euclaise/mathqa_programs huggingface dataset:
Problem: if a and b are positive integers and ( 3 ^ a ) ^ b = 3 ^ 3 , what is the value of 3 ^ a * 3 ^ b ?
Options: a ) 3 , b ) 9 , c ) 81 , d ) 27 , e ) 243
Rationale: 3 ^ ab = 3 ^ 3 therefore ab = 3 either a = 1 or 3 or b = 3 or 1 therefore 3 ^ a * 3 ^ b = 3 ^ ( a + b ) = 3 ^ 4 = 81 c
Answer: c
Python program:
a = 3 ** 3
b = a * 3
Problem: a gardener is going to plant 2 red rosebushes and 2 white rosebushes . if the gardener is to select each of the bushes at random , one at a time , and plant them in a row , what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) ½
Rationale: we are asked to find the probability of one particular pattern : wrrw . total # of ways a gardener can plant these four bushes is the # of permutations of 4 letters wwrr , out of which 2 w ' s and 2 r ' s are identical , so 4 ! / 2 ! 2 ! = 6 ; so p = 1 / 6 answer : b .
Answer: b
Python program:
a = 2 + 2 
b = math.comb(a, 2)
c = 1 / b
Problem: a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 138 , b ) 140 , c ) 142 , d ) 145 , e ) 148
Rationale: "1 c 5 * 2 c 8 = 5 * 28 = 140 the answer is ( b )"
Answer: b
Python program:
a = 8 * 3
b = a * 5
Problem: what will be the lcm of 8 , 24 , 36 and 54
Options: a ) 54 , b ) 108 , c ) 216 , d ) 432 , e ) none of these
Rationale: explanation : lcm of 8 - 24 - 36 - 54 will be 2 * 2 * 2 * 3 * 3 * 3 = 216 answer : option c
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 3
d = c * 3
e = d * 3
Problem: a number exceeds by 35 from its 3 / 8 part . then the number is ?
Options: a ) a ) 56 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: "x – 3 / 8 x = 35 x = 56 answer : a"
Answer: a
Python program:
a = 35 * 8
b = 8 - 3
c = a / b
Problem: if 0.75 : x : : 5 : 6 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 0.9 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 6 ) x = 4.5 / 5 = 0.9 answer : d"
Answer: d
Python program:
a = 0 * 75
b = a / 5
Problem: two trains of equal lengths take 10 sec and 14 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 11.7 , e ) 15
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 14 = 8.6 m / sec . relative speed = 12 + 8.6 = 20.6 m / sec . required time = ( 120 + 120 ) / 20.6 = 11.7 sec . answer : option d"
Answer: d
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: four equal circles are described about the four corners of a square so that each touches two of the others . if a side of the square is 14 cm , then the area enclosed between the circumferences of the circles is :
Options: a ) 24 cm 2
b ) 42 cm 2
c ) 154 cm 2
d ) 196 cm 2
e ) none of these
Rationale: the shaded area gives the required region . area of the shaded region = area of the square – area of four quadrants of the circles = ( 14 ) 2 - 4 × 1 ⁄ 4 π ( 7 ) 2 = 196 - 22 ⁄ 7 × 49 = 196 - 154 = 42 cm 2 answer b
Answer: b
Python program:
a = square_area - (
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 4 and a y - intercept of - 4 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 4 x - 4 4 x - 4 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Python program:
a = 4 - 4
b = a - 1
c = b / 1
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 10000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 10002
Rationale: "the required population is = 10000 ( 1 + 10 / 100 ) ^ 2 = 10000 * 11 / 10 * 11 / 10 = 12100 answer is a"
Answer: a
Python program:
a = 10 + 100 
b = a / 100
c = b * 10000
d = 10 + 100 
e = d / 100
f = c * e
Problem: the sum of two consecutive integers is 41 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 20,21 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 41 2 n + 1 = 41 2 n = 40 n = 20 answer : d"
Answer: d
Python program:
a = 41 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 41 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 41 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 41 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a certain company ’ s profit in 1996 was 15 percent greater than its profit in 1995 , and its profit in 1997 was 35 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 55.25 %
Rationale: "profit in 1995 - 100 profit in 1996 - 115 % increae profit in 1997 in comparison to 1995 = 15 + 115 * 35 % = 55.25 correct option : e"
Answer: e
Python program:
a = 35 / 100
b = a + 1 
c = 15 / 100
d = 1 + c 
e = b * d
f = e - 1
g = f * 100
Problem: a , b and c started a partnership business by investing rs . 12000 , rs . 16000 , rs . 20000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 86400 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 12000 : 16000 : 20000 = 3 : 4 : 5 let total profit = p then p ã — 5 / 12 = 36000 p = ( 36000 ã — 12 ) / 5 = 86400 answer is c ."
