euclaise/mathqa_programs huggingface dataset:
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 3 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "b work 1 / 8 * 3 = 3 / 8 remaining work = 1 - 3 / 8 = 5 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 remaining work is done in = 8 / 5 * 1 / 4 = 2 / 5 = 0.4 answer : d"
Answer: d
Python program:
a = 3 / 6
b = 3 / 8
c = a + b
Problem: what is the greatest 6 - digit number when divided by 8 , 9 , and 10 leaves a remainder of 6 , 7 , and 8 respectively ?
Options: a ) 456780 , b ) 678918 , c ) 997479 , d ) 997916 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so b is the only possible answer .
Answer: b
Python program:
a = 1000 * 1000
b = a - 1
c = math.lcm(8, 9)
d = math.lcm(10, 9)
e = math.lcm(c, d)
f = math.lcm(10, 9)
g = e * f
h = g * 10
i = b - h
Problem: a thief is spotted by a policeman from a distance of 160 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 240 m , c ) 440 m , d ) 640 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 160 m / 1000 ) x 1 / 2 hr = 2 / 25 hr . in 2 / 25 hr / s , the thief covers a distance of 8 x 2 / 25 km = 16 / 25 km = 640 m answer is d ."
Answer: d
Python program:
a = 160 * 8
b = 10 - 8
c = a / b
Problem: the average of runs of a cricket player of 20 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 120
Rationale: "average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 * 20 = 720 now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 720 = 120 answer : e"
Answer: e
Python program:
a = 20 + 1 
b = 4 + 36 
c = a * b
d = 20 * 36
e = c - d
Problem: the product of a and b is equal to 14 more than twice the sum of a and b . if b = 8 , what is the value of b - a ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 14 + 2 ( a + b ) 8 a = 14 + 2 a + 16 6 a = 30 a = 5 b - a = 8 - 5 = 3 b is the answer"
Answer: b
Python program:
a = 8 * 2
b = a + 14 
c = 8 - 2
d = b / c
e = 8 - d
Problem: excluding stoppages , the speed of a train is 42 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 7.5 , b ) 8.5 , c ) 9.5 , d ) 4.5 , e ) 6.5
Rationale: t = 6 / 42 * 60 = 8.5 answer : b
Answer: b
Python program:
a = 36 / 42
b = const_60 * a
c = const_60 - b
Problem: a can do a piece of work in 4 hours . a and c together can do it in just 2 hours , while b and c together need 3 hours to finish the same work . in how many hours b can complete the work ?
Options: a ) 10 hours , b ) 12 hours , c ) 16 hours , d ) 18 hours , e ) 20 hours
Rationale: "explanation : work done by a in 1 hour = 1 / 4 work done by b and c in 1 hour = 1 / 3 work done by a and c in 1 hour = 1 / 2 work done by a , b and c in 1 hour = ( 1 / 4 ) + ( 1 / 3 ) = 7 / 12 work done by b in 1 hour = ( 7 / 12 ) – ( 1 / 2 ) = 1 / 12 = > b alone can complete the work in 12 hour option b"
Answer: b
Python program:
a = 1/(3)
b = 1/(2)
c = 1/(4)
d = b - c
e = a - d
f = 1/(e)
Problem: a man can row downstream at the rate of 32 kmph and upstream at 17 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 7.5 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 32 + 17 ) = 24.5 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 32 - 17 ) = 1 / 2 ( 15 ) = 7.5 kmph answer is a ."
Answer: a
Python program:
a = 32 - 17
b = a / 2
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 15 minutes , a combustion reaction creates 15,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: "solution : 15,000 carbon dioxide molecules are created over a period of 15 minutes . therefore 15,000 / 15 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a ."
Answer: a
Python program:
a = 15 * 2
b = a - 15
c = b * 1000
d = c / 15
e = d / 1000
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 20 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 300 m , e ) 145 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 20 = x / 15 x = 300 m . answer : d"
Answer: d
Python program:
a = 2 - 1
b = 100 * a
Problem: the smallest number when increased by ` ` 1 ` ` is exactly divisible by 618 , 3648 , 60 is :
Options: a ) 724 , b ) 721 , c ) 720 , d ) 719 , e ) 700
Rationale: lcm = 720 720 - 1 = 719 answer : d
Answer: d
Python program:
a = 618 + 1 
b = 100 + a
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days g will the work get over ?
