euclaise/mathqa_programs huggingface dataset:
Problem: a certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 8 cards ?
Options: a ) 1 / 8 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 28
Rationale: "the average of the numbers is 4.5 the total number of ways to choose 2 cards from 8 cards is 8 c 2 = 28 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 28 = 1 / 14 the answer is c ."
Answer: c
Python program:
a = math.factorial(8)
b = math.factorial(2)
c = 8 - 2
d = math.factorial(c)
e = b * d
f = a / e
g = 4 / f
Problem: a positive number x is multiplied by 4 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: sq rt ( 4 x / 3 ) = x = > 4 x / 3 = x ^ 2 = > x = 4 / 3 ans - c
Answer: c
Python program:
a = 4 / 3
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 100 total = 100 + 100 = 200 answer ( d )"
Answer: d
Python program:
a = 60 / 100
b = 100 * a
c = 55 / 100
d = 100 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
Problem: a 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 270 / 9 = 500 / 9 x = 230 ans is 230 m answer : c"
Answer: c
Python program:
a = 120 + 80 
b = a * const_0_2778
c = 9 * b
d = c - 270
Problem: car z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 375.2 , c ) 400 , d ) 408 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 51 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40.8 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40.8 miles / gallon * 10 gallons = 408 miles . answer d ."
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = b * 51
d = c * 10
Problem: at what rate percent on simple interest will rs . 1800 amount to rs . 2000 in 5 years ?
Options: a ) 4 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 3.47 % , e ) 6 %
Rationale: "explanation : 250 = ( 1800 x 5 xr ) / 100 r = 3.47 % answer : option d"
Answer: d
Python program:
a = 2000 - 1800
b = a / 1800
c = b / 5
d = c * 100
Problem: what is 0.02 percent of 12,356 ?
Options: a ) 0.247 , b ) 2.47 , c ) 24.7 , d ) 0.0247 , e ) 0.00247
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.02 ( 1 / 100 ) 12,356 . the answer is 2.47 . hence , the correct answer is b .
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 0 * 2
p = o / 100
Problem: of 45 applicants for a job , 21 had at least 4 years ' experience , 27 had degrees , and 5 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "45 - 5 = 40 40 - 21 - 27 = - 8 then 8 are in the intersection between 4 years experience and degree . answer : b"
Answer: b
Python program:
a = 21 + 27 
b = 45 - 5
c = a - b
d = 27 - 21
e = c + d
Problem: 12,21 , 48,87 , __
Options: a ) 176 , b ) 186 , c ) 184 , d ) 174 , e ) 164
Rationale: "21 = 12 * 2 - 3 48 = 21 * 2 + 6 87 = 48 * 2 - 9 so next number is 87 * 2 + 12 = 186 answer : b"
Answer: b
Python program:
a = 12 / 21
b = a * 100
Problem: a man rows his boat 90 km downstream and 5 ` km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 7 kmph , b ) 5 kmph , c ) 2 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 51 / ( 3 ) = 17 kmph the speed of the stream = ( 30 - 17 ) / 2 = 7 kmph answer : a"
Answer: a
Python program:
a = 90 / 3
b = 5 / 3
c = a - b
d = c / 2
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 25 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 29 % , b ) 31 % , c ) 33 % , d ) 35 % , e ) 37 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 1.0 x = 1.45 x 1.45 x / 5 x = 0.29 the answer is a ."
Answer: a
Python program:
a = 45 / 100
b = 25 / 100
c = 4 * b
d = a + c 
e = 1 + 4 
f = d / e
g = 100 * f
Problem: reema took a loan of rs 1100 with simple interest for as many years as the rate of interest . if she paid rs . 704 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 1100 ∗ r ∗ r / 100 = 704 = > r 2 = 64 = > r = 8 % option d"
Answer: d
Python program:
a = 1100 / 100
b = 704 / a
c = math.sqrt(b)
Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 a for the digits ?
Options: a ) 30 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 number of possibilities = 3 * 3 * 3 = 27 . then , just add up the number of 1 digits numbers = 3 , so total is 27 + 3 = 30 . answer : a"
Answer: a
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: in a company , 52 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 80 % , e ) 85 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 48 % of all employees are women , so non - union women are 48 % - 18 % = 30 % 40 % of all employees are non - union . the percent of non - union employees who are women is 30 % / 40 % = 75 % the answer is c ."
