Cheukting/mathqa huggingface dataset:
Question (physics): a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 685 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 2 , d ) 17 , e ) 19
Rationale: "30 * 25 = 750 685 - - - - - - - - - - - 65 25 + 7.50 = 32.5 62 / 32.5 = 2 c"
Answer: c
Question (geometry): a box measuring 72 inches long by 48 inches wide by 24 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 54 , d ) 108 , e ) 162
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 8 is the biggest number that could divide all three , 72 , 48 and 24 . thus side of cube must be 8 , and total number of cubes = 72 / 8 * 48 / 8 * 24 / 8 = 162 ans e it is ."
Answer: e
Question (general): 80 370 860 1550 2440 ?
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 3530
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 (gain): if the cost price of 12 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 52 % loss
Rationale: "explanation : 12 cp = 25 sp cost price cp = 25 selling price sp = 12 formula = ( sp - cp ) / cp * 100 = ( 12 - 25 ) / 25 * 100 = 52 % loss answer : option e"
Answer: e
Question (gain): the cost of an article is decreased by 50 % . if the original cost is $ 200 , find the decrease cost .
Options: a ) 330 , b ) 200 , c ) 150 , d ) 100 , e ) 91
Rationale: original cost = $ 200 decrease in it = 50 % of $ 200 = 50 / 100 ã — 200 = 10000 / 100 = $ 100 therefore , decrease cost = $ 200 - $ 100 = $ 100 answer : d
Answer: d
Question (general): what is the 16 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0 , 7 thus 16 th digit is 0 . answer : a ."
Answer: a
Question (general): of the 3 - digit integers greater than 700 , how many have two digits t that are equal to each other and the remaining digit different from the other two ?
Options: a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: three - digit integers greater than 700 : 701 to 999 , inclusive . possible values for hundreds - digit - - > 7 , 89 possible values for tens - digit and ones - digit - - > 0 , 1 , 23 , 45 , 67 , 89 when hundreds - digit and tens - digit are the same : ( 3 x 1 x 10 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when hundreds - digit and ones - digit are the same : ( 3 x 10 x 1 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when tens - digit and hundreds - digit are the same : [ ( 3 x 10 x 1 ) - 3 ] - 1 = 26 - - - > we minus three to exclude 777 , 888 and 999 ; we minus one to exclude 700 t = 27 + 27 + 26 = 80 answer : c
Answer: c
Question (general): the ages of two person differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 5 ) = ( x + 20 - 5 ) = > 4 x = 40 = > x = 10 their present ages are 30 years and 10 year . answer : a"
Answer: a
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 10 % ?
Options: a ) 20 % , b ) 28 % , c ) 27 % , d ) 35 % , e ) 70 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 90 2 / 3 sp 1 = 90 sp 1 = 135 100 - - - 35 = > 35 % answer : d"
Answer: d
Question (general): out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many w applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) w = 20 - 15 = 5 answer : a"
Answer: a
Question (general): the average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 58 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 73 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 58 + 10 x 1.5 58 + 15 = 73 kg ans : ' b '"
Answer: b
Question (other): the price of a car and ac are in the ratio 3 : 2 . if the scooter costs $ 500 more than the ac . then the price of the ac ?
Options: a ) 1500 , b ) 200 , c ) 1700 , d ) 2000 , e ) 2500
Rationale: let the price of the car and ac is 3 x and 2 x 3 x - 2 x = 500 x = 500 price of ac = 3 * 500 = $ 1500 answer is a
Answer: a
Question (gain): a shopkeeper sold an article offering a discount of 4 % and earned a profit of 44 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 50
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 144 let marked price be rs . x . then , 96 / 100 x = 144 x = 14400 / 96 = rs . 150 now , s . p . = rs . 150 , c . p . = rs . 100 profit % = 50 % . answer : e"
Answer: e
Question (general): the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 70 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.45 for 3 lbs , how much did a pound of green tea cost in july ?