Options: a ) 60 , b ) 70 , c ) g = 75 , d ) g = 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Python program:
a = 10 * 20
b = a / const_0_25
c = 1 - const_0_25
d = b * c
e = 10 - 2
f = d / e
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.96 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 3.00 , b ) $ 3.20 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 3.80
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 96 4 x / 15 = 96 x = $ 3.60 = $ 3.60 the answer is d ."
Answer: d
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 96
Problem: how many prime numbers are between 78 / 14 and 55 / 4 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "78 / 14 = 39 / 7 = 6 - 55 / 4 = 14 - prime numbers between 6 and 14 are 7 , 11 and 13 - sign signifies that the number is marginally less . answer b"
Answer: b
Python program:
a = math.floor(2)
Problem: a person can swim in still water at 12 km / h . if the speed of water 10 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 10 us = 12 - 10 = 2 d = 12 t = 12 / 2 = 6 answer : d"
Answer: d
Python program:
a = 12 - 10
b = 12 / a
Problem: if 15 % of a class averages 100 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 63 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 76 % , b ) 77 % , c ) 78 % , d ) 79 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 15 % - 50 % = 35 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.15 x 100 + 0.50 x 78 + 0.35 x 63 = 76.05 the class average ( rounded ) is 76 % final answer a ) 76 %"
Answer: a
Python program:
a = 15 * 100
b = 50 * 78
c = a + b 
d = 15 + 50 
e = 100 - d
f = e * 63
g = c + f 
h = g / 100
Problem: what is x if x + 3 y = 10 and y = 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 3 in x + 3 y = 10 x + 3 ( 3 ) = 10 x + 9 = 10 if we substitute x by 1 in x + 9 = 10 , we have 1 + 9 = 10 . hence x = 1 correct answer a"
Answer: a
Python program:
a = 3 * 3
b = 10 - a
Problem: arun borrowed a sum of money from jayant at the rate of 8 % per annum simple interest for the first 4 years , 10 % per annum for the next 6 years and 12 % per annum for the period beyond 10 years . if he pays a total of 12160 as interest only at the end of 15 years , how much money did he borrow ?
Options: a ) 8000 , b ) 10000 , c ) 12000 , d ) 9000 , e ) none of these
Rationale: let the principal = p then p × 8 × 4 / 100 + p × 10 × 6 / 100 + p × 12 × 5 / 100 = 12160 ⇒ 152 p = 12160 × 100 or 12160 × 100 / 152 = 8000 answer a
Answer: a
Python program:
a = 12160 * 100
b = 8 * 4
c = 10 * 6
d = b + c 
e = 15 - 10
f = 12 * e
g = d + f 
h = a / g
Problem: what is the largest 4 digit number exactly divisible by 88 ?
Options: a ) 9999 , b ) 9944 , c ) 9988 , d ) 9900 , e ) 9991
Rationale: "largest 4 digit number = 9999 9999 ÷ 88 = 113 , remainder = 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer is b"
Answer: b
Python program:
a = 10 ** 4
b = a / 88
c = math.floor(b)
d = c * 88
Problem: a women travels from x to y distance of 1000 miles in 10 hours . she returns to x in 4 hours . find her average speed
Options: a ) 300 mph , b ) 150.2 mph , c ) 142.8 mph , d ) 200 mph , e ) 111.01 mph
Rationale: speed from x to y = 1000 / 10 = 100 mph speed from y to x = 1000 / 4 = 250 mph average speed = 2 * 100 * 250 / 350 = 142.8 mph answer is c
Answer: c
Python program:
a = 10 + 4 
b = a / 2
c = 1000 / b
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 45 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 3 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : d . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d"
Answer: d
Python program:
a = 11 ** 0
b = a + 1000 
c = b / 45
d = c + 1 
e = d * 45
f = reminder * (
g = f - 10
Problem: a vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 20 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.8 ) x = 0.4 x . the remaining pears are ( 0.5 ) ( 0.8 ) x = 0.4 x . on day two , the vendor throws away ( 0.8 ) ( 0.4 ) x = 0.32 x . the vendor throws away a total of 0.4 x + 0.32 x = 0.72 x . the vendor throws away 72 percent of the pears . the answer is e .
