euclaise/mathqa_programs huggingface dataset:
Problem: a man whose speed is 7.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 10 , b ) 8 , c ) 9 , d ) 7.2 , e ) 6
Rationale: "m = 7.5 s = 1.5 ds = 9 us = 6 as = ( 2 * 9 * 6 ) / 15 = 7.2 answer : d"
Answer: d
Python program:
a = 7 - 5
b = 7 + 5 
c = b / 2
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 16,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 5296
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 16000 . t = 3 years and r = 10 % p . a . c . i . = rs . 16000 x 1 + 10 3 - 1 100 = rs . 16000 x 331 1000 = 5296 . e"
Answer: e
Python program:
a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 60 / 6
g = f / 100
h = 1 + g 
i = 60 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: along a yard 255 metres long , 18 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 15 , c ) 10 , d ) 11 , e ) 12
Rationale: "explanation : 18 trees have 17 gaps between them , required distance ( 281 / 17 ) = 15 option b"
Answer: b
Python program:
a = 18 - 1
b = 255 / a
Problem: if the cost price is 92 % of the selling price , then what is the profit percent ?
Options: a ) 9 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 92 profit = $ 8 profit % = 8 / 92 * 100 = 25 / 6 = 9 % approximately answer is a"
Answer: a
Python program:
a = 100 - 92
b = a / 92
c = b * 100
Problem: how much time will a train of length 280 m moving at a speed of 72 kmph take to cross another train of length 360 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 99 , c ) 64 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 280 + 360 = 640 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 640 / 10 = 64 sec . answer : c"
Answer: c
Python program:
a = 280 + 360 
b = 72 - 36
c = b * const_0_2778
d = a / c
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 81 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 9 : 4 , c ) 4 : 5 , d ) 4 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 81 : √ 16 = 9 : 4 answer : b"
Answer: b
Python program:
a = math.sqrt(81)
b = math.sqrt(16)
c = a / b
Problem: sandy is younger than molly by 10 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 54 , e ) 63
Rationale: "s = m - 10 s / m = 7 / 9 9 s = 7 m 9 ( m - 10 ) = 7 m m = 45 the answer is c ."
Answer: c
Python program:
a = 9 - 7
b = 7 / a
c = b * 10
Problem: if x * y = xy – 2 ( x + y ) for all integers x and y , then 5 * ( – 3 ) =
Options: a ) – 19 , b ) – 11 , c ) – 4 , d ) 4 , e ) 16
Rationale: 5 * ( - 3 ) = 5 * ( - 3 ) - 2 ( 5 + ( - 3 ) ) = - 15 - 4 = - 19 option ( a )
Answer: a
Python program:
a = negate + ( 
b = a * 5
c = negate + (
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fourth widget , starting with the fourth , and steven 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 ) 52 , c ) 53 , d ) 55 , e ) 56
Rationale: "widgets inspected by lauren : ( ( 96 - 4 ) / 4 ) + 1 = 23 + 1 = 24 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 96 / 12 ) + 1 = 9 total : 24 + 32 - 9 = 45 hence , widgets not inspected : 98 - 45 = 53 option c"
Answer: c
Python program:
a = 4 + 1 
b = 98 / a
c = math.floor(b)
d = 98 / 4
e = math.floor(d)
f = c + e 
g = 4 + 1 
h = 10 + g 
i = 98 / h
j = math.floor(i)
k = f - j
l = 98 - k
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 9 %
Rationale: "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.2 * 4 = 8.8 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 8.8 % answer : e ."
Answer: e
Python program:
a = 2 * 2
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 9 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 36 , b ) 35 , c ) 34 , d ) 38 , e ) 40
Rationale: at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 9 strikes , there would be 8 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 9 strikes and 8 intervals will take 2 * ( 9 + 8 ) = 34 secs c
Answer: c
Python program:
a = 9 - 1
b = a + 9 
c = 6 - 1
d = c + 6 
e = 22 / d
f = b * e
Problem: find the compound interest on $ 50000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 4121.60 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: principle = $ 50000 rate = 2 % half yearly = 4 half years amount = 50000 * ( 1 + 2 / 100 ) ^ 4 = 50000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 54121.60 c . i . = 54121.60 - 50000 = $ 4121.60 answer is b
Answer: b
Python program:
a = 4 / 100
b = a / 2
c = b + 1 
d = c ** 4
e = d * 50000
f = e - 50000
Problem: i travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours . how long did the first part of my journey last ?
