euclaise/mathqa_programs huggingface dataset:
Problem: a semicircle has a radius of 9 . what is the approximate perimeter of the semicircle ?
Options: a ) 16 , b ) 25 , c ) 33 , d ) 46 , e ) 58
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 9 + 2 * 9 which is about 46 . the answer is d ."
Answer: d
Python program:
a = circumface / (
b = a + 2
Problem: if the average ( arithmetic mean ) of a and b is 210 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 210 = = = > a + b = 420 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 420 - 320 = = = > a + b - b - c = 100 = = = > a - c = 100 answer : c"
Answer: c
Python program:
a = const_60 * 0
b = 210 * 2
c = a - b
Problem: calculate 469158 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691110842
Rationale: "answer 469158 x 9999 = 469157 x ( 10000 - 1 ) = 4691580000 - 469158 = 4691110842 . option : e"
Answer: e
Python program:
a = 469158 * 9999
Problem: 33 1 / 3 % of 210 ?
Options: a ) 70 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 210 = 70 a )"
Answer: a
Python program:
a = 1 / 3
b = 33 + a 
c = b * 210
d = c / 100
Problem: on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 40 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: "0.20 p = rt + c 0.4 ( rt ) = no c = > 0.60 ( rt ) had c 0.20 p = 0.60 ( rt ) rt / p = 1 / 3 = 33 % answer - a"
Answer: a
Python program:
a = 100 - 40
b = a / 100
c = 20 / b
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 136 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 136 and x + y = 48 solving these two equations , we get x = 28 and y = 20 therefore , hens are 28 . answer : e"
Answer: e
Python program:
a = 48 * 4
b = a - 136
c = b / 2
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 5,100 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1100 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 14.0 , b ) 9.0 , c ) 10.0 , d ) 11.0 , e ) 12.0
Rationale: "solution : h stopped 800 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance between them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . e"
Answer: e
Python program:
a = 500 / 100
b = a - 1
c = 800 / 1100
d = b / c
e = 800 / 1100
f = 500 / 1100
g = e - f
h = d * g
i = 500 / 1100
j = i + 1 
k = h / j
l = 500 / 100
m = l - 1
n = 800 / 1100
o = m / n
p = k + o 
q = 6 + p
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 190 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 44 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 190 = 550 m required time = 550 * 2 / 25 = 44 sec answer : c"
Answer: c
Python program:
a = 45 - 190
b = a * const_0_2778
c = 360 / b
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 86 , b ) 88 , c ) 92 , d ) 94 , e ) 96
Rationale: "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . a"
Answer: a
Python program:
a = 6 * 3
b = a + 2 
c = 6 * 3
d = c + 2 
e = d / 5
f = b * e
g = f + 6
Problem: a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 20 years , d ) 24 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 22 . = > 2 ( x + 2 ) = ( x + 22 + 2 ) = > 2 x + 4 = x + 24 = > x = 20 years option c"
Answer: c
Python program:
a = 2 * 2
b = a - 2
c = 22 - b
d = 2 - 1
e = c / d
Problem: a train 55 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 5 sec , c ) 4 sec , d ) 6 sec , e ) 3 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 55 * 3 / 55 ] sec = 3 sec answer : e"
Answer: e
Python program:
a = 55 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: how long will a boy take to run round a square field of side 60 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 72 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 60 * 4 = 240 m time taken = 240 * 3 / 10 = 72 sec answer is c"
Answer: c
Python program:
a = 60 * 4
b = 1000 / 3600
c = 12 * b
d = a / c
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 6 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.20 , b ) 0.24 , c ) 20 , d ) 24 , e ) 55
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 24 = 24 cents . answer : d ."
