euclaise/mathqa_programs huggingface dataset:
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 53900 . how many times did he participate in the competition ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "53900 = 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 7 times . the answer is a ."
Answer: a
Python program:
a = 11 * 7
b = a * 5
c = b * 2
d = 53900 / c
e = math.sqrt(d)
f = math.floor(e)
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 15 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 31 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 15 % = 27 responded as satisfied , so remaining satisfied are 120 - 27 = 93 so 93 is what percentage of 300 - 31 % so the answer should be a"
Answer: a
Python program:
a = 40 / 100
b = a * 300
c = 15 / 100
d = 60 / 100
e = 300 * d
f = c * e
g = b - f
h = g / 300
i = h * 100
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 62 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.7 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 62 ) = 1174 kgs actual average weight is 1174 / 20 = 58.7 kgs c"
Answer: c
Python program:
a = 58 * 4
b = 62 - 56
c = a + b 
d = c / 20
Problem: 34 men can complete a piece of work in 18 days . in how many days will 17 men complete the same work ?
Options: a ) 36 , b ) 26 , c ) 97 , d ) 26 , e ) 19
Rationale: "explanation : let the required number of days be a . then , less men , more days ( indirect proportion ) 17 : 34 : : 18 : a 17 x a = 34 x 18 a = ( 34 x 18 ) / 17 a = 36 answer : a"
Answer: a
Python program:
a = 18 * 34
b = a / 17
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 60 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "b 80 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg ."
Answer: b
Python program:
a = 8 * 2
b = a + 60
Problem: the perimeter of one square is 48 cm and that of another is 24 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 13.4 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 48 4 a = 24 a = 12 a = 6 a 2 = 144 a 2 = 36 combined area = a 2 = 180 = > a = 13.4 d = 13.4 √ 2 answer : c"
Answer: c
Python program:
a = 48 / 4
b = a ** 2
c = 24 / 4
d = c ** 2
e = b + d 
f = e * 2
g = math.sqrt(f)
Problem: p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 30000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 45000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 30000 : q = 2 : 3 ⇒ 30000 × 3 = 2 q ⇒ q = ( 30000 × 3 ) / 2 = 45000 answer is c ."
Answer: c
Python program:
a = 30000 / 2
b = a * 3
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number q ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: ( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = q answer : b
Answer: b
Python program:
a = 12 / 5
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b - d
f = 30 / e
Problem: a man is 30 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 28 years , c ) 21 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 30 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 30 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 28 answer : b"
Answer: b
Python program:
a = 2 * 2
b = a - 2
c = 30 - b
d = 2 - 1
e = c / d
Problem: what is the value of ( 4 ) ^ - 6 ?
Options: a ) 1 / 1008 , b ) 1 / 6400 , c ) 1 / 6550 , d ) 1 / 6660 , e ) 1 / 4096
Rationale: "4 ^ - 6 = 1 / ( 4 ) ^ 6 = 1 / 4096 answer : e"
Answer: e
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: machine x takes 60 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 3
Rationale: machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 60 so , x = 60 . hence 6 x = 6 * 60 = 360 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 360 = 3 hence option ( e ) .
Answer: e
Python program:
a = 60 / 10
b = a * 60
c = 1080 / b
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 22 , b ) 35 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 10 x = > x = 35 . answer : b"
Answer: b
Python program:
a = 90 * 5
b = 5 * 20
c = a - b
d = 90 - 80
e = c / d
Problem: a train running at the speed of 52 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 130 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec length of train ( distance ) = speed * time ( 130 / 9 ) * 9 = 130 meter answer : a"
Answer: a
Python program:
a = 52 * 1000
b = a / 3600
c = b * 9
Problem: how many 1 / 4 s are there in 37 1 / 2 ?
Options: a ) 150 , b ) 450 , c ) 500 , d ) 650 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 4 ) = ( 75 / 2 x 4 / 1 ) = 150 . answer : a"
Answer: a
Python program:
a = 1 / 2
b = 37 + a 
c = 1 / 4
d = b / c
Problem: if x : y = 2 : 9 , find the value of ( 2 x + 2 y ) : ( 5 x – y )
Options: a ) 22 : 1 , b ) 22 : 3 , c ) 7 : 1 , d ) 5 : 3 , e ) 8 : 1
Rationale: "explanation : given : x / y = 2 / 9 ( 2 x + 2 y ) : ( 5 x – y ) = ( 2 * 2 + 2 * 9 ) : ( 5 * 2 – 9 ) = 22 : 1 answer : a"
Answer: a
Python program:
a = 2 ** 2
b = a + 2 
c = 2 + 9 
d = c + 2 
e = b / d
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 8 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 8 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 8 = 7 / 8 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 7 / 8 = 4 / 9 - - - > p ( of burning out in a six mnth period ) = 1 - 4 / 9 = 4 / 7 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 7 / 8 * 4 / 7 = 1 / 2 ans c"
Answer: c
Python program:
a = 1 / 8
b = 1 - a
c = 2 / 0
d = 1 - c
e = d / 1
f = 1 - e
g = b * f
Problem: a train 360 m long is running at a speed of 90 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 20 sec , e ) 34 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 25 = 20 sec answer : d"
Answer: d
Python program:
a = 90 - 140
b = a * const_0_2778
c = 360 / b
Problem: the sale price sarees listed for rs . 200 after successive discount is 20 % and 5 % is ?
