euclaise/mathqa_programs huggingface dataset:
Problem: a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252
Rationale: "first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d"
Answer: d
Python program:
a = 6 + 6 
b = math.comb(a, 6)
c = 2 / b
Problem: the average weight of 7 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 74 kg , b ) 78.5 kg , c ) 99.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 7 x 3.5 ) kg = 24.5 kg . weight of new person = ( 75 + 24.5 ) kg = 99.5 kg . answer : option c"
Answer: c
Python program:
a = 7 * 3
b = a + 75
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 32 people were made to stand in a column , how many columns could be formed ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "16 * 30 = 32 * n n = 15 the answer is a ."
Answer: a
Python program:
a = 32 / 16
b = 30 / a
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 10
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted answer : option e"
Answer: e
Python program:
a = 427398 / 10
b = math.floor(a)
c = b * 10
d = 427398 - c
Problem: the average age of applicants for a new job is 10 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34
Rationale: minimum age = average - 1 standard deviation = 10 - 8 = 2 maximum age = average + 1 standard deviation = 10 + 8 = 18 maximum number of different ages of the applicants = 18 - 2 + 1 = 17 answer c
Answer: c
Python program:
a = 10 + 8 
b = 10 - 8
c = a - b
d = c + 1
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 900 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: 1 hour he ride 50 km he ride 900 km in = 900 / 50 * 1 = 18 hours answer is e
Answer: e
Python program:
a = 900 / 50
Problem: a and b invests rs . 6000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 8 : 21 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 48000 : 126000 8 : 21 answer : b"
Answer: b
Python program:
a = 6000 * 4
b = 12000 / 3
c = 2 * 4
d = b * c
e = a + d 
f = 2 * 3
g = 12000 * f
h = 12000 / 3
i = 12000 - h
j = 2 * 3
k = i * j
l = g + k 
m = e / l
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 7 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 90 , c ) 56 , d ) 70 , e ) 60
Rationale: "c 56 sum = ( n x n ) + n hence , 7 x 7 = 49 + 7 = 56"
Answer: c
Python program:
a = 7 + 1 
b = a * 7
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 80 m = 80 / 5 = 16 seconds . answer : a"
Answer: a
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 80 / b
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 92 , d ) d . 46 , e ) e . 44
Rationale: at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c
Answer: c
Python program:
a = 1 + 4 
b = 6 + a 
c = 44 / b
d = 1 + 4 
e = 6 + d 
f = 12 + e 
g = c * f
Problem: each week , harry is paid x dollars per hour for the first 21 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 21 x + 1.5 x ( h - 21 ) = = > 42 = 21 + 1.5 ( h - 21 ) = = > h - 21 = 21 / 1.5 = 14 = > h = 35 answer is a"
Answer: a
Python program:
a = 40 + 2 
b = a - 21
c = b / 1
d = c + 21
Problem: a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30
Rationale: "first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of ways in which 4 girls can select 4 black balls = 4 c 4 = 1 therefore , total favorable outcomes / total outcomes = 2 / 70 = 1 / 35 a"
Answer: a
Python program:
a = 4 + 4 
b = math.comb(a, 4)
c = 2 / b
Problem: a can knit a pair of socks in 3 days . b can knit the same thing in 6 days . if they are knitting together , in how many days will they knit two pairs of socks ?
Options: a ) 4 days , b ) 2 days , c ) 4 1 ⁄ 2 days , d ) 3 days , e ) none of these
Rationale: explanationa ’ s one day ’ s work = 1 ⁄ 3 rd work . b ’ s one day ’ s work = 1 ⁄ 6 rd work . ( a + b ) ’ s one day ’ s work = 1 ⁄ 3 + 1 ⁄ 6 = 1 ⁄ 2 nd work . ∴ a and b together can complete the work ( knit a pair of socks ) in 2 days . ∴ they together knit two pair of socks in 4 days . answer a
Answer: a
Python program:
a = 1/(3)
b = 1/(6)
c = a + b 
d = c / 2
e = 1/(d)
Problem: the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 72 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 72 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 72 x = 0.06 the answer is b ."
Answer: b
Python program:
a = math.sqrt(72)
Problem: running at their respective constant rates , machine x takes 6 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 10 , e ) 12
Rationale: "together they make 5 / 4 w widgets in 3 days . so they make w widgets in 3 * 4 / 5 = 12 / 5 days . 1 / ( t + 2 ) + 1 / t = 5 / 12 now , calculating this is really cumbersome so try to plug in options to get to the answer . if machine x takes 12 days to produce 2 w widgets , it would take 6 days to make w widgets , t would be 4 . 1 / 6 + 1 / 4 = 5 / 12 it works so t = 4 . answer : a"
Answer: a
Python program:
a = 3 * 4
b = a * 6
c = 3 * 4
d = b - c
e = d / 6
Problem: find the ones digit of 73 ^ 353
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 353 will be the same as the units digit of 3 ^ 353 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 353 = 352 + 1 = ( multiple of 4 ) + 1 , then the units digit of 3 ^ 353 will be the first number in the pattern thus 3 . answer : a ."