Options: a ) 4 hours , b ) 2 hours , c ) 3 hours , d ) 2 hours 24 minutes , e ) none
Rationale: "explanatory answer the total time of journey = 5 hours . let ' x ' hours be the time that i traveled at 40 kmph therefore , 5 - x hours would be time that i traveled at 60 kmph . hence , i would have covered x * 40 + ( 5 - x ) 60 kms in the 5 hours = 240 kms . solving , for x in the equation 40 x + ( 5 - x ) * 60 = 240 , we get 40 x + 300 - 60 x = 240 = > 20 x = 60 or x = 3 hours . answer c"
Answer: c
Python program:
a = 60 * 5
b = a - 240
c = 60 - 40
d = b / c
Problem: the set s has 36 different subsets each of which contains exactly two elements . how many subsets of s could contain exactly 7 elements each ?
Options: a ) 81 , b ) 63 , c ) 54 , d ) 36 , e ) 90
Rationale: nc 2 = 36 = > n * ( n - 1 ) / 2 = 36 by middle term factor and n can not be negative = > n = 9 nc 7 = 9 c 7 = 9 ! / 7 ! * ( 9 - 7 ) ! = 9 * 8 * 7 ! / 7 ! * 2 = 36 so , answer is d .
Answer: d
Python program:
a = 36 * 2
b = 4 * a
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
g = math.factorial(f)
h = math.factorial(7)
i = g / h
j = i / 2
Problem: a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?
Options: a ) 17.5 litres , b ) 16.67 litres , c ) 17.67 litres , d ) 16.5 litres , e ) 16 litres
Rationale: "in 100 l mixture we have 36 l milk and 64 l water . hence m and w are in the ratio of 9 : 16 . x l of solution has been removed . hence we have 36 - 9 / 25 x of milk and 64 - 16 / 25 x of water . for calculation simplicity multiply and divide 9 / 25 x by 4 we get 36 / 100 x since this procedure is repeated 2 times . this was my equation 25 = 36 * ( 36 - 36 / 100 x ) ^ 2 ) / ( 36 ) ^ 2 by solving it . we get x = 100 / 6 or 50 / 3 or 16.67 answer : b"
Answer: b
Python program:
a = 25 / 36
b = math.sqrt(a)
c = 1 - b
d = 100 * c
Problem: x + ( 1 / x ) = 4 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 14 , e ) 6.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 4 ^ 2 x ^ 2 + 1 / x ^ 2 = 16 - 2 x ^ 2 + 1 / x ^ 2 = 14 answer : d"
Answer: d
Python program:
a = 4 ** 2
b = a - 2
Problem: a present value of a machine is $ 1200 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 972 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 795
Rationale: "p = $ 1200 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1200 * 9 / 10 * 9 / 10 = $ 972 answer is a"
Answer: a
Python program:
a = 10 / 100
b = 1 - a
c = b ** 2
d = 1200 * c
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 16 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 8 x 16 â ‡ ’ r 2 = ( 8 x 16 / 2 ) â ‡ ’ 64 â ‡ ’ r = 8 cm . answer d"
Answer: d
Python program:
a = 16 / 2
b = 16 * a
c = math.pi * b
d = c * 2
e = math.pi * 4
f = d / e
g = math.sqrt(f)
Problem: for what value of k will the two equations 2 x + 4 = 4 ( x - 2 ) and - x + k = 2 x - 1 have the same solution ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 19 , e ) 17
Rationale: solve the first equation 2 x + 4 = 4 ( x - 2 ) to obtain . x = 6 substitute x by 6 ( same solution ) in the second equation and solve for k . - 6 + k = 2 ( 6 ) - 1 solve for k . k = 17 correct answer e
Answer: e
Python program:
a = 4 + 3 
b = 10 + a
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 7967 for a computer table , then what was the cost price of the computer table ?