Answer: c
Python program:
a = 100 - 52
b = 70 / 100
c = 60 * b
d = 60 - c
e = a - d
f = 100 - 60
g = e / f
h = 100 * g
Problem: how long does a lorry 200 m long traveling at 80 kmph takes to cross a bridge of 200 m in length ?
Options: a ) 15 , b ) 17 , c ) 15 , d ) 16 , e ) 18
Rationale: d = 200 + 200 = 400 m s = 80 * 5 / 18 = 200 / 9 t = 400 * 9 / 200 = 18 sec answer : e
Answer: e
Python program:
a = 200 + 200 
b = 80 * const_0_2778
c = a / b
Problem: pradeep has to obtain 20 % of the total marks to pass . he got 160 marks and failed by 25 marks . the maximum marks are
Options: a ) 1925 , b ) 600 , c ) 925 , d ) 1325 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 20 % of x = 160 + 25 = > 20 / 100 x = 185 x = ( 18500 / 20 ) x = 925 . answer : c"
Answer: c
Python program:
a = 160 + 25 
b = 20 / 100
c = a / b
Problem: 1480 men have provisions for 14 days . if 460 more men join them , for how many days will the provisions last now ?
Options: a ) 9.9 , b ) 8.0 , c ) 12.5 , d ) 12.2 , e ) 12.1
Rationale: "1480 * 13 = 1940 * x x = 9.9 answer : a"
Answer: a
Python program:
a = 14 * 1480
b = 1480 + 460 
c = a / b
Problem: what is the difference between the c . i . on rs . 5000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) rs . 2.04 , b ) rs . 2.09 , c ) rs . 2.06 , d ) rs . 2.22 , e ) rs . 2.08
Rationale: "c . i . when interest is compounded yearly = [ 5000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 5000 * 26 / 25 * 51 / 50 = rs . 5304 c . i . when interest is compounded half - yearly = [ 5000 * ( 1 + 2 / 100 ) 2 ] = ( 5000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 5306.04 difference = ( 5306.04 - 5304 ) = rs . 2.04 . answer : a"
Answer: a
Python program:
a = 2 / 100
b = 1 + a 
c = 2 / 100
d = 1 + c 
e = b * d
f = 2 / 100
g = 1 + f 
h = e * g
i = 5000 * h
j = 2 / 100
k = 1 + j 
l = 4 / 100
m = 1 + l 
n = k * m
o = 5000 * n
p = i - o
Problem: the sum of three consecutive even numbers multiples of 3 is 72 . what is the largest number ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) none
Rationale: "solution let the number be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 ⇔ 4 x + 4 = 84 ⇔ 4 x = 80 ⇔ x = 20 . ∴ required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer c"
Answer: c
Python program:
a = 3 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 3 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 3 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 3 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back , how far is the place ?
Options: a ) 144 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 30 2 x + 3 x = 720 x = 144 km answer is a"
Answer: a
Python program:
a = 10 - 2
b = 10 + 2 
c = a * b
d = c * 30
e = 10 - 2
f = 10 + 2 
g = e + f 
h = d / g
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate q in miles per hour for the entire trip ?
Options: a ) q = 26.7 , b ) q = 30.0 , c ) q = 40.0 , d ) q = 53.3 , e ) q = 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Python program:
a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e 
g = 640 / 2
h = g / 80
i = f + h 
j = 640 / i
Problem: 6 friends went to a hotel and decided to pay the bill amount equally . but 5 of them could pay rs . 100 each as a result 6 th has to pay rs . 100 extra than his share . find the amount paid by him .