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 50 / 100
d = 20 / 100
e = 1 - d
f = c * e
g = b - f
h = 20 / 100
i = 1 - h
j = 50 / 100
k = 20 / 100
l = 1 - k
m = j * l
n = i - m
o = 20 / 100
p = n * o
q = g - p
r = 50 / 100
s = 20 / 100
t = 1 - s
u = r * t
v = q + u 
w = 100 * v
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 80 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 80 = 20 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 20 / 100 ) * 100 = ( 0.2 ) * 100 = 20 % . a"
Answer: a
Python program:
a = 100 - 80
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 75 . what is that number ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "explanation : let the number be v . then , 3 ( 2 x + 9 ) = 75 . 2 x + 9 = 25 = > 2 x = 16 = > x = 8 answer : d ) 8"
Answer: d
Python program:
a = 3 * 9
b = 75 - a
c = 3 * 2
d = b / c
Problem: the value of 489.1375 x 0.0483 x 1.956 / 0.0873 x 92.581 x 99.749 is closest to :
Options: a ) 0.48 , b ) 5.8 , c ) 0.58 , d ) 0.058 , e ) 0.0058
Rationale: = 489.1375 x 0.0483 x 1.956 / 0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2 / 0.09 x 93 x 100 = 489 / 9 x 93 x 10 = 163 / 279 x 1 / 10 = 0.58 / 10 = 0.058 ( or ) 0.06 . answer is d .
Answer: d
Python program:
a = 489 * 1375
b = a * 1
c = 0 * 873
d = c * 99
e = b / d
Problem: an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 15 % profit , offers a discount of 15 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 27.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 150 . s . p . = 85 % of rs . 150 = rs . 127.5 . ∴ gain % = 27.50 % . answer b"
Answer: b
Python program:
a = 50 / 100
b = 1 + a 
c = 50 / 100
d = 1 + c 
e = 15 / 100
f = d * e
g = b - f
h = g - 1
i = h * 100
Problem: on teacher ' s day , sweets were to be equally distributed among 190 children in a school . actually , on the teacher ' s day , 70 children were absent and therefore each child got 14 sweets extra . how many sweets did each child get on that day ?
Options: a ) 18 , b ) 22 , c ) 28 , d ) 32 , e ) 38
Rationale: total children = 190 . let each student gets x chocolates if all were present . so , total chocolates = 190 x . 70 students were absent . so , no of extra chocolates distributed among 120 students , = 14 * 70 = 980 . now , total chocolates = 190 x 120 * ( x + 14 ) = 190 120 x + 1680 = 190 x 70 x = 1680 x = 24 . total no of chocolates = 24 * 190 = 4560 . no of chocolates each student gets on that day = 4560 / 120 = 38 . answer : option e
Answer: e
Python program:
a = 190 * 14
b = a / 70
Problem: x , a , z , and b are single digit positive integers . x = ¼ a . z = ¼ b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 33 , b ) 36 , c ) 44 , d ) 63 , e ) 66
Rationale: from the given equations , a = 4 x , b = 4 z ( 10 a + b ) - ( 10 x + z ) = 40 x + 4 z - 10 x - z = 30 x + 3 z = 3 ( 10 x + z ) therefore the resultant should be divisible by 3 which is n ' t possible only in the case of c . hence c is the answer
Answer: c
Python program:
a = 4 * 10
b = a + 4
Problem: in what time will a train 140 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 3.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) 6 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 140 / 40 = 3.5 sec . answer : a"
Answer: a
Python program:
a = 144 * const_0_2778
b = 140 / a
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 157.20 , b ) 157.29 , c ) 157.50 , d ) 157.30 , e ) 157.23
Rationale: "( 3500 * 1.5 * 3 ) / 100 = > 157.50 answer : c"
Answer: c
Python program:
a = 3500 * 11
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: if a : b is 2 : 3 and b : c is 3 : 4 then a : c is equal to
Options: a ) 2 : 3 , b ) 6 : 7 , c ) 5 : 6 , d ) 1 : 2 , e ) 3 : 4
Rationale: "since a : b = 2 : 3 and b : c = 3 : 4 , we can deduce that a : b : c = 2 : 3 : 4 so , a : c = 2 : 4 = 1 : 2 . d is the correct answer ."