Options: a ) $ 4 , b ) $ 0.3 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: lets assume price of coffee in june = 100 x price of green tea in june = 100 x price of coffee in july = 200 x ( because of 100 % increase in price ) price of green tea in july = 30 x ( because of 70 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of green tea in july will be = 300 x + 45 x = 345 x as per question 345 x = 3.45 $ x = 0.01 s so the price of tea in july = 30 x = 30 x 0.01 = 0.3 $ / pound answer b
Answer: b
Question (general): the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weighs 53 kg is replaced by a new man . find the weight of the new man .
Options: a ) 69 , b ) 72 , c ) 75 , d ) 71 , e ) none of them
Rationale: "total weight increased = ( 1.8 x 10 ) kg = 18 kg . : . weight of the new man = ( 53 + 18 ) kg = 71 kg . answer is d"
Answer: d
Question (general): bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 49 more . what was his original selling price ?
Options: a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840
Rationale: let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 49 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 49 = > 0.07 x = 49 = > x = $ 700 original purchase price = $ 700 hence , original selling price ( at 10 % of profit ) = 1.1 ( 700 ) = $ 770 option a
Answer: a
Question (gain): on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 612 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: difference in c . i . and s . i for 2 years = $ 612 - $ 600 = $ 12 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 12 rate = ( 100 * 12 ) / ( 300 ) = 4 % the answer is b .
Answer: b
Question (general): 3 numbers which are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073 . the sum of the 3 numbers is :
Options: a ) 81 , b ) 82 , c ) 85 , d ) 90 , e ) 95
Rationale: since the numbers are co - prime , they contain only 1 as the common factor . also , the given two products have the middle number in common . so , middle number = h . c . f of 551 and 1073 = 29 ; first number = 551 / 29 = 19 third number = 1073 / 29 = 37 . required sum = 19 + 29 + 37 = 85 . answer : c
Answer: c
Question (physics): two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 17 km / hr , c ) 60 km / hr , d ) 77 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c"
Answer: c
Question (physics): i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 110 mph + 88 mph ) / 2 = 99 mph correct answer is : e"
Answer: e
Question (physics): a person is traveling at 65 km / hr and reached his destiny in 3 hr then find the distance ?
Options: a ) 205 km , b ) 195 km , c ) 295 km , d ) 115 km , e ) 215 km
Rationale: "t = 3 hrs d = t * s = 65 * 3 = 195 km answer is b"
Answer: b
Question (geometry): find the area of a parallelogram with base 12 cm and height 8 cm ?
Options: a ) 96 cm 2 , b ) 104 cm 2 , c ) 78 cm 2 , d ) 86 cm 2 , e ) 76 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 8 = 96 cm 2 answer : a"
Answer: a
Question (general): the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1260 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8235 , e ) 9255
Rationale: "you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1260 , we get the answer of 8235 . ( ans d )"
Answer: d
Question (gain): if the annual increase in the population of a town is 4 % and the present number of people is 15625 , what will the population be in 3 years ?
Options: a ) 15265 , b ) 16458 , c ) 25600 , d ) 17576 , e ) 14785
Rationale: "the required population is = 15625 ( 1 + 4 / 100 ) ^ 3 = 15625 * 26 / 25 * 26 / 25 * 26 / 25 = 17576 answer is d"
Answer: d
Question (general): n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 n is divided by 4 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 5
Rationale: "explanation : let n = 4 q + 3 . then 2 n = 8 q + 6 = 4 ( 2 q + 1 ) + 2 . thus , when 2 n is divided by 4 , the remainder is 2 . answer : b"
Answer: b
Question (general): a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 224
Rationale: "white : yellow = x : ( x + 70 ) = 8 : 13 - - > 13 x = 8 x + 560 - - > x = 112 . the total # of balls originally x + x = 112 + 112 = 224 . answer : e ."
Answer: e
Question (general): 80 x 100 + 80 x 11 = ?
