 67 sec , c ) 30 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 63 - 9 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . distance to be covered = 360 + 90 = 450 m . time taken = 450 / 15 = 30 sec . answer : c"
Answer: c
Python program:
a = 360 + 90 
b = 63 - 9
c = 10 / 2
d = 63 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: if price of t . v set is reduced by 18 % , then its sale increases by 72 % , find net effect on sale value
Options: a ) 41 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 72 + ( - 18 * 72 ) / 100 = - 18 + 72 - 13 = 41 answer : a"
Answer: a
Python program:
a = 100 - 18
b = a / 100
c = 100 + 72 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 155 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 177.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 155 ) / \ x â ˆ ’ 155 22.50 = > x â ˆ ’ ( 155 / 22.50 ) = 1 . = > x â ˆ ’ 155 = 22.50 . = > x = 177.50 rs . answer : c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 155 * b
d = 126 + 135 
e = c - d
f = e / 2
Problem: solution for 4.75 + . 303 + . 432
Options: a ) 2.91 , b ) 5.911 , c ) 5.485 , d ) 5.986 , e ) 2.999
Rationale: "4.75 + . 303 + . 432 = 0 0 = 0 - 4.75 - 0.303 - 0.432 0 = - 5.485 answer : c"
Answer: c
Python program:
a = 303 / 1000
b = 4 + 75 
c = 432 / 1000
d = b + c
Problem: what number is 70 more than one - fourth of itself ?
Options: a ) 93 , b ) 225 , c ) 288 , d ) 324 , e ) 336
Rationale: 1 / 4 x + 70 = x that means 70 = 3 / 4 x x = ( 70 * 4 ) / 3 = 280 / 3 = 93 a is the answer .
Answer: a
Python program:
a = 1 / 4
b = 1 - a
c = 70 / b
Problem: 2 / 3 rd of the boys and 3 / 4 th of the girls of a school participate in a function . if the no . of participating students is 550 , out of which 150 are girls , what is the total no . of students in the school ?
Options: a ) 500 , b ) 600 , c ) 800 , d ) 900 , e ) 1200
Rationale: let total number of boys be x and total number of girls be y . y = 400 = > x = 600 and ^ = i 50 = > y = 200 now , x + y = 800 c
Answer: c
Python program:
a = 550 - 150
b = a * 3
c = b / 2
d = 150 * 4
e = d / 3
f = c + e
Problem: length of a rectangular plot is 30 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 65 m , d ) 78 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 30 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 30 ) + x ] = 200 2 x + 30 = 100 2 x = 70 x = 35 . hence , length = x + 30 = 65 m c"
Answer: c
Python program:
a = 5300 / 26
b = 2 * 30
c = a + b 
d = c / 4
Problem: how many litres of pure acid are there in 5 litres of a 30 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.9
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 5 * 30 / 100 = 1.5 answer : option a
Answer: a
Python program:
a = 30 / 100
b = a * 5
Problem: in a college students can play cricket or basketball . 500 play cricket . 220 played both and 600 played basketball . what is the total strength of college ?
Options: a ) 800 , b ) 880 , c ) 920 , d ) 950 , e ) 980
Rationale: p ( c ) = 500 p ( b ) = 600 p ( c n b ) = 220 p ( c u b ) = p ( c ) + p ( b ) - p ( c n b ) = 500 + 600 - 220 = 880 answer : b
Answer: b
Python program:
a = 500 + 600 
b = a - 220
Problem: if an average hard drive had a capacity of 0.2 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 5122 , c ) 768 , d ) 2048 , e ) 1536
Rationale: "0.2 * 2 ^ 10 = 0.2 * 1024 = 204.8 the answer is d ."
Answer: d
Python program:
a = 0 * 2
b = a * 2
c = b * 2
d = c * 2
e = d * 2
f = e * 2
g = f * 2
h = g * 2
i = h * 2
j = i * 2
k = j + 0 
l = k * 10
Problem: the cricket team of 11 members is 24 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 24 + 27 ) = 9 ( x - 1 ) = > 11 x - 9 x = 42 = > 2 x = 42 = > x = 21 . so , average age of the team is 21 years . a"
Answer: a
Python program:
a = 24 + 3 
b = a + 24 
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
Problem: what is the least number . which should be added to 0.0320 to make it a perfect square ?