Answer: d
Python program:
a = 1 / 2
b = 6 / a
c = b / 12
d = 0 * 24
e = c * d
Problem: murali travelled from city a to city b at a speed of 40 kmph and from city b to city c at 60 kmph . what is the average speed of murali from a to c given that the ratio of distances between a to b and b to c is 1 : 2 ? a . 48 kmph
Options: a ) 33 , b ) 360 / 7 , c ) 28 , d ) 27 / 8 , e ) 16
Rationale: let the distances between city a to b and b to c be x km and 2 x km respectively . total time taken to cover from a to c = ( x ) / 40 + ( 2 x ) / 60 = ( 3 x + 4 x ) / 120 = 7 x / 120 average speed = ( x + 2 x ) / ( 7 x / 120 ) = 360 / 7 kmph . answer : b
Answer: b
Python program:
a = 40 + 60 
b = a / 2
Problem: a ’ s speed is 30 / 17 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 13 / 30 , c ) 17 / 30 , d ) 11 / 30 , e ) 11 / 13
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 30 meters , b covers 17 meters in that time . so if the race is 30 meters long , when a reaches the finish line , b would be 13 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 13 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 30 meters ) would be the same as the time required by b ( to cover 17 meters ) to reach the finish line . so b should get a head start of 13 / 30 th of the race . answer ( b )"
Answer: b
Python program:
a = 30 - 17
b = a / 30
Problem: a cycle is bought for rs . 670 and sold for rs . 780 , find the gain percent ?
Options: a ) 70 % , b ) 20 % , c ) 16 % , d ) 19 % , e ) 80 %
Rationale: "explanation : 670 - - - - 110 100 - - - - ? = > 16 % answer : c"
Answer: c
Python program:
a = 780 - 670
b = a / 670
c = b * 100
Problem: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 22 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.6 , b ) 987.6 , c ) 941.6 , d ) 637.6 , e ) 667.6
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 22 = 2 r a = 12 / 5 r and r = 66 a = 158.4 required total cost = 4 * 158.4 + 3 * 66 + 5 * 22 = 633.6 + 198 + 110 = $ 941.60 c"
Answer: c
Python program:
a = 24 / 10
b = 22 * 6
c = b / 2
d = a * c
e = 4 * d
f = 22 * 6
g = f / 2
h = 3 * g
i = e + h 
j = 5 * 22
k = i + j
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 20.65 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 27 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 120.65 let marked price be rs . x . then , 95 / 100 x = 120.65 x = 12065 / 95 = rs . 127 now , s . p . = rs . 127 , c . p . = rs . 100 profit % = 27 % . answer : b"
Answer: b
Python program:
a = 100 + 20 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 90 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 12 sec , b ) 24 sec , c ) 30 sec , d ) 60 sec , e ) 62 sec
Rationale: "relative speed = 90 + 30 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : c"
Answer: c
Python program:
a = 90 + 30
Problem: john was thrice as old as tom 6 years ago . john will be 7 / 5 times as old as tom in 6 years . how old is tom today ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 7 / 5 * ( t + 6 ) 5 j + 30 = 7 t + 42 5 ( 3 t - 12 ) + 30 = 7 t + 42 8 t = 72 t = 9 the answer is b ."
Answer: b
Python program:
a = 7 / 5
b = 6 * a
Problem: workers at a campaign office have 2000 fliers to send out . if they send out 1 / 10 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 1350 , c ) 1100 , d ) 1200 , e ) 1900
Rationale: "( 1 / 10 ) * 2000 = 200 remaining = 2000 - 200 = 1800 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 1800 = 450 remaining now = 1800 - 450 = 1350 answer : option b"
Answer: b
Python program:
a = 2000 / 10
b = 2000 - a
c = 2000 / 10
d = 2000 - c
e = d / 4
f = b - e
Problem: three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution q in the liquid in the tank after 3 minutes ?
Options: a ) 5 / 8 , b ) 6 / 8 , c ) 4 / 8 , d ) 2 / 8 , e ) 3 / 8
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : e"
Answer: e
Python program:
a = 3 / 30
b = 1 / 30
c = 1 / 20
d = 1 / 20
e = c + d 
f = b + e 
g = 3 * f
h = 1 / g
i = a * h
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 5 ] * [ 4 ] = ?
Options: a ) [ 33 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 5 ] * [ 4 ] = ( 2 * 5 + 1 ) ( 4 / 2 + 1 ) = [ 33 ] . ans - a"
Answer: a
Python program:
a = 5 / 2
b = a + 1 
c = 2 * 4
d = c + 1 
e = b * d
Problem: 765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns . how many chairs will be excluded to make this arrangement possible ?
Options: a ) 6 , b ) 36 , c ) 19 , d ) 27 , e ) none of these
Rationale: 27 ( 2 ) < 765 < 28 ( 2 ) ∴ required no . of chairs to be excluded = 765 – 729 = 36 answer b
Answer: b
Python program:
a = 765 - 12
b = a - 12
c = b - 12
d = 765 - c
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 40 percent .