Options: a ) 7297 , b ) 6425 , c ) 2871 , d ) 6725 , e ) 2981
Rationale: "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 7967 ( 100 / 124 ) = rs . 6425 . answer : b"
Answer: b
Python program:
a = 24 / 100
b = 1 + a 
c = 7967 / b
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 20 % goods during theft . his loss percent is ?
Options: a ) 16 , b ) 18 , c ) 17 , d ) 12 , e ) 12
Rationale: "suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 80 . s . p . of each item = rs . 1.10 total sale = 1.10 * 80 = rs . 88 hence , loss % = 12 / 100 * 100 = 12 % answer : d"
Answer: d
Python program:
a = 100 + 10 
b = 100 + 10 
c = b * 20
d = c / 100
e = a - d
f = 100 - e
Problem: a boat having a length 4 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 80 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 4 x 2 x 0.01 ) m 3 = 0.08 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.08 x 1000 ) kg = 80 kg . answer : d"
Answer: d
Python program:
a = 4 * 2
b = 1 / 100
c = a * b
d = c * 1000
Problem: for an international mathematics olympiad , country d will send 6 delegates in total — two will be supervisors and 4 will be contestants . there are 210 ways in which the 6 delegates can be chosen and there are 7 candidates competing for the 4 contestants ’ places available . how many candidates are competing for the two supervisors ’ slots available ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: option a wrong as 2 supervisor need to be selected . going by statement : 4 contestant chosen from 7 - - 7 c 4 = = 35 and total ways = 210 consider 2 supervisor will be chosen from : x people . so as per question : 35 * x = 210 x = 6 so by using options , option a already decided wrong . option b 2 c 2 will be 1 not 6 . option c 3 c 2 will be 3 not 6 option d 4 c 2 will be 6 correct answer option e 5 c 2 will be 10 not 6 . ans : d
Answer: d
Python program:
a = 210 / 6
b = 7 / 4
c = a + b 
d = c / 6
e = d - 2
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 80 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 80 mph ?
Options: a ) 15 % , b ) 16 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "total time for travelling 80 miles @ 60 mph = 80 / 80 = 1 hour = 60 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 80 mph . thus in 60 minutes it will use = 1.5 gallons . thus , full tank = 1.5 + 8 = 9.5 gallons - - - > 1.5 / 9.5 = 16 % of the fuel used . b is the correct answer ."
Answer: b
Python program:
a = 40 * 80
b = 80 * 80
c = a / b
d = 40 * 80
e = 80 * 80
f = d / e
g = f + 8 
h = c / g
Problem: the cross - section of a water channel is a trapezium in shape . if the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 700 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50
b ) 60
c ) 70
d ) 80
e ) 90
Rationale: 1 / 2 * d * ( 12 + 8 ) = 700 d = 70 the answer is c .
Answer: c
Python program:
a = 12 + 8 
b = a / 2
c = 700 / b
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 292 runs ?
Options: a ) 6 , b ) 6.5 , c ) 7.25 , d ) 7.5 , e ) 8
Rationale: "required run rate = 262 - ( 3.2 x 10 ) = 250 = 6.5 40 40 b"
Answer: b
Python program:
a = 3 * 2
b = 292 - a
c = b / 40
Problem: simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on rs . 4000 for 2 years at 10 % per annum . the sum placed on simple interest is :
Options: a ) 17523 , b ) 2788 , c ) 1750 , d ) 2787 , e ) 29899
Rationale: "explanation : c . i . = rs . [ 4000 * ( 1 + 10 / 100 ) ^ 2 - 4000 ] = rs . 840 sum = rs . ( 420 * 100 ) / 3 * 8 = rs . 1750 \ answer : c ) rs , 1750"
Answer: c
Python program:
a = 4000 * 10
b = a / 100
c = 4000 * 10
d = c / 100
e = 4000 + d 
f = e * 10
g = f / 100
h = b + g 
i = h / 2
j = i / 3
k = j * 100
l = k / 8
Problem: the product z of two prime numbers is between 20 and 56 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 14 but less than 30 then what is z ?
