euclaise/mathqa_programs huggingface dataset:
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 9 / 5 , d ) 9 / 8 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 4 lets say x machines are used to attain the desired rate , thus x / 36 + x / 4 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 9 x ) / 36 = 1 / 2 10 x / 36 = 1 / 2 x = 9 / 5 . qa = 9 / 5 ( answer c )"
Answer: c
Python program:
a = 1 / 36
b = 1 / 4
c = a + b 
d = 2 * 0
e = 1 / d
Problem: mike earns $ 15 per hour and phil earns $ 10 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 33.3 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 15 is 10 let it be x % less , then = 15 ( 1 - x / 100 ) = 10 1 - x / 100 = 10 / 15 x = 100 / 3 x = 33.3 % ans a"
Answer: a
Python program:
a = 10 / 15
b = a * 100
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 79 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 93 , d ) 82 , e ) 91
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 79 ( subtracting twice of incorrect from correct ) 3 x = 279 x = 93 answer : c"
Answer: c
Python program:
a = 100 - 79
b = a / 3
c = 100 - b
Problem: the edges of three metal cubes are 2 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 4.0 , b ) 4.2 , c ) 4.4 , d ) 4.6 , e ) 4.8
Rationale: "the total volume is 2 ^ 3 + 3 ^ 3 + 4 ^ 3 = 99 the edge of the new cube is the cube root of 99 which is about 4.6 cm . the answer is d ."
Answer: d
Python program:
a = 4 ** 3
b = 3 ** 3
c = 2 + b 
d = a + c 
e = d ** const_0_33
Problem: rahim bought 50 books for rs . 1000 from one shop and 40 books for rs . 800 from another . what is the average price he paid per book ?
Options: a ) 28 , b ) 20 , c ) 27 , d ) 29 , e ) 21
Rationale: "average price per book = ( 1000 + 800 ) / ( 50 + 40 ) = 1800 / 90 = rs . 20 answer : b"
Answer: b
Python program:
a = 1000 + 800 
b = 50 + 40 
c = a / b
Problem: in a hostel there were 100 students . to accommodate 40 more students the average is decreased by rupees 10 . but total expenditure decreased by rs . 400 . find the total expenditure of the hostel now ?
Options: a ) 1400 , b ) 2500 , c ) 3000 , d ) 1500 , e ) 2100
Rationale: "100 x - 400 = 140 ( x – 10 ) x = 25 100 * 25 - 400 = 2100 answer : e"
Answer: e
Python program:
a = 100 + 40 
b = a * 10
c = b + 400 
d = c / 40
e = d - 10
f = 100 + 40 
g = e * f
Problem: a store ’ s selling price of $ 2500 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 50 percent of the computer ’ s cost ?
Options: a ) $ 2678 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: 1.4 x = 2500 x = 2500 / 1.4 so , 1.5 x = 2500 * 1.5 / 1.4 = 2478 answer : - a
Answer: a
Python program:
a = 100 + 50 
b = 100 + 40 
c = a / b
d = 2500 * c
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 10 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 910 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? d"
Answer: d
Python program:
a = 1000 / 10
b = 1000 / 35
c = a + b 
d = 10 * 35
e = 1000 / d
f = c - e
g = 1000 - f
Problem: the average age of applicants for a new job is 31 , with a standard deviation of 9 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 19
Rationale: "within one standard deviation of the average age means 31 + / - 7 24 - - 31 - - 38 number of dif . ages - 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 total = 19 e"
Answer: e
Python program:
a = 9 * 2
b = a + 1
Problem: a man walks at a rate of 10 mph . after every ten miles , he rests for 8 minutes . how much time does he take to walk 50 miles ?
Options: a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 332
Rationale: "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 8 = 32 minutes . total time = 300 + 32 = 332 minutes . answer : e ."