Answer: c
Python program:
a = 12000 / 20000
b = a * 36000
c = 16000 / 20000
d = c * 36000
e = b + d 
f = e + 36000
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 24 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 3 : 1 , c ) 7 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 24 s = ( 27 x + 17 y ) / ( x + y ) = 24 = ( 27 x + 17 y ) / = 24 ( x + y ) = 3 x = 7 y = x / y = 7 / 3 answer : c"
Answer: c
Python program:
a = 27 - 24
b = 24 - 17
c = a / b
Problem: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 450 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
Rationale: 7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 450 - - > x = 2 . 1.25 x = ~ 2.50 . answer : d .
Answer: d
Python program:
a = 75 / 100
b = 32 * a
c = 4 + 1 
d = c * 2
e = b * d
f = e + 450 
g = 4 + 1 
h = g * 2
i = h - 3
j = i * 32
k = 100 + 25 
l = k / 100
m = l * 3
n = m * 32
o = j + n 
p = f / o
q = 100 + 25 
r = q / 100
s = p * r
Problem: at sandi ’ s pet shop , 25 cups of bird seed are used every 5 days to feed 15 parakeets . how many cups of bird seed would be required to feed 14 parakeets for 7 days ?
Options: a ) 40.5 , b ) 32.34 , c ) 6.23 , d ) 9 , e ) 15
Rationale: let ' s go step - by - step . 25 cups are used over a 5 day period , which means 5 cups a day . this feeds 15 parakeets , which means each parakeet needs 1 / 3 of a cup every day . for 14 parakeets , we need 14 * 1 / 3 cups = 4.62 cups a day . over 7 days , we need 32.34 cups . choice b .
Answer: b
Python program:
a = 14 * 25
b = a * 7
c = 5 * 15
d = b / c
Problem: there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability e that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: e probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d
Answer: d
Python program:
a = 50 / 2
b = a - 1
c = 50 - 1
d = b / c
e = 50 / 2
f = e / 50
g = d * f
h = g * 2
Problem: a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 80 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 50
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 160 + ( d / 2 ) / v 8 d / 480 - 3 d / 480 = ( d / 2 ) / v d / 96 = d / 2 v and so v = 48 km / hr the answer is d ."
Answer: d
Python program:
a = 80 * 60
b = 80 - 60
c = b * 60
d = a / c
e = 60 * d
f = 60 / 10
g = e / f
Problem: sonika deposited rs . 8000 which amounted to rs . 11200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 2277 , c ) 11680 , d ) 12068 , e ) 1212
Rationale: "( 8000 * 3 * 2 ) / 100 = 480 11200 - - - - - - - - 11680 answer : c"
Answer: c
Python program:
a = 2 / 100
b = 11200 - 8000
c = b / 3
d = c / 8000
e = a + d 
f = e * 8000
g = f * 3
h = g + 8000
Problem: a manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18 % . the wholesaler sells the same to retailer at a profit of 20 % . the retailer in turn sells them to a customer for rs . 30.09 , there by earning a profit of 25 % . the cost price for the manufacturer is :
Options: a ) rs . 15 , b ) rs . 16 , c ) rs . 17 , d ) rs . 18 , e ) rs . 19
Rationale: let the cost price for the manufacturer be rs . x . then , 125 % of 120 % of 118 % of x = 30.09 . 125 / 100 * 120 / 100 * 118 / 100 * x = 3009 / 100 177 / 100 x = 3009 / 100 = > x = 17 answer : c
Answer: c
Python program:
a = 1 + 2 
b = 20 / 2
c = a * b
d = 3 * 3
e = d / 100
f = c + e 
g = 100 + 25 
h = g / 100
i = f / h
j = 20 + 100 
k = j / 100
l = i / k
m = 100 + 18 
n = m / 100
o = l / n
Problem: how long will a boy take to run round a square field of side 40 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 48 sec , c ) 60 sec , d ) 25 sec , e ) 39 sec
Rationale: speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 40 * 4 = 160 m time taken = 160 * 3 / 10 = 48 sec answer is b
Answer: b
Python program:
a = 40 * 4
b = 1000 / 3600
c = 12 * b
d = a / c
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 602 to 700 inclusive ?
Options: a ) 24,550 , b ) 28,550 , c ) 32,550 , d ) 36,550 , e ) 40,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 602 + 604 + . . . + 700 = 50 ( 600 ) + ( 2 + 4 + . . . + 100 ) = 30,000 + 2550 = 32,550 the answer is c ."