Options: a ) 156 , b ) 220 , c ) 130 , d ) 240 , e ) none
Rationale: "explanation : average amount paid by 5 persons = rs . 100 increase in average due to rs . 120 paid extra by the 6 th men = rs . 100 / 5 = rs . 20 therefore , average expenditure of 6 friends = rs . 100 + rs . 20 = rs . 120 therefore , amount paid by the 6 th men = rs . 120 + rs . 100 = rs . 220 correct option : b"
Answer: b
Python program:
a = 100 * 5
b = a + 100 
c = b / 5
d = 100 + c
Problem: the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is :
Options: a ) 12 , b ) 24 , c ) 84 , d ) 48 , e ) 42
Rationale: "let the numbers be x and 4 x . then , x * 4 x = 84 * 21 x 2 = ( 84 * 21 ) / 4 = x = 21 . hence , larger number = 4 x = 84 . answer : c"
Answer: c
Python program:
a = 84 * 21
b = a / 4
c = math.sqrt(b)
d = c * 4
Problem: 15.06 * 0.00000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 1.506 e - 07 , e ) none of these
Rationale: "explanation : clearly after decimal 10 digits should be there . option d"
Answer: d
Python program:
a = 15 / 6
b = a * 100
Problem: evaluate 28 % of 450 + 45 % of 240
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 234
Rationale: "explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 240 = 126 + 108 = 234 answer : option e"
Answer: e
Python program:
a = 450 / 28
b = 28 / a
Problem: a straight line in the xy - plane has y - intercept of 12 and a slope of 4 / 7 . given the x - coordinate of the point is 49 , find it ' s y - coordinate .
Options: a ) 27 , b ) 16 , c ) 29.7 , d ) 28 , e ) 18
Rationale: "eq of line = y = mx + c m = 4 / 7 c = 12 x = 49 substitute the givens : y = ( 4 / 7 * 49 ) + 12 , y = 16 + 12 = 28 correct option is d"
Answer: d
Python program:
a = 7 - 12
b = a / 4
Problem: if 50 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 120 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: let the number be x . then 50 % of 3 / 5 of x = 36 50 / 100 * 3 / 5 * x = 36 x = ( 36 * 10 / 3 ) = 120 required number = 120 . correct option : a
Answer: a
Python program:
a = 50 / 100
b = 3 / 5
c = a * b
d = 36 / c
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability t that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) t = 5 / 6 . answer : c"
Answer: c
Python program:
a = 5 / 6
Problem: the manufacturing cost of a shoe is rs . 180 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) rs 222 , b ) rs 216 , c ) rs 220 , d ) rs 210 , e ) rs 217
Rationale: explanation : total cost of a watch = 180 + ( 500 / 100 ) = 185 . gain = 20 % = > sp = 1.2 cp = 1.2 x 185 = 222 answer : a
Answer: a
Python program:
a = 500 / 100
b = 180 + a 
c = 20 / 100
d = 500 / 100
e = 180 + d 
f = c * e
g = b + f
Problem: a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 20 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 64 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 80 then it is marked down by 20 % = 80 - 16 = 64 . hence it is 64 % od the original price . hence answer is d ."
Answer: d
Python program:
a = 80 / 100
b = a * 20
c = 80 - b
Problem: in a factory , there are 30 % technicians and 70 % non - technicians . if the 30 % of the technicians and 70 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 22 % , e ) 48 %
Rationale: "total = 100 t = 30 nt = 70 30 * ( 70 / 100 ) = 21 70 * ( 30 / 100 ) = 21 21 + 21 = 42 = > 100 - 42 = 58 % answer : e"
Answer: e
Python program:
a = 70 / 100
b = 30 * a
c = 30 / 100
d = c * 70
e = b + d 
f = 100 - e
Problem: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 14 hours a day ?
Options: a ) 24 , b ) 23 , c ) 24 , d ) 20.57 , e ) 22
Rationale: man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 14 = 280 therefore number of days = 5760 / 280 = 20.57 days ans = d
Answer: d
Python program:
a = 30 * 12
b = a * 8
c = b * 2
d = 20 * 14
e = c / d
Problem: if a * b = 2 a – 3 b + ab , then 3 * 5 + 5 * 3 is equal to :
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 29
Rationale: "solution 3 × 5 + 5 × 3 = ( 2 × 3 - 3 × 5 + 3 × 5 ) + 2 ( 2 × 5 - 3 × 3 + 5 × 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer a"
Answer: a
Python program:
a = 3 * 5
Problem: average temperature of first 4 days of a week is 6 ° c and that of the last 4 days is 40.3 ° c . if the average temperature of the week be 39.1 ° c , the temperature on 4 th day is ?
Options: a ) 36.7 ° c , b ) 38.6 ° c , c ) 39.8 ° c , d ) 41.9 ° c , e ) 51.9 ° c
Rationale: let temperature on 4 th day be x ° c therefore , 4 x 38.6 + 4 x 40.3 - x = 7 x 39.1 = > x = 41.9 therefore , temperature on 4 th day = 41.9 ° c . answer : d
Answer: d
Python program:
a = 6 * 6
b = 40 * 3
c = 39 * 1
d = b - c
e = const_0_33 / 3
f = d + e 
g = a + f
Problem: what annual installment will discharge a debt of rs . 4600 due in 4 years at 10 % simple interest ?