Options: a ) 187 , b ) 169 , c ) 152 , d ) 178 , e ) 175
Rationale: "200 * ( 80 / 100 ) * ( 95 / 100 ) = 152 answer : c"
Answer: c
Python program:
a = 200 * 20
b = a / 100
c = 200 - b
d = 200 * 20
e = d / 100
f = 200 - e
g = f * 5
h = g / 100
i = c - h
Problem: bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ?
Options: a ) 40 , b ) 80 , c ) 120 , d ) 160 , e ) 180
Rationale: bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ? average speed = total distance / total time we know the total distance is 5 + 5 ( going from a to b then from b to a ) time = distance / speed time = 5 / 15 time = 1 / 3 hour average speed = ( 10 ) / ( 1 hr + 1 / 3 hr ) average speed ( bexi ) = 10 / 1.33 therefore , if ben ' s average speed is 1 / 2 of bexi ' s then his speed = 10 / 2.66 . this means it took him 2.66 hours to cover the same 10 miles bexi did . 2.66 hours = roughly 160 minutes . answer : d ) . 160
Answer: d
Python program:
a = 15 - 5
b = 15 / 2
c = b / 2
d = a / c
e = d * const_60
Problem: the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 260
Rationale: "x - y = 1365 divide larger number by the smaller , we get 6 as quotient and the 15 as remainder x / y = 6 quotient and 15 reminder convert this as x = 6 y + 15 apply this x in above eqn therefore , 6 y + 15 - y = 1365 5 y + 15 = 1365 y + 3 = 273 y = 270 answer : b"
Answer: b
Python program:
a = 1365 + 15 
b = 6 - 1
c = a / b
Problem: running at the same constant rate , 4 identical machines can produce a total of 16 bottles per minute . at this rate , how many bottles could 8 such machines produce in 3 minutes ?
Options: a ) 11 , b ) 92 , c ) 96 , d ) 174 , e ) 115
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 16 / 4 = 4 . 8 machines = 32 per minute . 3 minutes worth = 96 bottles . looking at the answers it is clear . . . we can only choose ( c ) the correct answer is c ."
Answer: c
Python program:
a = 16 / 4
b = a * 3
c = b * 8
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 12 , the how old is b ?
Options: a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )"
Answer: b
Python program:
a = 12 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: how many digits are required to number a book containing 300 pages ?
Options: a ) 792 , b ) 684 , c ) 492 , d ) 372 , e ) 340
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 300 - ( 90 + 9 ) = 201 pages will require 201 * 3 = 603 digits . the total number of digits is 9 + 180 + 603 = 792 . the answer is a ."
Answer: a
Python program:
a = 10 - 1
b = 10 - 1
c = b * 10
d = c * 2
e = a + d 
f = 300 - 100
g = f + 1 
h = g * 3
i = e + h
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 4 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.25 , e ) 3.5
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 4 km / hour x / 3 = 4 x = 12 km the average speed while climbing = distance / time = 12 / 4 = 3 km / h the answer is c ."
Answer: c
Python program:
a = 4 + 2 
b = a * 4
c = b / 2
d = c / 4
Problem: there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 36 , then find the smaller number ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 60 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 36 3 x = 36 = > x = 12 = > smaller number = 5 x = 60 . answer : d"
Answer: d
Python program:
a = 36 * 5
b = a / 4
Problem: if x = 1 - q and y = 2 q + 1 , then for what value of q , x is equal to y ?
Options: a ) 0 , b ) 1 , c ) - 1 , d ) - 2 , e ) 3
Rationale: explanation : x = y < = > 1 - q = 2 q + 1 < = > 3 q = 0 < = > q = 0 . answer : a
Answer: a
Python program:
a = 1 - 1
b = 1 + a
Problem: if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 , then the third part is ?