Answer: c
Python program:
a = 700 + 602 
b = a / 2
c = 700 - 602
d = c / 2
e = d + 1 
f = b * e
Problem: the average runs scored by a batsman in 10 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 20 matches ?
Options: a ) 31 , b ) 35 , c ) 88 , d ) 13 , e ) 12
Rationale: "total score of the batsman in 10 matches = 400 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 20 matches = 700 . average score of the batsman = 700 / 20 = 35 . answer : b"
Answer: b
Python program:
a = 40 * 10
b = 30 * 10
c = a + b 
d = 10 + 10 
e = c / d
Problem: there are 300 giraffes at a large zoo . the number of giraffes is 3 times the number of all the other animals combined . how many more giraffes are there than non giraffes animals at the zoo ?
Options: a ) 400 , b ) 360 , c ) 300 , d ) 290 , e ) 200
Rationale: answer is d . total giraffes = 300 = 3 * other animals ( x ) or x = 10 . so , difference in giraffes and x = 300 - 10 = 290 .
Answer: d
Python program:
a = 300 / 3
b = a / 10
c = 300 - b
Problem: bucket a is 1 / 4 full of sand , and bucket b , which has one - half the capacity of bucket a , is 3 / 8 full of sand . jana pours the contents of bucket b into bucket a . bucket a is now filled to what fraction of its capacity ?
Options: a ) 3 / 8 , b ) 7 / 16 , c ) 1 / 2 , d ) 5 / 8 , e ) 7 / 8
Rationale: let capapcity of a = x sand = x / 4 capacity of b = x / 2 sand = 3 x / 16 a total = x / 4 + 3 x / 16 = 7 x / 16 answer : b
Answer: b
Python program:
a = 4 + 3 
b = 8 * 2
c = a / b
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 15 . what is the value of f ( 6 ) ?
Options: a ) 4 , b ) 0 , c ) 1 , d ) 2 , e ) 24
Rationale: since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 15 then f ( 5 ) = 15 - 5 = 10 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 10 - 6 = 4 . answer : a . questions on funtions to practice :
Answer: a
Python program:
a = 1 + 4 
b = 15 - a
c = b - 6
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1100 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 14000 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 12012
Rationale: "[ 1100 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 14000 answer : a"
Answer: a
Python program:
a = 5 / 100
b = 600 / a
Problem: andy solves problems 78 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 52 , c ) 51 , d ) 50 , e ) 48
Rationale: "125 - 78 + 1 = 48 ' e ' is the answer"
Answer: e
Python program:
a = 125 - 78
b = a + 1
Problem: a fair 2 sided coin is flipped 3 times . what is the probability that tails will be the result at least twice , but not more than 3 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 3 / 8 , d ) 7 / 4 , e ) 5 / 6
Rationale: "at least twice , but not more than 3 timesmeans exactly 2 times , 3 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 3 c 2 / 2 ^ 3 = 3 / 8 option : c"
Answer: c
Python program:
a = 2 ** 3
b = 1/(a)
c = b * 3
d = 2 ** 3
e = 1/(d)
f = 2 ** 3
g = 1/(f)
h = e + g 
i = c + h 
j = 1 - i
Problem: a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition of the maximum and minimum possible values of ' a + b ' ?
Options: a ) 21 , b ) 34 , c ) 30 , d ) 25 , e ) 12
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 21 + 9 = 30 ans c"
Answer: c
Python program:
a = 20 + 20 
b = 1 + 1 
c = a - b
Problem: 3 / 5 of all married couples have more than one child . 2 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 2 / 5 of 100 couples have more than 3 kids = 40 couples . this implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 20 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 40 = 20 . fraction will be 20 / 100 = 1 / 5 . option a
Answer: a
Python program:
a = 3 / 5
b = 2 / 5
c = a - b
Problem: one pump drains one - half of a pond in 2 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1.3 hour , b ) 1.2 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 2 = 1 / 4 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 4 = 3 / 4 - - > time taken for the 2 nd pump to finish : 1 : 3 / 4 = 4 / 3 = 1.3 hours . a"
Answer: a
Python program:
a = 2 * 2
b = 1 / a
c = 1 - b
d = 1 / c
Problem: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 , then n =
Options: a ) 3 , b ) 6 , c ) 17 , d ) 23 , e ) 24
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 = > 4 x 2 ^ 2 n = 4 ^ 24 = 2 ^ 36 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 36 = > 2 ^ ( 2 n + 2 ) = 2 ^ 36 = > 2 n + 2 = 36 = > n = 17 so . answer will be c ."