Options: a ) 120 , b ) 150 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 40 percent 120 min . answer : a
Answer: a
Python program:
a = 40 / 20
b = a * const_60
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 11 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 110 , b ) 106 , c ) 105 , d ) 107 , e ) 109
Rationale: "( 3500 * 1 * 3 ) / 100 = > 105 answer : c"
Answer: c
Python program:
a = 3500 * 11
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: x and y began business with rs . 10000 and rs . 8000 after 6 months , x advances rs . 2000 and y advances rs . 2000 more . at the end of the year , their profits amounted to rs . 2000 find the share of x and y respectively .
Options: a ) 10001000 , b ) 9001100 , c ) 1200800 , d ) 8001200 , e ) 1100 , 900
Rationale: ( 10 * 6 + 12 * 6 ) : ( 8 * 6 + 10 * 6 ) 11 : 9 x share = 11 / 20 * 2000 = 1100 . y share = 9 / 20 * 2000 = 900 . x and y share respectively is 1100 , 900 . answer : e
Answer: e
Python program:
a = 10000 * 6
b = 10000 + 2000 
c = b * 6
d = a + c 
e = 10000 * 6
f = 10000 + 2000 
g = f * 6
h = e + g 
i = 8000 * 6
j = 2000 + 2000 
k = 8000 + j 
l = k * 6
m = i + l 
n = math.gcd(h, m)
o = d / n
p = 10000 * 6
q = 10000 + 2000 
r = q * 6
s = p + r 
t = 10000 * 6
u = 10000 + 2000 
v = u * 6
w = t + v 
x = 8000 * 6
y = 2000 + 2000 
z = 8000 + y 
A = z * 6
B = x + A 
C = math.gcd(w, B)
D = s / C
E = 8000 * 6
F = 2000 + 2000 
G = 8000 + F 
H = G * 6
I = E + H 
J = 10000 * 6
K = 10000 + 2000 
L = K * 6
M = J + L 
N = 8000 * 6
O = 2000 + 2000 
P = 8000 + O 
Q = P * 6
R = N + Q 
S = math.gcd(M, R)
T = I / S
U = D + T 
V = o / U
W = V * 2000
Problem: in a group of ducks and cows , the total number of legs are 30 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 30 = > 2 x = 30 = > x = 15 d"
Answer: d
Python program:
a = 30 / 2
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 2 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 72
Rationale: "let the numbers be 1 x and 2 x . then , their l . c . m = 2 x . so , 2 x = 48 or x = 24 . the numbers are 24 and 48 . hence , required sum = ( 24 + 48 ) = 72 . answer : e"
Answer: e
Python program:
a = 1 * 48
b = a / 2
Problem: a certain fraction has the same ratio to 1 / 36 , as 4 / 7 does to 5 / 9 . what is this certain fraction ?
Options: a ) 1 / 35 , b ) 1 / 42 , c ) 1 / 49 , d ) 1 / 56 , e ) 1 / 63
Rationale: x / ( 1 / 36 ) = ( 4 / 7 ) / ( 5 / 9 ) x = 4 * 9 * 1 / 36 * 7 * 5 = 1 / 35 the answer is a .
Answer: a
Python program:
a = 1 / 36
Problem: there are 780 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 130 , e ) 225
Rationale: "female = x male = 780 - x x / 2 + 780 - x / 4 = 1 / 3 * ( 780 ) = 260 x = 260 x / 2 = 130 is supposed to be the answer m is missing something correct option d"
Answer: d
Python program:
a = 780 / 3
b = a * 4
c = b - 780
d = c / 2
Problem: two goods trains each 2000 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 278 , c ) 192 , d ) 27 , e ) 21
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 2000 + 2000 = 4000 m . required time = 4000 * 6 / 125 = 192 sec . answer : c"
Answer: c
Python program:
a = 45 + 30
Problem: what sum of money will produce rs . 70 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 289 , b ) 500 , c ) 188 , d ) 666 , e ) 155
Rationale: "70 = ( p * 4 * 7 / 2 ) / 100 p = 500 answer : b"
Answer: b
Python program:
a = 1 / 2
b = 3 + a 
c = 4 * b
d = c / 100
e = 70 / d
Problem: a man is 34 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 32 , e ) 40
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 34 ) + 2 = 2 ( x + 2 ) x + 36 = 2 x + 4 = > x = 32 . answer : d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 34 - b
d = 2 - 1
e = c / d
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : c"
Answer: c
Python program:
a = 240 + 130 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 360 - meter long platform ?