Options: a ) a ) 426 , b ) b ) 306 , c ) c ) 207 , d ) d ) 204 , e ) e ) 297
Rationale: given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 1 st part = 782 * 9 / 23 = rs . 306 . answer : b
Answer: b
Python program:
a = 100 + 2 
b = 2 * 3
c = 2 * 3
d = c + 3 
e = 2 * 3
f = e + 2 
g = d + f 
h = 2 * 3
i = g + h 
j = b / i
k = j * 782
l = a + k
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.65 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,628
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.65 = 0.55 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer e"
Answer: e
Python program:
a = 250 / 22
b = a * 250
Problem: a start walking from a place at a uniform speed of 5 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 5.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 5 + 5 / 9 = 5.55 answer b"
Answer: b
Python program:
a = const_60 + 48 
b = a / const_60
c = 1 / b
d = c + 5
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 7 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 5 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 5 ) , which indeed is 5 / 22 . e"
Answer: e
Python program:
a = math.comb(7, 2)
b = math.comb(3, 1)
c = a * b
d = 7 + 4 
e = d + 3 
f = math.comb(e, 3)
g = c / f
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 49 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 7
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 49 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 50 incorrect c . 2 / 2 = 2 / 3 + 2 / 51 incorrect d . 2 / 3 = 2 / 4 + 2 / 54 incorrect e . 2 / 4 = 2 / 5 + 2 / 56 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Python program:
a = 2 + 2 
b = a + 1 
c = 49 / b
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 35,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 35000 × 21 / 50 = 700 × 21 = 14700 answer is a ."
Answer: a
Python program:
a = 5000 * 10
b = 4000 + 5000 
c = b + 5000 
d = a - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 75 , then what is the value of k ?
Options: a ) 158 , b ) 161 , c ) 164 , d ) 167 , e ) 170
Rationale: k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 75 ) / 5 + 32 = 167 the answer is d .
Answer: d
Python program:
a = 75 * 9
b = a / 5
c = b + 32
Problem: ( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) =
Options: a ) 99 , b ) 9.9 , c ) 990 , d ) 0.99 , e ) 0.099
Rationale: "( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 450 / 5 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : c"
Answer: c
Python program:
a = 0 * 77
b = 0 * 5
c = b * 0
d = a / c
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 2904 cm is ?
Options: a ) 22 , b ) 33 , c ) 17 , d ) 12 , e ) 88
Rationale: "2 * 22 / 7 * 14 * x = 2904 = > x = 33 answer : b"
Answer: b
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 2904 / g
Problem: jerry went to a shop and bought things worth rs . 25 , out of which 30 $ went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 21.7
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 $ is given as tax = > total tax incurred = 30 $ = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 b )"
Answer: b
Python program:
a = 30 / 100
b = 100 / 6
c = a * b
d = 30 / 100
e = c + d 
f = 25 - e
Problem: the average age of a class of 25 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 47 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 19 , average would not have changed . since average increased by 2 , age of the teacher = 25 + 22 × 1 = 47 answer : c"
Answer: c
Python program:
a = 25 + 2 
b = 19 + 2 
c = a * b
d = 25 * 19
e = c - d
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 6 = ( r - 10 ) / r 4 r = 6 r - 60 r = 30 the answer is e ."
Answer: e
Python program:
a = 6 + 10 
b = a + 6
Problem: of 70 players on a football team , 40 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 60 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 40 rest = 70 - 40 = 30 left handed = 30 / 3 = 10 right handed = 20 if all throwe 0 r are right handed then total right handed is 40 + 20 = 60 so c . 60 is the right answer"
Answer: c
Python program:
a = 1 / 3
b = 1 - a
c = 70 - 40
d = b * c
e = d + 40
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38000 , 2 have an annual salary of 45700 each , 2 have an annual salary of 42500 each , 3 have an annual salary of 40000 each and 5 have an annual salary of 48500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,700 , e ) 48,500
Rationale: median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.7 so , answer is d .
Answer: d
Python program:
a = 42500 * 1
Problem: average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c"
Answer: c
Python program:
a = 735 * 4
b = 4 - 1
c = 650 * b
d = a - c
Problem: a car travels a certain distance taking 7 hrs in forward journey , during the return journey increased speed 12 km / hr takes the times 5 hrs . what is the distance traveled
Options: a ) 210 kms , b ) 30 kms , c ) 20 kms , d ) 40 kms , e ) none of these
Rationale: if x is the distance , then difference in speeds = x / 5 - x / 7 = 12 2 x / 35 = 12 x = 12 * 35 / 2 = 210 kms . answer : a
Answer: a
Python program:
a = 12 * 5
b = 7 - 5
c = a / b
d = c * 7