Cheukting/mathqa huggingface dataset:
Question (physics): one man can do a piece of work in 10 days . one boys join him & he complete the work in 6 days . if he gets 50 rs for his work then what will be the share of the boy .
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: 1 day work of man = 1 / 10 , if boy ' s 1 day work = 1 / x , then ( 1 / 10 ) + ( 1 / x ) = 1 / 6 , x = 15 ratio of work of man & boy = 1 / 10 : 1 / 15 = 3 : 2 so out of 50 rs . boy ' s share = 2 * 50 / ( 3 + 2 ) = 20 answer : b
Answer: b
Question (general): evaluate : 10111 - 10 * 2 * 5 = ?
Options: a ) 10101 , b ) 10110 , c ) 11100 , d ) 11001 , e ) 11011
Rationale: according to order of operations , 10 ? 2 ? 5 ( division and multiplication ) is done first from left to right 10 / 2 = 5 * 2 = 10 hence 10111 - 10 * 2 * 5 = 10111 - 10 = 10101 correct answer a
Answer: a
Question (gain): seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 35 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 35 % 0.4 x + ( m - x ) 0.25 = 0.35 m 0.15 x = 0.10 m x = 0.6666 m x = 66.66 % of m e"
Answer: e
Question (geometry): a rectangular garden is to be twice as long as it is wide . if 150 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 150 so , 2 ( l + b ) = 150 or , l + b = 75 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 80 l = 80 ; b = 40 l + b = 120 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( b )
Answer: b
Question (general): a jar of 364 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "364 = 26 * 14 = 28 * 13 there are 26 people in the group today . the answer is d ."
Answer: d
Question (general): 80 370 860 ? 2440 3530
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 1550
Rationale: "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : e"
Answer: e
Question (general): marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 15,000 and the marginal cost is $ 200 , and the total cost is $ 25,000 , what is the value of n ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 25,000 = $ 15,000 + n * $ 200 - - > n = 50 . answer : b ."
Answer: b
Question (gain): peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 6.67 % , d ) 6.25 % , e ) 8.33 %
Rationale: "now after a time of 3 years the principal p amounts to $ 300 and after a time of 8 years ( question says after another 5 years so 3 + 5 ) p becomes $ 400 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 300 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 8 r / 100 ) = 400 dividing a 2 by a 1 we get ( 1 + 8 r / 100 ) / ( 1 + 3 r / 100 ) = 4 / 3 after cross multiplication we are left with 12 r = 100 which gives r = 8.33 % answer : e"
Answer: e
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 900 in 5 years ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 78 , e ) 2
Rationale: "150 = ( 750 * 5 * r ) / 100 r = 4 % . answer : c"
Answer: c
Question (physics): the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 24 kmph ?
Options: a ) 21.21 , b ) 22.26 , c ) 90.9 , d ) 24.86 , e ) 25.25
Rationale: "distance covered in 1 min = ( 24 * 1000 ) / 60 = 400 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 400 / 4.4 = 90.90 answer : c"
Answer: c
Question (gain): a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 5000 * 6 * 2 ) / 100 ] - [ ( 5000 * 4 * 2 ) / 100 ] 600 - 400 = 200 gain in 1 year = ( 200 / 2 ) = 100 rs answer : a"
Answer: a
Question (gain): how many liters of water must be added to 18 liters of milk and water containing 10 % water to make it 70 % water ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "by rule of alligation : 70 % - 10 % = 60 % 100 % - 70 % = 30 % quantity of pure water : quantity of the mixture = 6 : 3 there are 18 liters of mixture , so we need to add 36 liters of pure water . the answer is c ."
