euclaise/mathqa_programs huggingface dataset:
Problem: if p represents the product of the first 14 positive integers , then p is not a multiple of :
Options: a ) a ) 99 , b ) b ) 84 , c ) c ) 51 , d ) d ) 65 , e ) e ) 57
Rationale: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 51 = 17 * 3 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 17 is not there in first 15 positive numbers it is the only possibility c
Answer: c
Python program:
a = 14 + 3 
b = a * 3
Problem: the average weight of 10 girls increases by 5 kg when a new girl comes in place of one of them weighing 50 kg . what might be the weight of the new girl ?
Options: a ) 90 kg , b ) 100 kg , c ) 95 kg , d ) 85 kg , e ) 92 kg
Rationale: "total weight increased = 10 x 5 kg = 50 kg . weight of new person = 50 + 50 kg = 100 kg answer : b"
Answer: b
Python program:
a = 10 * 5
b = a + 50
Problem: on dividing 144 by a number , the quotient is 13 and the remainder is 1 . find the divisor .
Options: a ) a ) 11 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 144 - 1 ) / 13 = 143 / 13 = 11 a )"
Answer: a
Python program:
a = 144 / 13
b = math.floor(a)
Problem: a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1100 . how many workers were part of the latter production run ?
Options: a ) 26 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 23.5
Rationale: the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1100 . . thus for the current period = 1100 - 500 = 600 ( 5 n + 45 ) k = 600 k = 600 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 600 / 5 n + 45 500 ( 5 n + 45 ) = 600 ( 5 n + 20 ) 2500 n + 22500 = 3000 n + 12000 - 500 n = - 10500 n = 21 thus n + 5 = 26 hence a
Answer: a
Python program:
a = 20 + 5
Problem: find the area of a parallelogram with base 24 cm and height 16 cm ?
Options: a ) 298 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 297 cm 2 , e ) 278 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : b"
Answer: b
Python program:
a = 24 * 16
Problem: the principal that amounts to rs . 4893 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4893 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4085 . answer : c
Answer: c
Python program:
a = 1 / 4
b = 6 + a 
c = b / 100
d = 1 + c 
e = d ** 3
f = 4893 / e
Problem: what is the remainder when 46 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 46 * 49 ) / 8 } } = remainder of ( 46 / 8 ) * remainder of ( 49 / 8 ) = 6 * 1 = 6 answer : d"
Answer: d
Python program:
a = 8 / 2
b = 46 * 46
c = a - b
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 25 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 25 ( x - y ) - - > x + y = 25 . answer : d ."
Answer: d
Python program:
a = math.floor(25)
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 15 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 67 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 15 = 67"
Answer: c
Python program:
a = 1 / 5
b = 2 / 3
c = a + b 
d = 1 - c
e = 1/(d)
f = 15 * e
Problem: if 18 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "18 - 3 * 3 * 2 15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 8 is allowed . imo e ."
Answer: e
Python program:
a = 18 / 3
b = 18 / 3
c = 3 / b
d = a + c
Problem: the ratio of 2 numbers is 3 : 7 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 220 , b ) 210 , c ) 252 , d ) 236 , e ) 260
Rationale: "let the numbers be 3 x and 7 x their h . c . f . = 10 so the numbers are 3 * 10 , 7 * 10 = 30,70 l . c . m . = 210 answer is b"
Answer: b
Python program:
a = 7 ** 3
b = 2 ** 3
c = 3 ** 3
d = b + c 
e = a + d 
f = 10 / e
g = math.sqrt(f)
Problem: two trains are moving in opposite directions @ 100 kmph and 120 kmph . their length are 500 m and 700 m . the time taken by the slower train to cross faster train in second is ?