Options: a ) 26 , b ) 35 , c ) 39 , d ) 51 , e ) 55
Rationale: "the smallest possible product is 51 which is 3 * 17 . all other products are too big . the answer is d ."
Answer: d
Python program:
a = 20 - 4
b = a * 3
Problem: 5800 * 99
Options: a ) 574580 , b ) 574200 , c ) 584250 , d ) 576460 , e ) none of these
Rationale: "explanation : 5800 * ( 100 - 1 ) = 580000 - 5800 = 574200 option b"
Answer: b
Python program:
a = 5800 / 99
b = a * 100
Problem: 3 numbers are such that the second is as much lesser than thr third as the first is lesser than the second . if the product of the two smaller numbers is 85 and product of two larger number is 115 then find the middle number
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: explanation : its a bit funny sum . if you see the first sentence actually it saying that the numbers are in a . p . now as the first two numbers product is 85 so if you take factor 85 you get 5 and 17 . . now as per option 17 can not be the middle number so from intuition and seeing the option only 10 could be the middle number where 8.5 is the first number and 11.5 is the last answer : c
Answer: c
Python program:
a = 115 + 85 
b = 2 * 10
c = a / b
Problem: after decreasing 20 % in the price of an article costs rs . 200 . find the actual cost of an article ?
Options: a ) 280 , b ) 250 , c ) 260 , d ) 270 , e ) 300
Rationale: "cp * ( 80 / 100 ) = 200 cp = 2.5 * 100 = > cp = 250 answer : b"
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 200 / b
Problem: the sale price sarees listed for rs . 480 after successive discount is 15 % and 25 % is ?
Options: a ) 298 , b ) 237 , c ) 306 , d ) 876 , e ) 291
Rationale: "480 * ( 85 / 100 ) * ( 75 / 100 ) = 306 answer : c"
Answer: c
Python program:
a = 480 * 15
b = a / 100
c = 480 - b
d = 480 * 15
e = d / 100
f = 480 - e
g = f * 25
h = g / 100
i = c - h
Problem: the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 4 | + 7 is equal to :
Options: a ) – 7 , b ) 7 , c ) 10 , d ) 12 , e ) 16
Rationale: "x ^ 2 - 8 x + 14 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 9 x + 18 = 0 x ^ 2 - 7 x + 10 = 0 x = 6,5 , 3,2 we test all 4 values in original equation , all ok . thus , sum = 6 + 5 + 3 + 2 = 16 ans ( e )"
Answer: e
Python program:
a = 7 * 4
Problem: p , q and r together earn rs . 1620 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) rs . 40 , b ) rs . 70 , c ) rs . 90 , d ) rs . 100 , e ) rs . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1620 / 9 = 180 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 180 = 70 = > amount earned by r in 1 day = 70 answer : option b"
Answer: b
Python program:
a = 600 / 5
b = 910 / 7
c = a + b 
d = 1620 / 9
e = c - d
Problem: a certain university will select 1 of 9 candidates eligible to fill a position in the mathematics department and 2 of 15 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 ) 351 , b ) 425 , c ) 748 , d ) 854 , e ) 945
Rationale: "1 c 9 * 2 c 15 = 9 * 105 = 945 the answer is ( e )"
Answer: e
Python program:
a = 15 * 3
b = a * 9
Problem: two motor cycles a & b are started from one point at 4 kmph & 6 kmph ; after 45 min b starts returning , at what time they will meet ?
Options: a ) 54 mins , b ) 55 mins , c ) 56 mins , d ) 57 mins , e ) 58 mins
Rationale: distance covered by a in 45 mins = 3 kms . distance covered by b in 45 mins = 4.5 kms . distance between and b after 45 mins = 1.5 kms . relative speed when b is returning = 4 + 6 = 10 kmph distance between a and b is covered in 1.5 / 10 = 0.15 hrs = 9 mins so they will meet again after 54 mins from starting time . answer : a
Answer: a
Python program:
a = 45 / const_60
b = 6 * a
c = 45 / const_60
d = 4 * c
e = b - d
f = 4 + 6 
g = e / f
h = g * const_60
i = 45 + h
Problem: if 20 % of a number = 1000 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 6000 , e ) 820
Rationale: "let the number x . then , 20 % of x = 1000 x = ( 1000 * 100 ) / 20 = 5000 120 % of x = ( 120 / 100 * 5000 ) = 6000 . answer : d"
Answer: d
Python program:
a = 120 * 1000
b = a / 20
Problem: the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidates who passed the examination is ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 120 , e ) 140
Rationale: "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c"
Answer: c
Python program:
a = 120 * 35
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 32 , find the sum of money ?