Answer: e
Python program:
a = 8 * 4
b = 50 / 10
c = b * const_60
d = a + c
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 6 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 20 km , c ) 65 km , d ) 18 km , e ) 36 km
Rationale: distance = relative speed * time = ( 6 + 3 ) * 4 = 36 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : e
Answer: e
Python program:
a = 6 + 3 
b = a * 4
Problem: the price of a book is increased from $ 300 to $ 360 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: "explanation : change in the price = rs 360 – rs 300 = rs 60 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 60 300 ) * 100 = 20 % b"
Answer: b
Python program:
a = 360 - 300
b = a / 300
c = b * 100
Problem: the simple interest on rs . 26 for 6 months at the rate of 7 paise per rupeeper month is
Options: a ) 1.2 , b ) 10.92 , c ) 12.98 , d ) 12.38 , e ) none
Rationale: "sol . s . i . = rs . [ 26 * 7 / 100 * 6 ] = rs . 10.92 answer b"
Answer: b
Python program:
a = 26 * 6
b = a * 7
c = b / 100
Problem: ms . mary sold two properties , x and y , for $ 25000 each . she sold property x for 20 % more than she paid for it and sold property y for 20 % less than she paid for it . if expenses are disregarded , what was her total net gain or loss , if any , on the two properties ?
Options: a ) $ 2100 , b ) $ 2222 , c ) $ 2320 , d ) $ 2083.33 , e ) $ 2183.33
Rationale: there is a property to solve such questions withcommon selling priceandcommon % gain and loss . such cases always result in a loss and . . . total % loss = ( common gain % or loss % / 10 ) ^ 2 hence here loss % = ( 20 / 10 ) ^ 2 = 4 % which means he recovered only 96 % of his investment which amount to a total revenue = 25000 + 25000 = 50000 i . e . 96 % of cost = 40000 therefore , 4 % of cost ( loss ) = $ 2083.33 answer : d
Answer: d
Python program:
a = 20 / 100
b = a * 25000
c = b - 1000
d = c / 2
e = 100 - 20
f = e + 3 
g = f + const_0_33 
h = d + g
Problem: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 3 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 3 m = 20 books total = 30 books m ' = 30 = 1 / 2 * 60 ratio : 1 / 2 ans : a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 2
c = a * b
d = 1 - c
Problem: an engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose . after 50 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 22 , b ) 30 , c ) 15 , d ) 18 , e ) 20
Rationale: "30 workers working already let x be the total men required to finish the task in next 100 days 2 km done hence remaining is 8 km also , work has to be completed in next 100 days ( 150 - 50 = 100 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 50 ) / ( 2 * 100 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : b"
Answer: b
Python program:
a = 10 - 2
b = 30 * a
c = b * 50
d = 150 - 50
e = 2 * d
f = c / e
g = f - 30
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 280 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 7 , c ) 9 , d ) 7.5 , e ) 6
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 280 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 it takes a total of nine hours to cover the 280 mile distance . answer : b"
Answer: b
Python program:
a = 10 + 20 
b = 30 + a 
c = 280 / b
Problem: the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 8 years will be
Options: a ) 4 : 3 , b ) 12 : 11 , c ) 7 : 4 , d ) 6 : 5 , e ) 6 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 8 ) : ( 12 + 8 ) = 24 : 20 = 6 : 5 answer : d"
Answer: d
Python program:
a = 4 + 3 
b = 28 / a
c = 4 * b
d = c + 8 
e = 4 + 3 
f = 28 / e
g = 3 * f
h = g + 8 
i = d / h
Problem: a certain junior class has 1000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 1 / 1000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 60 / 1000 first then we can only pick 1 other pair from the 800 so total will be 60 / 600 * 1000 simplify and you get 1 / 10000 answer is b"
Answer: b
Python program:
a = 1 / 3
Problem: what is the difference between the place values of two 1 ' s in the numeral 135.21
Options: a ) 99.999 , b ) 100.2 , c ) 134 , d ) 99.99 , e ) 99.9
Rationale: required difference = 100 - 0.01 = 99.99 answer is d
Answer: d
Python program:
a = 1 * 100
b = 1 / 100
c = a - b
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 36 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 12 : 2 = > for 12 soap , salt = 2 = > for 2 soap , salt = ( 2 / 12 ) * 2 = 1 / 3 so , water : soap : salt = 3 : 2 : 1 / 3 = 36 : 24 : 4 after open container , water : soap : salt = 18 : 24 : 4 so , water : salt = 18 : 4 = 36 : 8 e"
Answer: e
Python program:
a = 2 * 3
b = a * 3
c = 2 * 2
d = c * 2
e = b / d
Problem: if x + ( 1 / x ) = 5 , what is the value of e = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) e = 21 , b ) e = 22 , c ) e = 23 , d ) 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Python program:
a = 5 ** 2
b = a - 2
Problem: find the smallest number of five digits exactly divisible by 16 , 24,36 and 54 .