Options: a ) 15 sec , b ) 18.3 sec , c ) 19.6 sec , d ) 20.4 sec , e ) 22.5 sec
Rationale: relative speed = 100 + 120 = 220 * 5 / 18 = 550 / 9 m / s distance covered = 500 + 700 = 1200 m required time = 1200 * 9 / 550 = 19.6 sec answer is c
Answer: c
Python program:
a = 500 + 700 
b = 100 + 120 
c = b * const_0_2778
d = a / c
Problem: if two positive numbers are in the ratio 1 / 8 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 65 %
Rationale: "given ratio = 1 / 8 : 1 / 5 = 5 : 8 let first number be 5 x and the second number be 8 x . the second number is more than first number by 3 x . required percentage = 3 x / 5 x * 100 = 60 % . answer : c"
Answer: c
Python program:
a = 1 / 5
b = a * 100
Problem: if the price of a certain bond on may 1 st was 1 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 100 % , b ) 150 % , c ) 155 % , d ) 300 % , e ) 355 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 4 * 12 = 3 ; the price on july 1 st = 3 * 1.25 = 3.75 . the average price of the bond on may 1 st and july 1 st = ( 3 + 3.75 ) / 2 = 3.375 . the price of the bond on june 1 st ( 12 ) is 32 / 9 times ( 355.55 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
Answer: e
Python program:
a = 25 * const_0_33
b = 100 + const_0_33 
c = a + b
Problem: how many seconds will a 250 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 , b ) 30 , c ) 40 , d ) 15 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 250 * 3 / 50 = 15 sec . answer : option d"
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 250 / b
Problem: the last two - digits in the multiplication 122 × 123 × 125 × 127 × 129 will be
Options: a ) 20 , b ) 50 , c ) 30 , d ) 40 , e ) 10
Rationale: solution the answer will be 50 since , ( 125 × 122 ) will give 50 as the last two digits . answer b
Answer: b
Python program:
a = 4 + 1 
b = a * 10
Problem: riya and priya set on a journey . riya moves eastward at a speed of 20 kmph and priya moves westward at a speed of 30 kmph . how far will be priya from riya after 30 minutes
Options: a ) 25 kms , b ) 10 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 20 kmph * 1 / 2 hr = 10 km total westward distance = 30 kmph * 1 / 2 hr = 15 km total distn betn them = 10 + 15 = 25 km ans 25 km answer : a"
Answer: a
Python program:
a = 20 + 30 
b = speed * (
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 10 sec . what is the length of the platform ?
Options: a ) 187 m , b ) 350 m , c ) 267 m , d ) 287 m , e ) 870 m
Rationale: "speed = 300 / 10 = 30 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 30 = > x = 870 m . answer : e"
Answer: e
Python program:
a = speed * (
b = a - 39
Problem: how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 2 ?
Options: a ) 22 , b ) 20 , c ) 21 , d ) 18 , e ) 17
Rationale: "whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 2 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 x 10 ^ 2 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 x 10 ^ 2 = 2 * 11 ^ 2 * 10 ^ 16 x 10 ^ 2 = 242 * 10 ^ 18 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 18 = 21 correct option : c"
Answer: c
Python program:
a = 10 * 2
b = a - 2
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 2 and 4 parts , respectively . this will give us in the final mixture ( 5 + 2 ) : ( 3 + 4 ) , which means 7 : 7 , or 1 : 1 . answer a ."
Answer: a
Python program:
a = 4 * 5
b = 5 + 3 
c = b / 2
d = 3 * c
e = a + d 
f = 4 * 3
g = 5 + 3 
h = g / 2
i = 3 * h
j = f + i 
k = e / j
Problem: running at the same constant rate , 15 identical machines can produce a total of 45 bags per minute . at this rate , how many bags could 150 such machines produce in 8 minutes ?
Options: a ) 9,00 , b ) 1,800 , c ) 2,700 , d ) 3,600 , e ) 4,800
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 45 / 15 = 3 bags per minute per machine . 150 machines = 450 per minute . 8 minutes worth = 3600 bags . looking at the answers it is clear . . . we can only choose ( d ) . the correct answer is d ."
Answer: d
Python program:
a = 45 / 15
b = a * 8
c = b * 150
Problem: a train 700 m long can cross an electric pole in 40 sec and then find the speed of the train ?
Options: a ) 987 , b ) 271 , c ) 72 , d ) 27 , e ) 63
Rationale: "length = speed * time speed = l / t s = 700 / 40 s = 17.5 m / sec speed = 17.5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 63 kmph answer : e"
Answer: e
Python program:
a = 700 / 1000
b = 40 / 3600
c = a / b
Problem: a is twice as good a work man as b and together they finish the work in 12 days . in how many days a alone can finish the work ?