Answer: c
Question (general): if 1 / 5 th of a number decreased by 5 is 5 , then the number is
Options: a ) 25 , b ) 50 , c ) 60 , d ) 75 , e ) none
Rationale: explanation : let the number be a , then a / 5 − 5 = 5 ⇒ a / 5 = 10 ⇒ a = 50 correct option : b
Answer: b
Question (physics): earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 240 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 240 envelopes they will take 240 / 60 mins . i . e . , 4 mins . answer : e"
Answer: e
Question (general): if ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 , then the difference between the two possible values of x is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 ( x + 3 ) ^ 2 = 3 ( 2 x + 15 ) x ^ 2 + 6 x + 9 = 6 x + 45 x ^ 2 - 36 = 0 ( x - 6 ) ( x + 6 ) = 0 x = 6 or x = - 6 the answer is c .
Answer: c
Question (gain): a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand b ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 55 %
Rationale: "yes there is a simple method : consider the following method brand a : 40 % millet and 60 % sunflower brand b : 65 % millet and 35 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 40 % millet , which is 10 % less than the weighted average of mix = - 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 65 % millet , which is 15 % more than the weighted average of mix = + 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand b i . e . b : ( a + b ) = 2 : 5 = ( 2 / 5 ) * 100 = 40 % here is a pictorial representation : brand a = 40 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 below average , a times - - - - - - - - - - - - - - - - - total below = - 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 65 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 above average , b times - - - - - - - - - - - - - - - - - total above = + 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore b / total = 2 : 5 = 40 % answer : a"
Answer: a
Question (geometry): what is the measure of the angle y made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"
Answer: c
Question (general): a placed 3 sheets with two carbons to get two extra copies of the original . then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half . then he typed . how many carbon copies did he get ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : since the number of carbons is 2 , only two copies can be obtained . answer : b
Answer: b
Question (physics): the sum of four consecutive even numbers is 84 . what would be the largest number ?
Options: a ) 33 , b ) 88 , c ) 24 , d ) 123 , e ) 12
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 84 = > x = 11 smallest number is : 2 ( x + 1 ) = 24 . answer : c"
Answer: c
Question (general): the average age of applicants for a new job is 30 , 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 = 30 - 8 = 22 maximum age = average + 1 standard deviation = 30 + 8 = 38 maximum number of different ages of the applicants = 38 - 22 + 1 = 17 answer c"
Answer: c
Question (physics): hcf and lcm two numbers are 16 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 176 , e ) 364
Rationale: "16 * 396 = 36 * x x = 176 answer : d"
Answer: d
Question (physics): a 10000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 60
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 5,000 by that net inflow to get the minutes ) - 60 min . answer e ."
Answer: e
Question (general): mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 3 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 16.25 % , b ) 8.25 % , c ) 4.25 % , d ) 6.25 % , e ) 7.25 %
Rationale: "25 / 4 = 6.25 answer : d"
Answer: d
Question (gain): in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 60 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 4 / 5 , b ) 5 / 7 , c ) 13 / 15 , d ) 37 / 45 , e ) 79 / 90
Rationale: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.4 * 1200 = 480 the number of males older than 70 years old is 900 - 480 = 420 the number of people who are either male or younger than 70 is 1800 + 420 = 2220 . p ( a person is younger than 70 or male ) = 2220 / 2700 = 37 / 45 the answer is d ."
Answer: d
Question (general): . 04 × ? = . 000016 .
Options: a ) 0.0004 , b ) 0.04 , c ) 4 , d ) 0.4 , e ) none of these
Rationale: "solution let . 04 × x = . 000016 . then , x = . 000016 / . 04 = . 0016 / 4 = . 0004 . answer a"
Answer: a
Question (general): the cost of 8 dozen pencil and 2 dozen note book is 520 rupee . if cost of 3 pencil and 4 note book is 60 rupee , then sum of the cost of 1 pencil and 1 note book will be ( in rupee )
Options: a ) rs 13.51 , b ) rs 15.51 , c ) rs 16.51 , d ) rs 14.51 , e ) rs 17.51
Rationale: let cost of pencil = rs x cost of notebook = rs y cost of 8 dozen pencils are 96 x cost of 2 dozen pencils are 24 y cost of 3 pencils are 3 x cost of 4 notebooks are 4 y equations are 96 x + 24 y = 520 - - - - - 1 3 x + 4 y = 60 - - - - - 2 multiplying 6 with equation ( 2 ) and then subtracting eqn ( 1 ) - eqn ( 2 ) , we get 96 x + 24 y = 520 18 x + 24 y = 360 after solving the equations , we get x = 2.05 y = 13.46 cost of 1 pencil and 1 notebook is 2.05 + 13.46 = rs 15.51 answer : b
Answer: b
Question (general): 8 years ago , p was half of q ' s age . if the ratio of their present ages is 3 : 4 what will be the total of their present ages ?