Options: a ) 1000 , b ) 1030 , c ) 1100 , d ) none of these , e ) 1101
Rationale: "let the 1 st installment = 100 / - it is 3 yrs before due iind is 2 yr before due iii 3 rd is 1 yr before due ivth is 0 yrs before due on 1 st installment interest will be paid for 3 yrs 2 nd installment interest will be paid for 2 yrs 3 rd installment interest will be paid for 1 yr 4 th installment interest will be paid for 0 yr interest = p [ ( 100 ( 3 + 2 + 1 + 0 ) x 10 ) / 100 ] = 60 / - total loan discharged = 4 * 100 + 60 / - = 460 / - now installment of 100 / - loan discharged = 460 / - loan discharged 4600 / - ? installment = 1000 / - answer : a ."
Answer: a
Python program:
a = 10 / 4600
b = 4600 * a
c = b * 4
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 21,700 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 3000 = $ 21700 correct option : a
Answer: a
Python program:
a = 2 * 10
Problem: there are 18 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 1370 , b ) 1530 , c ) 1790 , d ) 1950 , e ) 2110
Rationale: "the number of ways to choose two teams is 18 c 2 = 18 * 17 / 2 = 153 the total number of games in the season is 10 * 153 = 1530 . the answer is b ."
Answer: b
Python program:
a = 18 - 1
b = 18 * a
c = b * 10
d = c / 2
Problem: how many multiples of 9 are there between 1 and 50 , exclusive ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 3
Rationale: "5 multiples of 9 between 1 and 50 exclusive . from 9 * 1 upto 9 * 5 , ( 1 , 2,3 , 4,5 ) . hence , 5 multiples ! correct option is a"
Answer: a
Python program:
a = 50 - 1
b = a / 9
c = b + 1
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 7 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 840 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 7 / 100 x 12000 ) = rs . 840 . answer b
Answer: b
Python program:
a = 10 * 1000
b = 4 * 1000
c = a + b 
d = 4 * 100
e = c + d 
f = 20 / 100
g = 100 * f
h = 100 + g 
i = e / h
j = 100 * i
k = 7 / 100
l = j * k
Problem: the distance between delhi and mathura is 130 kms . a starts from delhi with a speed of 25 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 30 kmph at 9 p . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 77 , c ) 16 , d ) 10 , e ) 98
Rationale: "d = 130 – 25 = 105 rs = 30 + 25 = 55 t = 105 / 55 = 2 hours 8 a . m . + 2 = 11 a . m . . answer : a"
Answer: a
Python program:
a = 25 + 30 
b = 130 / a
c = 9 + b
Problem: how is 1 / 2 % expressed as a decimal fraction ?
Options: a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5
Rationale: as 1 / 2 = 0.5 and its percent value will be 0.5 / 100 = 0.005 answer : c
Answer: c
Python program:
a = 1 / 2
b = a / 100
Problem: a hostel had provisions for 250 men for 28 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 35 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: a hostel had provisions for 250 men for 28 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 28 250 × 28 = 200 x 5 × 28 = 4 x x = 5 × 7 = 35 answer a
Answer: a
Python program:
a = 250 * 28
b = 250 - 50
c = a / b
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 20 percent of b , what is the value of m / x ?
Options: a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "x equals a increased by 25 percent of a = > x = a + 25 % a = 1.25 a m equals b decreased by 20 percent of b = > m = b - 20 % b = 0.8 b m / x = 0.8 b / 1.25 a putting the value of b / a = 5 / 4 we get m / x = 4 / 5 answer : c"
Answer: c
Python program:
a = 100 - 20
b = 100 + 25 
c = a / b
d = 5 / 4
e = c * d
Problem: if rs . 480 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 570 , e ) s . 585
Rationale: "80 = ( 480 * 4 * r ) / 100 r = 3.125 % i = ( 480 * 6 * 3.125 ) / 100 = 90 480 + 90 = 570 answer : d"
Answer: d
Python program:
a = 540 - 480
b = a * 6
c = 540 - 480
d = b - c