Options: a ) 12 days , b ) 14 days , c ) 28 days , d ) 18 days , e ) 16 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 12 = > x = 1 / 36 2 x = 1 / 18 a can do the work in 18 days . answer : d"
Answer: d
Python program:
a = 1/(12)
b = 2 + 1 
c = a / b
d = 1/(c)
Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 100 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 3 / 16,000 , b ) 1 / 4,800 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: solution provided by stanford 2012 is correct : 100 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 100 / 800 * 1 / 600 = 1 / 4,800 . answer : b .
Answer: b
Python program:
a = 100 / 800
b = 1 / 600
c = a * b
Problem: total 85 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 85 , b ) 81 , c ) 53 , d ) 82 , e ) 84
Rationale: 84 players answer : e
Answer: e
Python program:
a = 85 + 1
Problem: if log 27 = 1.431 , then the value of log 9 is : 0.934 b . 0.945 c . 0.954 d . 0.958
Options: a ) 0.954 , b ) 0.93 , c ) 0.933 , d ) 0.96 , e ) 0.974
Rationale: "if log 27 = 1.431 , then the value of log 9 is : a . 0.934 b . 0.945 c . 0.954 d . 0.958 answer : option c explanation : log 27 = 1.431 log ( 33 ) = 1.431 3 log 3 = 1.431 log 3 = 0.477 log 9 = log ( 32 ) = 2 log 3 = ( 2 x 0.477 ) = 0.954 . answer a"
Answer: a
Python program:
a = 3 + 4 
b = a * 0
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 8 % p . a . in 5 years . what is the sum ?
Options: a ) rs . 10060.625 , b ) rs . 10040.62 , c ) rs . 12040.62 , d ) rs . 20040.625 , e ) rs . 10030.625
Rationale: "principal = ( 100 * 4016.25 ) / ( 8 * 5 ) = rs . 10040.625 . answer : b"
Answer: b
Python program:
a = 4016 * 25
b = a / 8
c = b / 5
Problem: the population of a bacteria culture doubles every 5 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 45
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 5 minutes so answer is 9 * 5 = 45 minutes answer ( e )"
Answer: e
Python program:
a = 4 + 1 
b = a * 1
c = b * 100
d = c / 1
e = math.log(d)
f = e * 5
Problem: a woman complete a journey in 25 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 560 km .
Rationale: 0.5 x / 21 + 0.5 x / 24 = 25 - - > x / 21 + x / 24 = 50 - - > x = 560 km . e
Answer: e
Python program:
a = 25 * 24
b = 24 + 21 
c = a / b
d = c * 21
e = d * 2
Problem: set j consists of 10 consecutive even numbers . if the smallest term in the set is - 4 , what is the range of the positive integers in set j ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "since there are only 10 integers , another approach is the just list all 10 . we get : - 4 , - 2 , 0,2 , 4 , 6 , 8 , 10 , 12 , 14 range of positive integers = 14 - 2 = 12 answer : b"
Answer: b
Python program:
a = negate + ( 
b = 10 - 1
c = b * 2
d = a - c
Problem: a man two flats for $ 675958 each . on one he gains 12 % while on the other he loses 12 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.44 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 12 / 10 ) ^ 2 = 36 / 25 = 1.44 % answer is a"
Answer: a
Python program:
a = 100 + 12 
b = 100 / a
c = b * 675958
d = 100 - 12
e = 100 / d
f = e * 675958
g = c + f 
h = 675958 + 675958 
i = g - h
j = 100 + 12 
k = 100 / j
l = k * 675958
m = 100 - 12
n = 100 / m
o = n * 675958
p = l + o 
q = i / p
r = q * 100
Problem: in a certain company , a third of the workers do not have a retirement plan . 10 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 91
Rationale: 20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 90 * 1 + 40 * 2 ) / 3 = 170 / 3 % are men total = 120 * 300 / 170 = 211 no . of women = 211 - 120 = 91 e
Answer: e
Python program:
a = 1 / 3
b = 1 / 3
c = 10 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i 
k = 120 / j
l = 1 / 3
m = 10 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 60 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 40
Rationale: the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 3 hours for the trip . dan needs to exceed a constant speed of 120 / 3 = 40 miles per hour . the answer is e .