Answer: c
Python program:
a = 18 * 2
b = a - 2
c = b / 2
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 40 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 42 % , c ) 34 % , d ) 12 % , e ) 22 %
Rationale: explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 60 . s . p . of each item = rs . 1.10 total sale = 1.10 * 60 = rs . 66 hence , loss % = 34 / 100 * 100 = 34 % answer : c
Answer: c
Python program:
a = 100 + 10 
b = 100 + 10 
c = b * 40
d = c / 100
e = a - d
f = 100 - e
Problem: a and b go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 60 sec , c ) 186 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 300 / ( 36 * 5 / 18 ) , 300 / ( 54 * 5 / 18 ) } = lcm ( 30 , 20 ) = 60 sec . answer : b"
Answer: b
Python program:
a = 50 * const_0_2778
b = 34 * const_0_2778
c = a - b
d = 300 / c
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 3 / 4 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 120 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 3 / 4 ) of total igneous rocks . ( 2 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 4 / 3 ) = 40 total sedimentary rocks = 2 * total igneous rocks = 2 * 40 = 80 total number of rocks = 40 + 80 = 120 answer ( d )"
Answer: d
Python program:
a = 3 * 4
b = a * 30
c = b / 3
d = c * 4
e = d / 3
Problem: two assembly line inspectors , smithy and glen , inspect widgets as they come off the assembly line . if smithy inspects every fifth widget , starting with the fifth , and glen inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 50 , b ) 53 , c ) 55 , d ) 60 , e ) 65
Rationale: widgets inspected by smithy : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by glen : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 - 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 98 - 45 = 53 option b
Answer: b
Python program:
a = 10 / 2
b = 98 / a
c = 98 / 3
d = b + c 
e = 10 / 2
f = e * 3
g = 98 / f
h = d - g
i = 98 - h
Problem: what is the sum of the numbers between 1 and 12 , inclusive ?
Options: a ) 99 , b ) 65 , c ) 79 , d ) 78 , e ) 80
Rationale: "sol . add the numbers between 1 and 12 . answer is d , 78 ."
Answer: d
Python program:
a = 1 * 12
b = a / 4
Problem: the speed of a car is 120 km in the first hour and 70 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 75 kmph , c ) 95 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "s = ( 120 + 70 ) / 2 = 95 kmph answer : c"
Answer: c
Python program:
a = 120 + 70 
b = a / 2
Problem: in a class of 60 children , 30 % children can speak only english , 20 % hindi and english both and the rest of the children can speak only hindi . how many children can speak hindi ?
Options: a ) 42 , b ) 36 , c ) 30 , d ) 48 , e ) none of these
Rationale: number of students who speak only english = 30 % of 60 = 18 ∵ number of students who speak hindi and english = 20 % of 60 = 12 ∵ number of students who speak only hindi = ( 60 – 30 = ) 30 ∵ no . of students who speak hindi = 30 + 12 = 42 answer a
Answer: a
Python program:
a = 60 - 30
b = 20 * 60
c = b / 100
d = a + c
Problem: 25 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 267 , e ) 1280
Rationale: "( 25 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 4 x = 320 x = 1280 answer : e"
Answer: e
Python program:
a = 650 * 20
b = a / 100
c = b + 190 
d = c * 100
e = d / 25
Problem: george ' s car calls for 8 ounces of oil for each cylinder used . his car ' s engine has 6 cylinders . if 16 ounces of oil has already been put into the engine used , then how many additional ounces of oil are needed ?
Options: a ) 16
b ) 48
c ) 64
d ) 32
e ) 8
Rationale: number of ounces per cylinder 8 number of cylinders 6 ounces needed 48 ounces used 16 answer d
Answer: d
Python program:
a = 8 * 6
b = a - 16
Problem: a car traveled 35 % of the way from town x to town y at an average speed of 35 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 45 , b ) 65 , c ) 55 , d ) 75 , e ) 85
Rationale: "assume total distance = 100 miles time taken for 35 miles = 35 / 35 = 1 hour time taken for the rest of the 65 miles = 65 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 65 / v hence v = 65 mph answer : b"
Answer: b
Python program:
a = 100 - 35
b = 35 / 35
c = a / b
Problem: if the compound interest on a certain sum of money for 2 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 600 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 2 yrs = ( 3000 x 10 x 2 ) / 100 = 600 / - answer : a ."
Answer: a
Python program:
a = 3 * 0
b = a * 10
c = b * 10
d = c * 2
e = d / 100
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and two 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 ) 3 / 2 , e ) 2
Rationale: x be the weight of a hammer and y be the weight of a wrench . ( 2 x + 2 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 2 x + 2 y ) = ( 8 x + 5 y ) 6 x + 6 y = 8 x + 5 y y = 2 x ans - e
Answer: e
Python program:
a = 3 * 2
b = 8 - a
c = 3 * 2
d = c - 5
e = b / d