Answer: d
Python program:
a = 3 / 4
b = 2 / 3
c = a * b
Problem: carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 5 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 11 8 / 2 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 30 / 11 = 11 8 / 2 answer is c"
Answer: c
Python program:
a = 1 / 6
b = 1 / 5
c = a + b 
d = const_60 / c
e = 1 / 6
f = 1 / 5
g = e + f 
h = d * g
Problem: on a two - dimensional coordinate plane , the line z = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: apparently it ' s z = x ^ 2 - x ^ 3 instead of z = x ^ 2 - z ^ 3 . in this case : the x - intercept is the value ( s ) of x for z = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .
Answer: c
Python program:
a = max(3)
b = a - 1
Problem: find the value of 72514 x 9999 = m ?
Options: a ) 725067486 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 357889964
Rationale: "72514 x 9999 = 72514 x ( 10000 - 1 ) = 72514 x 10000 - 72514 x 1 = 725140000 - 72514 = 725067486 a"
Answer: a
Python program:
a = 9999 - 4
b = a * 72514
Problem: a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?
Options: a ) 120 , b ) 122 , c ) 124 , d ) 128 , e ) 126
Rationale: "length = 9 feet breadth = 37 − 92 = 14 feet area = 9 × 14 = 126 square feet answer is e ."
Answer: e
Python program:
a = 37 + 37 
b = a + 37 
c = b + 10 
d = c + 4
Problem: a man ' s speed with the current is 20 kmph and speed of the current is 1 kmph . the man ' s speed against the current will be
Options: a ) 11 kmph , b ) 12 kmph , c ) 18 kmph , d ) 17 kmph , e ) none of these
Rationale: explanation : speed with current is 20 , speed of the man + it is speed of the current speed in s ɵ ll water = 20 - 1 = 19 now speed against the current will be speed of the man - speed of the current = 19 - 1 = 18 kmph answer : c
Answer: c
Python program:
a = 20 - 1
b = a - 1
Problem: if | x - 12 | = 100 , what is the sum of all the possible values of x ?
Options: a ) - 12 , b ) - 22 , c ) 24 , d ) 36 , e ) 42
Rationale: "there will be two cases x - 12 = 100 or x - 12 = - 100 = > x = 112 or x = - 88 sum of both the values will be - 88 + 112 = 24 answer is c"
Answer: c
Python program:
a = 100 + 12 
b = 100 - 12
c = a - b
Problem: calculate the l . c . m of 4 / 9 , 5 / 7 , 9 / 13 , 7 / 15 is :
Options: a ) 1230 , b ) 1290 , c ) 1260 , d ) 1240 , e ) 2260
Rationale: "required l . c . m = l . c . m . of 4 , 5 , 9 , 7 / h . c . f . of 9 , 7 , 13 , 15 = 1260 / 1 = 1260 answer is c"
Answer: c
Python program:
a = 4 * 5
b = 9 * 7
c = a * b
Problem: kanul spent $ 3000 in buying raw materials , $ 2000 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 5555.555 , b ) $ 5543.22 , c ) $ 5568.000 , d ) $ 5366.521 , e ) $ 5365.66
Rationale: let the total amount be x then , ( 100 - 10 ) % of x = 3000 + 2000 90 % of x = 5000 90 x / 100 = 5000 x = $ 50000 / 9 x = $ 5555.555 answer is a
Answer: a
Python program:
a = 3000 + 2000 
b = 10 / 100
c = 1 - b
d = a / c
Problem: the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 5 | + 4 is equal to :
Options: a ) – 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14
Rationale: x ^ 2 - 8 x + 17 = | x - 5 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 12 = 0 x = 11,4 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 4 + 3 + 2 = 20 ans ( c )
Answer: c
Python program:
a = 4 * 5
Problem: 1.20 can be expressed in terms of percentage as
Options: a ) 120 % , b ) 0.120 % , c ) 1.20 % , d ) 0.209 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 1.20 * 100 = 120 answer : option a"
Answer: a
Python program:
a = 1 * 20
Problem: if the radius of a cylinder is doubled and height 5 times , what is the new volume of the cylinder divided by the old one ?