Options: a ) 7500 , b ) 8880 , c ) 6200 , d ) 5200 , e ) none of them
Rationale: "= 80 x ( 100 + 11 ) ( by distributive law ) = 80 x 111 = 8880 answer is b"
Answer: b
Question (gain): find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 3.2 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 397.2
Rationale: "explanation : cost of each share = ( 20 + 3.2 % of 20 ) = rs . 20.64 therefore , number of shares = 8200 / 20.64 = 397.2 answer : e"
Answer: e
Question (gain): in a school of 850 boys , 44 % of muslims , 14 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 153 , d ) d ) 721 , e ) e ) 272
Rationale: "44 + 14 + 10 = 68 % 100 – 68 = 32 % 850 * 32 / 100 = 272 answer : e"
Answer: e
Question (geometry): the diagonals of a rhombus are 13 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 130 , c ) 150 , d ) 179 , e ) 172
Rationale: "1 / 2 * 13 * 20 = 130 answer : b"
Answer: b
Question (physics): a train 125 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 51 , d ) 79 , e ) 80
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 45 = > x = 51 km / hr . answer : option c"
Answer: c
Question (general): what could be the range of a set consisting of odd multiples of 11 ?
Options: a ) 21 , b ) 24 , c ) 44 , d ) 62 , e ) 70
Rationale: range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 11 * ( 2 n + 1 ) where n is any positive integer . range = 11 * ( 2 m + 1 ) - 11 * ( 2 n + 1 ) = 11 * 2 * ( m - n ) = 22 * ( m - n ) . m , n - any positive integers the answer must be divisible by 22 , which is only 44 . the correct answer is c
Answer: c
Question (physics): a train covers a distance of 18 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 , b ) 168 , c ) 120 , d ) 882 , e ) 180
Rationale: "speed = ( 18 / 10 * 60 ) km / hr = ( 108 * 5 / 18 ) m / sec = 30 m / sec . length of the train = 30 * 6 = 180 m . answer : e"
Answer: e
Question (gain): what quantity of water should be added to reduce 5 litres of 45 % acidic liquid to 25 % acidic liquid ?
Options: a ) 3 litres , b ) 2 litres , c ) 4 litres , d ) 4.5 litres , e ) 5 litres
Rationale: "quantity of acid in 5 litres = 45 * 5 / 100 = 2.25 litres let x litres of water is added to the solution , then there is 2.25 litres of acid in ( 5 + x ) litres of liquid . 25 % of ( 5 + x ) = 2.25 , 25 / 100 * ( 5 + x ) = 2.25 x = 225 - 125 / 25 = 4 answer : d"
Answer: d
Question (general): a certain company had a total annual expenditure of 2.55 ∗ 10 ^ 7 on employee salaries last year . if the company employed 425 people , what was the average employee salary ?
Options: a ) $ 60,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 2.55 ∗ 10 ^ 7 on employee salaries total employees = 425 observe that 425 * 6 = 2550 therefore try to bring the numerator in terms of 2550 average salary = ( 2550 * 10 ^ 4 ) / 425 = 6 * 10 ^ 4 = 60,000 option a"
Answer: a
Question (general): a no . when divided by 242 gives a remainder 100 , what remainder will be obtainedby dividingthe same no . 18 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "242 + 100 = 342 / 18 = 19 ( remainder ) e"
Answer: e
Question (gain): if each year the population of the country grows by 40 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 140 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 196 . . . . . . . . . . . . . 2 year elapsed year 2003 : population > 200 . . . . . . . . . . . . . . . . . . 3 year elapsed answer : a"
Answer: a
Question (physics): two pipes can fill a tank in 18 minutes and 20 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 21 - 1 / 45 = 1 / 12 so , the tank becomes full in 12 minutes . answer : e"
Answer: e
Question (gain): a certain sum is invested at simple interest at 14 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 14000 , d ) s . 17000 , e ) s . 42000
Rationale: "let the sum be rs . x . ( x * 14 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 28 x / 100 - 24 x / 100 = 840 = > 4 x / 100 = 840 = > x = 42000 . answer : e"
Answer: e
Question (probability): a box contains 23 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 37 , d ) 21 / 95 , e ) none
Rationale: solution p ( none is defective ) = 19 c 2 / 23 c 2 = 25 / 37 . p ( at least one is defective ) = ( 1 - 25 / 37 ) = 12 / 37 . answer c
Answer: c
Question (physics): aarti can do a piece of work in 5 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 3 days , e ) 15 days
Rationale: we have the important relation , more work , more time ( days ) a piece of work can be done in 5 days . three times of work of same type can be done in 5 x 3 = 15 days answer e
Answer: e
Question (geometry): a rectangular lawn 70 m × 30 m has two roads each 5 metres wide , running in the middle of it , one parallel to the length and the other parallel to the breadth . find the cost of gravelling the road at the rate of 4 per square metre .