Options: a ) 0.0005 , b ) 0.0004 , c ) 0.0006 , d ) 0.0002 , e ) 0.0001
Rationale: 0.0320 + 0.0004 = 0.0324 ( 0.18 ) ^ 2 answer : b
Answer: b
Python program:
a = 12 + 4 
b = a + 2 
c = b / 100
d = 12 + 4 
e = d + 2 
f = e / 100
g = c * f
h = g - 0
Problem: a 21 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 6 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 21 = 6 answer : b"
Answer: b
Python program:
a = 2 / 5
b = a + 1 
c = 21 / b
d = 21 - c
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 340 . how much does c have ?
Options: a ) 50 , b ) 40 , c ) 267 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 340 - - - - - - - - - - - - - - a + b + 2 c = 540 a + b + c = 500 - - - - - - - - - - - - - - - - c = 40 answer : b"
Answer: b
Python program:
a = 200 + 340 
b = a - 500
Problem: light glows for every 15 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 381 , b ) 332 , c ) 383 , d ) 334 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 13 = 331 . so total 332 times light ll glow answer : b"
Answer: b
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 15
Problem: the average age of 29 students in a group is 15 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 36 , c ) 29 , d ) 53 , e ) 57
Rationale: age of the teacher = ( 29 * 16 - 29 * 15 ) = 29 years . answer : c
Answer: c
Python program:
a = 29 + 1
Problem: in may mrs lee ' s earnings were 30 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 34 , b ) 67 , c ) 85 , d ) 25 , e ) 38
Rationale: "lets say the family income is 100 in may , lee earned 30 family income is 70 in june , lee earned 20 % more than may , so it is ( 30 + 20 * 30 / 100 = 36 ) family income is same 70 in june lee ' s income percent is 36 * 100 / 106 ~ 34 ans is a"
Answer: a
Python program:
a = 100 + 20 
b = 100 + 20 
c = b + 100 
d = a / c
e = d * 100
Problem: a and b invests rs . 6000 and rs . 9000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 82 : 31 , c ) 24 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 9000 * 6 ) + ( 6000 * 6 ) 48000 : 90000 24 : 45 answer : c"
Answer: c
Python program:
a = 6000 * 4
b = 9000 / 3
c = 2 * 4
d = b * c
e = a + d 
f = 2 * 3
g = 9000 * f
h = 9000 / 3
i = 9000 - h
j = 2 * 3
k = i * j
l = g + k 
m = e / l
Problem: what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 8 ?
Options: a ) 4 , b ) 0 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 8 , which yields remainder of 0 upon division by 8 . answer : b"
Answer: b
Python program:
a = 8 ** 1
b = 8 ** 1
c = a - b
d = c / 8
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 2 ] ] ?
Options: a ) 3 , b ) 9 , c ) 12 , d ) 19 , e ) 25
Rationale: these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 2 ] ] = 2 ^ 2 + 2 * 2 + 4 = 12 . option c
Answer: c
Python program:
a = 2 ** 2
b = 2 * 2
c = a + b 
d = c + 4
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 13 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.81 % , e ) 11.50 %
Rationale: 13 = 1.1 * x x = 11.81 % answer d )
Answer: d
Python program:
a = 13 * 100
b = 13 + 100 
c = a / b
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 62000 ?
Options: a ) 81000 , b ) 78468.75 , c ) 81008 , d ) 81066 , e ) 81022
Rationale: "62000 * 9 / 8 * 9 / 8 = 78468.75 answer : b"
Answer: b
Python program:
a = 1 / 8
b = a * 62000
c = 62000 + b 
d = 1 / 8
e = 1 / 8
f = e * 62000
g = 62000 + f 
h = d * g
i = c + h
Problem: if p ( a ) = 2 / 15 , p ( b ) = 7 / 15 , and p ( a â ˆ ª b ) = 16 / 15 find p ( a | b )
Options: a ) 1 / 2 , b ) 16 / 7 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a â ˆ ª b ) / p ( b ) p ( a | b ) = ( 16 / 15 ) / ( 7 / 15 ) = 16 / 7 . b"
Answer: b
Python program:
a = 16 / 15
b = 2 / 15
c = a / b
Problem: tanks m and b are each in the shape of a right circular cylinder . the interior of tank m has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank m is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: b . for m , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi m / b = 160 pi / 200 pi = 0.8
Answer: b
Python program:
a = 8 / 2
b = 8 / 2
c = a * b
d = c * 10
e = 10 / 2
f = 10 / 2
g = e * f
h = g * 8
i = d / h
j = i * 100
Problem: in a class , 20 % of the students were absent for an exam . 30 % failed by 20 marks and 10 % just passed . find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40 .