Options: a ) 8 . , b ) 2 . , c ) 6 . , d ) 20 . , e ) 10 .
Rationale: "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 2 r ) ^ 2 ( 5 h ) v ' = 20 v d ) 20"
Answer: d
Python program:
a = 1 * 2
b = 1 * 2
c = volume_cylinder / (
Problem: ( x ) + 4671 + 6514 - 7687 = 19190 . calculate the value of x
Options: a ) 15615 , b ) 15692 , c ) 15687 , d ) 15112 , e ) 15690
Rationale: "x + 4671 + 6514 - 7687 = 19190 = x + 4671 + 6514 = 19190 + 7687 = x + 11185 = 26877 = x = 26877 - 11185 = 15692 answer is b"
Answer: b
Python program:
a = 19190 + 7687 
b = a - 6514
c = b - 4671
d = const_60 / 2
e = c * d
Problem: in some quantity of ghee , 60 % is pure ghee and 40 % is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 18 , e ) 22
Rationale: let the original quantity be x then , vanaspati ghee in xkg = 40 x / 100 kg = 2 x / 5 kg ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 2 x / ( 5 x + 50 ) = 1 / 5 x = 10 answer is a
Answer: a
Python program:
a = 20 * 10
b = 40 - 20
c = a / b
Problem: a motorist travels for 6 hours , the first half at 60 kmph and the rest at 48 kmph . find the distance traveled by him .
Options: a ) 234 , b ) 124 , c ) 324 , d ) 452 , e ) 352
Rationale: distance = 3 * 60 + 3 * 48 = 180 + 144 = 324 km answer c .
Answer: c
Python program:
a = 6 / 2
b = 60 * a
c = 6 / 2
d = 48 * c
e = b + d
Problem: in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the error percent in the area calculated from these measurements .
Options: a ) 0.8 % , b ) 0.2 % , c ) 0.4 % , d ) 0.9 % , e ) 0.6 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 * x ) * ( 96 / 100 * y ) = 504 / 500 * xy . error in measurement = 504 / 500 * xy ) - xy = 4 / 500 * xy . error % = [ 4 / 500 * xy * 1 / xy * 100 ] % = 4 / 5 = 0.8 % . answer is a"
Answer: a
Python program:
a = 5 - 4
b = 5 * 4
c = b / 100
d = a - c
Problem: in a group of ducks and cows , the total number of legs are 24 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 24 more than twice the number of heads = > 2 ( d + 2 c ) = 24 + 2 ( c + d ) = > d + 2 c = 12 + c + d = > 2 c = 12 + c = > c = 12 i . e . , total number of cows = 12 answer is a ."
Answer: a
Python program:
a = 24 / 2
Problem: a can do a piece of work in 6 days . b can do it in 5 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8.7 days , b ) 2.0 days , c ) 6.6 days , d ) 7.5 days , e ) 4.4 days
Rationale: "c = 1 / 2 - 1 / 6 - 1 / 5 = 2 / 15 = > 7.5 days answer : d"
Answer: d
Python program:
a = 6 * 5
b = 6 * 5
c = 6 * 5
d = c / 6
e = 6 * 5
f = e / 5
g = d + f 
h = g * 2
i = b - h
j = i / 2
k = a / j
Problem: if 250 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 65 , b ) 66 , c ) 62 , d ) 69 , e ) 97
Rationale: "the question actually asks the highest power of 10 which divides 250 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 250 factorial will have 62 as - 250 / 5 = 50 50 / 5 = 10 10 / 5 = 2 so answer will be ( c ) 62"
Answer: c
Python program:
a = 4 + 1 
b = 250 / a
c = 4 + 1 
d = b / c
e = 4 + 1 
f = 250 / e
g = d + f