Options: a ) 2,000
b ) 1,800
c ) 1,900
d ) 1,700
e ) none of these
Rationale: total area of road = area of road which parallel to length + area of road which parallel to breadth – overlapped road = 70 × 5 + 30 × 5 – 5 × 5 = 350 + 150 – 25 = 500 – 25 = 475 m 2 ∴ cost of gravelling the road = 475 × 4 = 1900 answer c
Answer: c
Question (general): in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 11 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 92 , c ) 95 , d ) 88 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 11 total people can seat = 81 + 11 = 92 answer : b"
Answer: b
Question (general): in a 300 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 79 , b ) 77 , c ) 85 , d ) 83 , e ) 61
Rationale: "solution simple out of 300 20 % are male i . e 60 and 25 % are female i . e 75 , so total homeowner is 135 . now min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option . so ans is 61 . answer : e"
Answer: e
Question (physics): two cars , one from austin to dallas and the other from dallas to austin , start simultaneously . after they meet , the cars reach their destinations after 4 hours and 9 hours respectively the ratio of their speeds is
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 3 : 6 , d ) 4 : 5 , e ) none
Rationale: solution let us name the cars as a and b . = ( car a ' s speed ) : ( car b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 4 : â ˆ š 9 = 2 : 3 answer a
Answer: a
Question (gain): chlorination is used in industry for the purification of water ; 1 gm solution of chlorine will remove half of the germs in 1 liter of water . if water containing less than 0.09 % of germs is considered clean , what is the minimum amount of chlorine required to purify 150 liter of water containing 0.3 liter of harmful substances ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assuming that it ' s supposed to state ` ` 0.3 ' ' liters of harmful substances , here ' s how you can answer this question . first , we have to figure out what . 09 % of 150 liters is . . . 1 % = . 01 . 1 % = . 001 . 09 % = . 0009 so , . 0009 ( 150 ) = . 135 liters we need enough doses of chlorine to get the 0.3 liters down to less than . 135 liters . each ` ` dose ' ' of chlorine will remove half of the harmful substances . . . start = 0.3 liters after 1 st dose = . 15 liters after 2 nd dose = . 075 liters we ' re now below the . 135 liters that we need to be less than . final answer : b
Answer: b
Question (physics): a train 175 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 49 , b ) 50 , c ) 12 , d ) 13 , e ) 68
Rationale: "speed of the train relative to man = ( 175 / 10 ) m / sec = ( 35 / 2 ) m / sec . [ ( 35 / 2 ) * ( 18 / 5 ) ] km / hr = 63 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 63 = = > x = 68 km / hr . answer : option e"
Answer: e
Question (gain): on a purchase of $ 127 , a store offered a payment plan consisting of a $ 27 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 18.3 % , b ) 15.3 % , c ) 21.3 % , d ) 22.3 % , e ) 25.3 %
Rationale: "12 * 10 + 27 = 147 ( 27 / 127 ) * 100 = 21.3 answer : c"
Answer: c
Question (geometry): in how many r ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: r = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e