Answer: a
Python program:
a = 3 + 4 
b = a * 10
c = 73 - b
d = 353 / 4
e = math.floor(d)
f = e * 4
g = 353 - f
h = c ** g
i = 2 * 10
j = h - i
Problem: if 2 x + y = 26 and x + 2 y = 10 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 26 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 36 divide both sides by 3 to get : x + y = 12 so , ( x + y ) / 3 = 12 / 3 = 4 answer : e"
Answer: e
Python program:
a = 26 * 2
b = a - 10
c = 2 * 2
d = c - 1
e = b / d
f = 26 * 2
g = f - 10
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 26 - k
m = e + l 
n = m / 3
Problem: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 16 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 1584
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 16 = 1584 answer : e"
Answer: e
Python program:
a = 3 / 2
b = volume_cylinder * (
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1015 . find the cost of each ice - cream cup ?
Options: a ) 34 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1015 96 + 225 + 490 + 6 x = 1015 6 x = 204 = > x = 34 . answer : a"
Answer: a
Python program:
a = 16 * 6
b = 1015 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
Problem: a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more thanc . out of a total profit of rs . 35000 , a receives :
Options: a ) 14700 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 * 21 / 50 ) = rs . 14,700 . answer : a ) 14700
Answer: a
Python program:
a = 5000 + 4000 
b = a + 5000 
c = 50000 - b
d = c / 3
e = 5000 + 4000 
f = d + e 
g = f / 50000
h = 35000 * g
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 $ 2,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,700 , 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 + 2000 = $ 20700 correct option : d"
Answer: d
Python program:
a = 2 * 10
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 6 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11.5 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 6 days = 6 * ( 1 / 24 + 1 / 30 ) = 9 / 20 remaining work = 11 / 20 the number of days required for this initial work = 5.5 days . the total number of days required = 6 + 5.5 = 11.5 days . answer : d"
Answer: d
Python program:
a = 1 / 24
b = 1 / 30
c = a + b 
d = c * 6
e = 1 - d
f = 2 + 3 
g = 2 * 6
h = f * g
i = 1 / h
j = 1 / 24
k = 1 / 30
l = j + k 
m = i + l 
n = e / m
o = n + 6
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?
Options: a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1800 , e ) $ 1900
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a"
Answer: a
Python program:
a = 3 / 4
b = 1 - a
c = 300 / b
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 6 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 42 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 6 - - - - - - - - - ? = 42 m answer : d"
Answer: d
Python program:
a = 6 * 7
Problem: a jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 35 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 230 + 120 ) m = 350 m . ∴ time taken = ( 350 ⁄ 10 ) sec = 35 sec . answer c"
Answer: c
Python program:
a = 230 + 120 
b = a / 1000
c = 45 - 9
d = b / c
e = d * const_60
f = e * const_60
Problem: a train covers a distance of 36 km in 12 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 300 m , b ) 1000 m , c ) 120 m , d ) 200 m , e ) 500 m
Rationale: "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 10 = 500 m . answer : e"
Answer: e
Python program:
a = 36 / 12
b = a - 10
c = 36 / b
Problem: 8 people decided to split the restaurant bill evenly . if the bill was $ 214.18 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.24
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 418 not divisible by a hence , we need to add 6 to this number for it to be divisible by 8 correct option : e"
Answer: e
Python program:
a = 3 / 100
b = 214 + 18
Problem: if 4 women can color 48 m long cloth in 2 days , then 6 women can color 36 m long cloth in
Options: a ) 2 days , b ) 3 days , c ) 1 day , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 women = 36 / 6 × 6 = 1 day . c"
Answer: c
Python program:
a = 4 * 2
b = 48 / a
c = 6 * b
d = 36 / c
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 4 cubic feet . if a large block has twice the width , twice the depth , and twice the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 16
b ) 20
c ) 36
d ) 32
e ) 28
Rationale: volume of cube = lbh = 4 new cube l , b , h are increases of 2 l , 2 b , 2 h new volume of cube = 2 l * 2 b * 2 h = 8 * lbh = 8 * 4 = 32 answer : d
Answer: d
Python program:
a = 2 * 2
b = a * 2
c = b * 4
Problem: a man is 32 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is
Options: a ) 26 years , b ) 27 years , c ) 28 years , d ) 29 years , e ) 30 years
Rationale: "explanation : let ' s son age is x , then father age is x + 32 . = > 2 ( x + 6 ) = ( x + 32 + 6 ) = > 2 x + 12 = x + 38 = > x = 26 years answer : option a"
Answer: a
Python program:
a = 2 * 2
b = a - 2
c = 32 - b
d = 2 - 1
e = c / d
Problem: the monthly rent of a shop of dimension 20 feet × 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ?