Answer: e
Python program:
a = 120 / 30
b = 60 / const_60
c = a - b
d = 120 / c
Problem: jack and christina are standing 150 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 7 feet per second and christina walks in a straight line toward jack at a constant speed of 8 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the relative speed of jack and christina is 7 + 8 = 15 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 150 / 15 = 10 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 10 = 100 feet . answer : d ."
Answer: d
Python program:
a = 7 + 8 
b = 150 / a
c = b * 10
Problem: how many different positive integers exist between 10 ^ 4 and 10 ^ 5 , the sum of whose digits is equal to 2 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "10001 10010 10100 11000 20000 total no . = 5 c"
Answer: c
Python program:
a = 4 + 3 
b = a + 1
Problem: a man by motorcycle goes from delhi to bharatpur , a distance of 192 km , at an average speed of 32 kmph . another man starts from delhi by car 2.5 h after the motorcyclist starts and reaches bharatpur half an hour late . what is the ratio of person on the motorcycle to the person going by car ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 10 : 27 , d ) 5 : 4 , e ) 4 : 5
Rationale: a man by motorcycle goes from delhi to bharatpur the time take by the motorcyclist = 192 / 32 = 6 hours another man start from delhi be car after 2.5 hour the man starts = 6 - 2.5 = 3.5 and the man on can reaches half and hour late which is = 3.5 + . 5 = 4 thus , the ratio between motorcycle to car is 4 : 6 or , 2 : 3 . answer : b
Answer: b
Python program:
a = 192 / 32
b = a - 2
c = 1 / 2
d = b + c 
e = 192 / 32
f = d / e
Problem: if p / q = 4 / 5 , then the value of 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 18 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 18 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 18 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 18 / 7 + 6 / 14 = 18 / 7 + 3 / 7 = 21 / 7 = 3 correct option : e"
Answer: e
Python program:
a = 18 / 7
b = 4 / 5
c = 2 - b
d = 4 / 5
e = 2 + d 
f = c / e
g = a + f
Problem: a scuba diver descends at a rate of 30 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 2400 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 80 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 2400 / 30 = 80 minutes answer : c"
Answer: c
Python program:
a = 2400 / 30
Problem: how many zeroes are there at the end of the number n , if n = 150 ! + 300 ! ?
Options: a ) 28 , b ) 31 , c ) 34 , d ) 37 , e ) 40
Rationale: "the number of zeroes at the end of 150 ! will be less than the number of zeroes at the end of 300 ! hence it is sufficient to calculate the number of zeroes at the end of 150 ! the number of zeroes = [ 150 / 5 ] + [ 150 / 25 ] + [ 150 / 125 ] = 30 + 6 + 1 = 37 the answer is d ."
Answer: d
Python program:
a = 4 + 1 
b = 150 / a
c = b + 2
Problem: how many prime numbers are between 26 / 3 and 85 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "26 / 3 = 8 . xxx 85 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"
Answer: b
Python program:
a = math.floor(2)
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 5 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 87
Rationale: "explanation : average after 11 innings should be 37 so , required score = ( 11 * 37 ) - ( 10 * 32 ) = 407 - 320 = 87 answer : option e"
Answer: e
Python program:
a = 32 + 5 
b = 10 + 1 
c = a * b
d = 10 * 32
e = c - d
Problem: if there are 4 peanuts in a box and mary puts 2 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 11 , e ) 12
Rationale: "2 + 4 = 6 correct answer is c ) 6"
Answer: c
Python program:
a = 4 + 2
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 6840 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 868.6 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 6840 / 18 + 6840 / 14 = 380 + 488.6 = 868.6 hours answer : option d"
Answer: d
Python program:
a = 16 + 2 
b = 6840 / a
c = 16 - 2
d = 6840 / c
e = b + d
Problem: in august , a cricket team that played 120 matches won 22 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 68 , d ) 75 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 26.4 + x by solving we get x = 75 answer : d"
Answer: d
Python program:
a = 52 / 100
b = a * 120
c = 22 / 100
d = c * 120
e = b - d
f = 52 / 100
g = 1 - f
h = e / g
Problem: jane started baby - sitting when she was 16 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "check two extreme cases : jane = 16 , child = 8 , years ago = 32 - 16 = 16 - - > child ' s age now = 8 + 16 = 24 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : e ."
Answer: e
Python program:
a = 16 / 2
b = 32 - 16
c = a + b