Options: a ) 33 , b ) 67 , c ) 28 , d ) 31 , e ) 35
Rationale: let present age of p and q be 3 x 3 x and 4 x 4 x respectively . eight years ago , p was half of q ' s age â ‡ ’ ( 3 x â ˆ ’ 8 ) = 1 / 2 ( 4 x â ˆ ’ 8 ) â ‡ ’ 6 x â ˆ ’ 16 = 4 x â ˆ ’ 8 â ‡ ’ 2 x = 8 â ‡ ’ x = 4 total of their present ages = 3 x + 4 x = 7 x = 7 ã — 4 = 28 c
Answer: c
Question (gain): selling an kite for rs . 30 , a shop keeper gains 15 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 3.5 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 20 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 115 * 30 = rs . 26.08 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.92 / 26.08 * 100 = 3.5 % . answer : a"
Answer: a
Question (gain): john makes $ 40 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 100 %
Rationale: increase = ( 40 / 40 ) * 100 = ( 1 ) * 100 = 100 % . e
Answer: e
Question (gain): a part of certain sum of money is invested at 16 % per annum and the rest at 20 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 4 : 3 , d ) 4 : 1 , e ) 5 : 4
Rationale: "20 : 16 = 5 : 4 answer : e"
Answer: e
Question (general): the average of 6 no . ' s is 4.60 . the average of 2 of them is 3.4 , while the average of the other 2 is 3.8 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 6.6 , c ) 3.6 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 4.6 * 6 ) - [ ( 3.4 * 2 ) + ( 3.8 * 2 ) ] = 27.60 - ( 6.8 + 7.6 ) = 27.60 - 14.40 = 13.20 . required average = ( 13.2 / 2 ) = 6.6 . answer : b"
Answer: b
Question (physics): at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 1.25 to bowl 2 games . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 19 , e ) 21
Rationale: "after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 1.25 = 9.84 ( 2 ) = 19.68 < 21 . ~ 19 games answer : d ."
Answer: d
Question (general): if the product of the integers from 1 to n is divisible by 378 , what is the least possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "378 = 2 x 3 x 3 x 3 x 7 n must include at least 3 , 2 * 3 , and 3 * 3 . the answer is c ."
Answer: c
Question (general): what is the value of ( 3 ) ^ - 4 ?