Options: a ) 10368 , b ) 10638 , c ) 10836 , d ) 10846 , e ) none of them
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 16,24 , 36,54 i . e 432 , on dividing 10000 by 432 , we get 64 as remainder . therefore , required number = 10000 + ( 432 – 64 ) = 10368 . answer is a ."
Answer: a
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 24
Problem: 8 is 4 % of a , and 4 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 32 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 5
Rationale: "explanation : given , = > 4 a / 100 = 8 . = > a = 8 × ( 100 / 4 ) = 200 . - - - - - - - - - ( i ) and , = > ( 8 / 100 ) × b = 4 . = > b = 50 . - - - - - - - - - ( ii ) now , c = b / a ( from ( i ) and ( ii ) ) = > 50 / 200 . = > 1 / 4 . answer : b"
Answer: b
Python program:
a = 4 / 8
b = a * 100
c = 8 / 4
d = c * 100
e = b / d
Problem: the volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 2 : 5
b ) 2 : 9
c ) 2 : 2
d ) 2 : 9
e ) 2 : 1
Rationale: the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 10 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 2 / 5 i . e . h 1 : h 2 = 2 : 5 answer : a
Answer: a
Python program:
a = 1 / 10
b = 1 / 2
c = b ** 2
d = a / c
Problem: the average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added . if average weight of the whole group after including the additional 30 members is 40 kg , what is the average weight of the additional friends ?
Options: a ) 50 kg , b ) 60 kg , c ) 61 kg , d ) 62 kg , e ) 91 kg
Rationale: let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a
Answer: a
Python program:
a = 30 + 30 
b = a * 40
c = 40 - 10
d = 30 * c
e = b - d
f = e / 30
Problem: sum of two numbers is 50 . two times of the difference of first and seceond is 20 . then the numbers will be ?
Options: a ) 10 , 40 , b ) 20 , 30 , c ) 35 , 15 , d ) 30 , 20 , e ) 15 , 35
Rationale: explanation : x + y = 50 2 x ã ¢ â ‚ ¬ â € œ 2 y = 20 x = 30 y = 20 answer : d
Answer: d
Python program:
a = 20 / 2
b = 50 - a
c = b / 2
d = 50 - c
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 25 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 67.5 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 25 % , price = 81 - 20.25 = 60.75 which is 60.75 / 90 * 100 of the sale price on day 1 = ~ 67.5 % answer b"
Answer: b
Python program:
a = 25 / 100
b = 1 / 10
c = 1 - b
d = a / c
e = d * 100
f = e + 2
Problem: if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 220 - 320 = = = > a + b - b - c = - 100 = = = > a - c = - 100 answer : b"
Answer: b
Python program:
a = const_60 * 0
b = 110 * 2
c = a - b
Problem: if a and b are the roots of the equation x 2 - 7 x + 7 = 0 , then the value of a 2 + b 2 is :
Options: a ) 35 , b ) 24 , c ) 17 , d ) 6 , e ) 5
Rationale: sol . ( b ) the sum of roots = a + b = 7 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 49 - 14 = 35 answer a
Answer: a
Python program:
a = 7 ** 2
b = 4 * 7
c = a - b
d = math.sqrt(c)
e = 7 - d
f = e / 2
g = f ** 2
h = 7 ** 2
i = 4 * 7
j = h - i
k = math.sqrt(j)
l = 7 + k 
m = l / 2
n = m ** 2
o = g + n
Problem: each machine of type a has 4 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 1 chrome parts . if a certain group of type a and type b machines has a total of 30 steel parts and 33 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 16 , e ) 19
Rationale: "look at the below representation of the problem : steel chrome total a 4 2 30 > > no . of type a machines = 30 / 6 = 5 b 2 1 33 > > no . of type b machines = 33 / 3 = 11 so the answer is 16 i . e d . hope its clear ."