Options: a ) 44 , b ) 46 , c ) 48 , d ) 50 , e ) 52
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 360 ) / 10 = 50 seconds the answer is d ."
Answer: d
Python program:
a = 36 * const_0_2778
b = a * 14
c = b + 360 
d = 36 * const_0_2778
e = c / d
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Python program:
a = 72 / 2
b = math.sqrt(a)
c = b * 2
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27000
Rationale: 27 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 27 = 1 / 100 * x = > x = 27000 answer : e
Answer: e
Python program:
a = 27 * 100
b = 2 * 100
c = a * b
d = 0 * 75
e = c * d
f = e / 20
g = f / 10
h = g / 7
Problem: one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 72 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 4
Rationale: "there are total 72 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 18 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 72 = 45 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 18 - b have read saramago but not kureishi . so , ( 18 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 72 = 18 + 45 - b + ( 18 - b - 1 ) b = 4 answer ( e )"
Answer: e
Python program:
a = 72 / 4
b = 72 / 4
c = a + b 
d = 72 / 8
e = d * 5
f = c + e 
g = f - 72
h = g - 1
i = h / 2
Problem: in traveling from a dormitory to a certain city , a student went 1 / 4 of the way by foot , 1 / 2 of the way by bus , and the remaining 10 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 10 , b ) 45 , c ) 30 , d ) 20 , e ) 40
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 4 x + 1 / 2 x + 10 x - 1 / 4 x - 1 / 2 x = 10 x = 40 km option : e"
Answer: e
Python program:
a = 1 / 4
b = 1 / 2
c = a + b 
d = 1 - c
e = 1/(d)
f = 10 * e
Problem: if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 4 = 1 / ( 16 * ( 10 ) ^ 4 ) , then m =
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 8
Rationale: "( 1 / 5 ) ^ m ( 1 / 4 ) ^ 4 = 1 / { 16 ( 10 ) ^ 4 } 16 ( 10 ) ^ 4 / 4 ^ 4 = 5 ^ m [ 16 ( 2 ^ 4 ) ( 5 ^ 4 ) ] / [ 2 ^ 8 ] = 5 ^ m 5 ^ 4 = 5 ^ m m = 4 d"
Answer: d
Python program:
a = 1 / 4
b = a * 16
c = 1 / 5
d = c * 16
e = b + d 
f = 5 / 16
g = e - f
Problem: in the faculty of reverse - engineering , 220 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 636 .
Rationale: answer is e : 636 solution : total number of students studying both are 423 + 220 - 134 = 509 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 509 , so 100 % is approx . 636 .
Answer: e
Python program:
a = 220 + 423
Problem: what would be the minimum number of pumps required to fill a tank of 1000 m 3 to 85 % in one hour ? the capacity of the pump is 150 m 3 / hour and operates at an efficiency of 75 % .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: volume handled by pump in one hour = 150 x . 75 = 112.5 volume of the tank that needs to be filled = 1000 x . 85 = 850 number of pumps needed = 850 / 112.5 = 7.55 â ‰ ˆ 8 answer : b
Answer: b
Python program:
a = 1000 * 85
b = a / 100
c = 150 * 75
d = c / 100
e = b / d
f = e + 1 
g = math.floor(f)
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 60 percent was planted with grapes and 30 percent of the cleared land was planted with potato . if the remaining 360 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 3250 , b ) 3450 , c ) 4000 , d ) 3750 , e ) 3800
Rationale: 60 % of 90 % = 54 % , 30 % 0 f 90 % = 27 % so the remaining 90 - 54 - 27 = 9 % = 360 acres or 10 % of 90 % = 9 % - - > 360 / 9 * 100 = 4000 acres answer ( c )
Answer: c
Python program:
a = 100 - 60
b = a - 30
c = b / 100
d = 90 / 100
e = c * d
f = 360 / e
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 8 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 18 , d ) 16 , e ) 12
Rationale: "7 * 5 : 8 * x = 7 : 10 x = 16 answer : d"
Answer: d
Python program:
a = 7 / 5
b = 10 / 7
c = a * b
d = c * 8