Options: a ) 1 / 4 , b ) 1 / 81 , c ) 1 / 65 , d ) 1 / 9 , e ) 1 / 3
Rationale: "3 ^ - 4 = 1 / ( 3 ) ^ 4 = 1 / 81 answer : b"
Answer: b
Question (general): what least number must be subtracted from 13294 so that the remainder is exactly divisible by 97 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "sol . on dividing 13924 by 97 , we get remainder = 5 . ∴ required number to be subtracted = 5 . answer b"
Answer: b
Question (gain): the price of an item is discounted 5 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 15 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 76.5 % , e ) 78 %
Rationale: "let initial price be 1000 price in day 1 after 5 % discount = 950 price in day 2 after 10 % discount = 855 price in day 3 after 15 % discount = 726.75 so , price in day 3 as percentage of the sale price on day 1 will be = 726.75 / 950 * 100 = > 76.5 % answer will definitely be ( d )"
Answer: d
Question (physics): amar takes as much time in running 18 meters as a car takes in covering 12 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 6200 m , b ) 2400 m , c ) 300 m , d ) 4300 m , e ) 1200 m
Rationale: "b 2400 m distance covered by amar = 18 / 1.2 ( 1.6 km ) = 3 / 8 ( 1600 ) = 2400 m answer is b"
Answer: b
Question (physics): with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity w of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Question (general): if n = 2 ^ 0.15 and n ^ b = 1 , b must equal
Options: a ) 3 / 80 , b ) 20 / 3 , c ) 4 , d ) 5 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 1 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 1 b = 20 / 3 answer : b"
Answer: b
Question (general): the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 300 km , b ) 320 km , c ) 360 km , d ) 390 km , e ) 400 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 4 h is 90 × 4 = 360 km ans . ( c )"
Answer: c
Question (general): find the sum of first 89 odd numbers
Options: a ) 7921 , b ) 4800 , c ) 7900 , d ) 4980 , e ) 4960
Rationale: "explanation : n 2 = 892 = 7921 answer : option a"
Answer: a
Question (gain): a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 5 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 960 , b ) 980 , c ) 900 , d ) 970 , e ) 1000
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 1 = > x = 1000 answer : e ) rs 1000"
Answer: e
Question (general): the difference between a number and its 3 - fourth is 100 . what is 25 % of that number ?
Options: a ) 120 , b ) 100 , c ) 125 , d ) 150 , e ) none of these
Rationale: explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b
Answer: b
Question (general): i chose a number and divide it by 4 . then i subtracted 175 from the result and got 10 . what was the number i chose ?
Options: a ) 200 , b ) 740 , c ) 780 , d ) 500 , e ) 100
Rationale: "let x be the number i chose , then x / 4 − 175 = 10 x / 4 = 185 x = 740 answer is b ."
Answer: b
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 15000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 13.8 , b ) 77 , c ) 18 , d ) 99 , e ) 88
Rationale: "total cp = rs . 42000 + rs . 15000 = rs . 57000 and sp = rs . 64900 profit ( % ) = ( 64900 - 57000 ) / 57000 * 100 = 13.8 % answer : a"
Answer: a
Question (general): how many 3 digit numbers n 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 n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b
Answer: b
Question (geometry): the length and breadth of a rectangle is increased by 3 % and 6 % respectively . what is the increase in the area ?
Options: a ) 9.18 , b ) 9.25 , c ) 9.5 , d ) 8.98 , e ) 8.88
Rationale: "100 * 100 = 10000 103 * 106 = 10918 - - - - - - - - - - - 918 10000 - - - - - - - 918 100 - - - - - - - - - - 9.18 ans a"
Answer: a
Question (gain): a sells a bicycle to b and makes a profit of 60 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 112.5
Rationale: "explanation : let cp be 100 a sells at 60 % profit so sp = 160 b sells at 25 % profit = 160 x ( 1 + 25 / 100 ) = 200 cp sp 100 - - - 200 x - - - 225 cp = 225 x 100 / 200 = 112.5 answer : e"
Answer: e
Question (gain): a shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 2 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 30 % , c ) 50 % , d ) 150 % , e ) 33 %
Rationale: "the total number of mangoes bought by the shopkeeper be 10 . if he buys 5 a rupee , his cp = 2 he selling at 2 a rupee , his sp = 5 profit = sp - cp = 5 - 2 = 3 profit percent = 3 / 2 * 100 = 150 % answer : d"
Answer: d
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm .
Options: a ) 335 cm 2 , b ) 885 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 266 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : e"
Answer: e
Question (general): if x is 50 percent greater than 88 , then x =
Options: a ) 68 , b ) 132 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.5 = 132 so the answer is b ."
Answer: b
Question (general): if x represents the product of the first 15 positive integers , then x is not a multiple of :
Options: a ) a ) 99 , b ) b ) 84 , c ) c ) 72 , d ) d ) 57 , e ) e ) 67
Rationale: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 72 = 9 * 11 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 19 is not there in first 15 positive numbers it is the only possibility d )
Answer: d