Options: a ) 36 , b ) 302 , c ) 272 , d ) 292 , e ) 271
Rationale: explanation : let total students be 100 . hence , marks of 20 students is 0 as they were absent . 30 students scored 20 marks ( as they failed by 20 marks ) 10 students scored 40 marks ( just passed ) 40 students scored 65 marks ( average of 65 ) therefore , average score of the class is : ( 0 + 600 + 400 + 2600 ) / 100 = 3600 / 100 = 36 answer : a
Answer: a
Python program:
a = 30 * 20
b = 10 * 40
c = a + b 
d = 65 * 40
e = c + d 
f = e / 100
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 150 , b ) 225 , c ) 285 , d ) 315 , e ) 374
Rationale: "since the month begin with sunday , so there will be five sundays in the month required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 answer is c"
Answer: c
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 40 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 60
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 40 = > 20 = x - 40 = > x = 20 + 40 = 60 answer is e ."
Answer: e
Python program:
a = 8 * 2
b = a + 40
Problem: how long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 16.5 , b ) 16.0 , c ) 16.4 , d ) 14 , e ) 16.1
Rationale: "d = 110 + 170 = 280 m s = 72 * 5 / 18 = 20 t = 280 * 1 / 20 = 14 sec answer : d"
Answer: d
Python program:
a = 110 + 170 
b = 72 * const_0_2778
c = a / b
Problem: find large number from below question the difference of two numbers is 250 . on dividing the larger number by the smaller , we get 5 as quotient and the 14 as remainder
Options: a ) 120 , b ) 135 , c ) 140 , d ) 309 , e ) 369
Rationale: "let the smaller number be x . then larger number = ( x + 250 ) . x + 250 = 5 x + 14 4 x = 236 x = 59 large number = 59 + 250 = 309 d"
Answer: d
Python program:
a = 250 - 14
b = 5 - 1
c = a / b
d = c * 5
Problem: what is the probability of drawn an ace or a space or both from a dew of cards .
Options: a ) 14 / 52 , b ) 15 / 52 , c ) 16 / 52 , d ) 17 / 52 , e ) 18 / 52
Rationale: "there are 13 spades in a standard deck of cards . there are four aces in a standard deck of cards . one of the aces is a spade . so , 13 + 4 - 1 = 16 spades or aces to choose from . since we have a total of 52 cards , the probability of selecting an ace or a spade is 16 / 52 answer : c"
Answer: c
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 4 days ago , the water level was at w inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 126 , b ) w − 112 , c ) w − 14 , d ) w + 14 , e ) w + 126
Rationale: "drop = 14 inches / day 4 days ago = w , means now it ' s equal w - 56 and in 4 days = w - 56 - 56 = w - 112 answer b"
Answer: b
Python program:
a = 4 / 4
b = 14 * a
Problem: thirty percent of the women in a college class are science majors , and the non - science majors make up 80 % of the class . what percentage of the men are non - science majors if 40 % of the class are men ?
Options: a ) 2 % , b ) 5 % , c ) 28 % , d ) 30 % , e ) 95 %
Rationale: "3 / k + 2 / m = 6 / t assuming total # is 100 : [ science - women ] will have - 0.3 * 60 = 18 [ non - science - women ] will have - 42 [ science - men ] will have = 20 - 18 = 2 [ non - science - men ] will have - 38 s 0 38 / 40 * 100 = 95 % answer - e"
Answer: e
Python program:
a = 100 - 80
b = 10 * 3
c = b / 100
d = 100 - 40
e = c * d
f = a - e
g = f / 40
h = g * 100
Problem: an amount of rs . 1000 is to be distributed amongst p , q , r and s such that “ p ” gets twice as that of “ q ” and “ s ” gets 4 times as that of “ r ” . if “ q ” and “ r ” are to receive equal amount , what is the difference between the amounts received by s and p ?