Answer: d
Python program:
a = 1 + 2 
b = 33 / a
c = 4 + 2 
d = 30 / c
e = b + d
Problem: there are 750 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 750 - x x / 2 + 750 - x / 4 = 1 / 3 * ( 750 ) = 250 x = 250 x / 2 = 125 is supposed to be the answer answer : c"
Answer: c
Python program:
a = 750 / 3
b = a * 4
c = b - 750
d = c / 2
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 16 !
Options: a ) 8 , b ) 10 , c ) 6 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 - - - - count 3 ' s = 6 so answer is 6"
Answer: c
Python program:
a = 16 / 3
b = math.floor(a)
c = 3 ** 2
d = 16 / c
e = math.floor(d)
f = b + e
Problem: if 25 % of x is 5 less than 10 % of 500 , then x is ?
Options: a ) 188 , b ) 180 , c ) 156 , d ) 840 , e ) 121
Rationale: "25 % of x = x / 4 ; 10 % of 500 = 10 / 100 * 500 = 50 given that , x / 4 = 50 - 5 = > x / 4 = 45 = > x = 180 . answer : b"
Answer: b
Python program:
a = 10 / 100
b = 500 * a
c = b - 5
d = 25 / 100
e = c / d
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 675 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 45 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 675 / 7 + 8 = 45 sec answer is c"
Answer: c
Python program:
a = 8 + 7 
b = 675 / a
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 16 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 10 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 16 x < = 3 x > = - 5 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 5 × - 6 = 30 minimum possible value of xy is - 5 × 8 = - 40 - 40 + 30 = - 10 answer : b"
Answer: b
Python program:
a = math.sqrt(16)
b = math.sqrt(64)
c = a + b
Problem: what is the least possible value of expression e = ( x - 1 ) ( x - 3 ) ( x - 4 ) ( x - 6 ) + 10 for real values of x ?
Options: a ) 1 , b ) 10 , c ) 9 , d ) 0 , e ) 8
Rationale: explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a
Answer: a
Python program:
a = 10 + 1 
b = 6 + 4 
c = a - b
Problem: a and b can finish a work in 12 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 30 days , c ) 98 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 12 – 1 / 20 = 2 / 60 = 1 / 30 = > 30 days answer : b"
Answer: b
Python program:
a = 1/(12)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 32 sec
Rationale: speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e
Answer: e
Python program:
a = 200 + 120 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a certain tax rate is $ 82 per $ 100.00 . what is the rate , expressed as a percent ?
Options: a ) 82 % , b ) 8.2 % , c ) 0.82 % , d ) 0.082 % , e ) 0.0082 %
Rationale: "here in question it is asking $ . 82 is what percent of $ 100 . suppose $ . 82 is x % of 100 means 100 * ( x / 100 ) = 82 hence x = 82 % so answer is a"
Answer: a
Python program:
a = 82 / 100
b = a * 100
Problem: how many integers from 101 to 600 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 5 = 5 6 is not possible here because it would result in a number greater than 6 ( i . e 606 , 616 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 5 * 10 = 50 answer is a ."
Answer: a
Python program:
a = 100 / 0
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 30 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 19 , d ) 20 , e ) 28
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 30 , it is 14 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 30 is already 14 more than 16 and hence we only have 29 - 14 = 15 extra to distribute between r and s . since s must be greater than r , r can be 16 + 12 = 28 and s can be 16 + 13 = 29 . so r is 28 . answer ( e )"
Answer: e
Python program:
a = 16 * 5
b = a - 30
c = b / 2
d = c - 2