Options: a ) 288 , b ) 262 , c ) 72 , d ) 205 , e ) 164
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 32 41 - - - - ? = > rs . 164 answer : e"
Answer: e
Python program:
a = 32 / 40
b = 100 + 65 
c = b + 40 
d = a * c
Problem: an article is bought for rs . 675 and sold for rs . 945 , find the gain percent ?
Options: a ) 40 % , b ) 33 8 / 3 % , c ) 33 1 / 3 % , d ) 33 2 / 3 % , e ) 33 1 / 2 %
Rationale: "675 - - - - 270 100 - - - - ? = > 40 % answer : a"
Answer: a
Python program:
a = 945 * 100
b = a / 675
c = 100 - b
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 1.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "if the interest were compounded annually instead of quarterly then in one year the interest would be 1.5 * 4 = 6 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 6 % . answer : b ."
Answer: b
Python program:
a = 1 * 5
Problem: a 1 , a 5 , a 13 ( terms of ap ) are in gp and a 6 + a 15 = 63 . find a 23
Options: a ) 181 / 3 , b ) 182 / 3 , c ) 183 / 3 , d ) 184 / 3 , e ) 182 / 5
Rationale: a 1 a 5 = a 1 + 4 d a 13 = a 1 + 12 d now a 5 / a 1 = a 13 / a 5 - - - - > > a 1 = 4 d . . . . . . . . ( 1 ) given a 6 + a 15 = 63 - - - - > a 1 + 5 d + a 1 + 14 d = 63 - - - - > 2 a 1 + 19 d = 63 - - - - > 8 d + 19 d = 63 from ( 1 ) - - - - > d = 63 / 27 = 7 / 3 so a = 4 d = 4 * 7 / 3 = 28 / 3 from ( 1 ) a 23 = a 1 + 22 d = 28 / 3 + 22 * 7 / 3 = 182 / 3 answer : b
Answer: b
Python program:
a = 13 - 5
b = 2 * a
c = 6 + 15 
d = c - 2
e = b + d 
f = 63 / e
g = 13 - 5
h = f * g
i = 23 - 1
j = 13 - 5
k = 2 * j
l = 6 + 15 
m = l - 2
n = k + m 
o = 63 / n
p = i * o
q = h + p 
r = q + 4
Problem: if 3 / p = 4 & 3 / q = 18 then p - q = ?
Options: a ) 5 / 24 , b ) 7 / 12 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 3 / 4 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 4 ) - ( 1 / 6 ) = 7 / 12 answer : b"
Answer: b
Python program:
a = 3 / 4
b = 3 / 18
c = a - b
Problem: a number when divided by 899 gives a remainder 63 . if the same number is divided by 29 , the remainder will be
Options: a ) 11 , b ) 13 , c ) 15 , d ) data inadequate , e ) none
Rationale: "sol . number = ( 31 x q ) + 29 . given data is inadequate . answer d"
Answer: d
Python program:
a = 29 * 2
b = 63 - a
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2700 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 101 , e ) 30
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2700 3 b 2 = 2700 b 2 = 900 = 30 ( b > 0 ) b = 30 m . answer : e"
Answer: e
Python program:
a = 2700 / 3
b = math.sqrt(a)
Problem: two trains a and b start simultaneously in the opposite direction from two points p and q and arrive at their destinations 16 and 9 hours respectively after their meeting each other . at what speed does the second train b travel if the first train travels at 120 km / h
Options: a ) 334 , b ) 160 , c ) 387 , d ) 278 , e ) 112
Rationale: answer : b ) 160 km / h
Answer: b
Python program:
a = math.sqrt(16)
b = a * 120
c = math.sqrt(9)
d = b / c