Options: a ) 2378 , b ) 2697 , c ) 250 , d ) 5000 , e ) 6971
Rationale: explanation : we have , p = 2 q & s = 4 r further q = r & p + q + r + s = 1,000 thus we get , 2 q + q + q + 4 q = 1,000 8 q = 1,000 or q = rs . 125 thus , r = rs . 125 , p = 250 & s = rs . 500 hence , the required difference = ( s – p ) = ( 500 – 250 ) = rs . 250 answer : c
Answer: c
Python program:
a = 2 + 1 
b = a + 1 
c = b + 4 
d = 1000 / c
e = 4 * d
f = 2 + 1 
g = f + 1 
h = g + 4 
i = 1000 / h
j = 2 * i
k = e - j
Problem: a certain galaxy is known to comprise approximately 4 x 10 ^ 10 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 4 * 10 ^ 10 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 10 / 50 * 10 ^ 6 = 40 * 10 ^ 2 / 5 = 800 therefore answer is a"
Answer: a
Python program:
a = 4 * 10
b = a / 50
c = 10 ** 4
d = b * c
e = d / 1000
f = e * 4
Problem: ajay can walk 6 km in 1 hour . in how many hours he can walk 45 km ?
Options: a ) 5 hrs , b ) 10 hrs , c ) 7.5 hrs , d ) 20 hrs , e ) 30 hrs
Rationale: "1 hour he walk 6 km he walk 45 km in = 45 / 6 * 1 = 7.5 hours answer is c"
Answer: c
Python program:
a = 45 / 6
Problem: a man sells a car to his friend at 13 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 21724.14 , b ) rs . 31724.14 , c ) rs . 51724.14 , d ) rs . 61724.14 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 13 % . now s . p = rs . 45000 and loss = 13 % c . p . rs . [ 100 / 87 ã — 45000 ] = rs . 51724.14 . correct option : c"
Answer: c
Python program:
a = 54000 * 100
b = 100 + 20 
c = a / b
d = c * 100
e = 100 - 13
f = d / e
Problem: n 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is
Options: a ) 22 , b ) 897 , c ) 268 , d ) 20 , e ) 48
Rationale: a + 10 = 2 ( b - 10 ) . . . . . . . . ( 1 ) a = b + 9 . . . . . . . . . ( 2 ) from equations . 1 & 2 we get b = 39 a will be 39 + 9 = 48 years old . answer : e
Answer: e
Python program:
a = 2 * 10
b = a + 10 
c = b + 9 
d = 9 + c
Problem: rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is
Options: a ) rs 429 , b ) rs 412 , c ) rs 400 , d ) rs 129 , e ) rs 122
Rationale: "let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) * 700 ) = 400 answer : c"
Answer: c
Python program:
a = 1 + 2 
b = 4 + a 
c = 4 / b
d = c * 700
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 5 ?
Options: a ) 10 ^ 6 , b ) 10 ^ 7 , c ) 10 ^ 8 , d ) 10 ^ 9 , e ) 10 ^ 10
Rationale: "0.1 = 10 ^ - 1 ( 0.01 ) ^ 5 = ( 10 ^ - 2 ) ^ 5 = 10 ^ - 10 10 ^ 9 * 10 ^ - 10 = 10 ^ - 1 the answer is d ."
Answer: d
Python program:
a = 0 ** 1
b = 0 / 1
Problem: a number exceeds by 15 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 24 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: x – 3 / 8 x = 15 x = 24 answer : b
Answer: b
Python program:
a = 15 * 8
b = 8 - 3
c = a / b
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 20 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 752 , c ) 656 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 20 / 100 = 188 so the cut in amount is 188 the less amount to be spend is 940 - 188 = 752 answer : b"
Answer: b
Python program:
a = 100 - 20
b = a / 100
c = b * 940
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are
Options: a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) none of these
Rationale: explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark = > total mark × ( 33 / 100 ) = 165 = > total mark = 16500 / 33 = 500 answer : option b
Answer: b
Python program:
a = 125 + 40 
b = 33 / 100
c = a / b
Problem: find the number of shares that can be bought for rs . 8800 if the market value is rs . 20 each with brokerage being 2.5 % .
Options: a ) 429.3 , b ) 270 , c ) 177 , d ) 166 , e ) 111
Rationale: explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8800 / 20.5 = 429.3 answer : a
Answer: a
Python program:
a = 2 / 5
b = 20 + a 
c = 8800 / b
d = math.floor(c)