Options: a ) 48
b ) 56
c ) 68
d ) 87
e ) 92
Rationale: sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a
Answer: a
Python program:
a = 10 + 2 
b = 1440 / rectangle_area
c = a * b
Problem: ashley and betty start a business with $ 9000 each , and after 3 months , betty adds another $ 5000 . how should they share the profits at the end of the 24 months ?
Options: a ) 72 : 107 , b ) 4 : 5 , c ) 17 : 23 , d ) 3 : 4 , e ) 68 : 95
Rationale: ashley invests $ 9000 for 24 months , but betty invests $ 9000 for the first 3 months and then adds $ 5000 . so , the investment of betty for remaining 21 months is $ 14000 . ashley : betty 9000 * 24 : ( 9000 * 3 ) + ( 14000 * 21 ) 216000 : 321000 a : b = 72 : 107 answer : a
Answer: a
Python program:
a = 9000 * 24
b = 9000 * 3
c = 9000 + 5000 
d = 24 - 3
e = c * d
f = b + e 
g = a / f
Problem: in an examination , 25 % of total students failed in hindi , 50 % failed in english and 25 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 37 , c ) 28 , d ) 40 , e ) 50
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 50 â € “ 25 = 50 therefore students who passed = 100 â € “ 50 = 50 . answer : e"
Answer: e
Python program:
a = 25 + 50 
b = a - 25
c = 100 - b
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 12 units ?
Options: a ) 140 sq . units , b ) 170 sq . units , c ) 190 sq . units , d ) 168 sq . units , e ) 149 sq . units
Rationale: "explanation : given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 12 units area of the rectangle = lb = 14 * 12 = 168 sq . units answer : option d"
Answer: d
Python program:
a = math.sqrt(1225)
b = 12 / 2
c = a / b
d = 2 * c
e = 12 * d
Problem: a pineapple costs rs 9 each and a watermelon costs rs . 6 each . if i spend rs 51 on total what is the number of pineapple i purchased ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 3 , e ) 2
Rationale: "5 * 9 + 6 = 51 5 pineapples answer : c"
Answer: c
Python program:
a = 4 * 9
b = 51 - a
c = b / 6
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a"
Answer: a
Python program:
a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c 
e = a / d
f = 4000 / e
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : b"
Answer: b
Python program:
a = 26 - 6
b = a * 3
c = b / 4
Problem: a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability j that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability j of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e .
Answer: e
Python program:
a = 3 / 5
b = 3 / 5
c = a * b
d = 3 / 5
e = 2 / 5
f = d * e
g = 3 / 5
h = 2 / 5
i = g * h
j = f + i 
k = c + j
Problem: how many multiples of 7 are there between 14 and 343 , exclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44
Rationale: "7 * 2 = 14 7 * 49 = 343 total multiples = ( 49 - 2 ) + 1 = 48 exclude 7 343 = 48 - 2 = 46 answer is ( c )"
Answer: c
Python program:
a = 343 - 14
b = a / 7
c = b + 1
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 10.8 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 5 = 20 kmph = 20 * 5 / 18 = 50 / 9 m / s hence time taken to cover 60 m = 60 * 9 / 50 = 10.8 seconds . answer : c"
Answer: c
Python program:
a = 15 + 5 
b = a * const_0_2778
c = 60 / b
Problem: david and lewis leave chennai for hyderabad simultaneously at 8 p . m in the night driving in two cars at speeds of 50 mph and 70 mph respectively . as soon as lewis reaches hyderabad he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 350 miles , how far from chennai did david and lewis meet ?
Options: a ) 250 miles , b ) 240 miles , c ) 230 miles , d ) 235 miles , e ) 75 miles
Rationale: time taken by lewis to reach hyderabad = 350 / 70 = 5 hours in 5 hours , david travels 50 * 5 = 250 miles so distance at which they meet should be greater than 250 miles . only a satisfies . answer is a .
Answer: a
Python program:
a = 350 / 70
b = a * 50
Problem: divide $ 600 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: sum of ratio terms = 1 + 2 = 3 a = 600 * 1 / 3 = $ 200 answer is e
Answer: e
Python program:
a = 600 / 1
Problem: how many three digit numbers w are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples w - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Python program:
a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10