Cheukting/mathqa huggingface dataset:
Question (general): a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 998 in total compensation , how many total hours did he work that week ?
Options: a ) 54 , b ) 51 , c ) 58 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 998 - 560 = 438 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 438 / 24.5 = 17.8 = 18 approx . total hrs = 40 + 18 = 58 answer c"
Answer: c
Question (general): when n is divided by 24 , the remainder is 6 . what is the remainder when 3 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2
Rationale: "let n = 6 ( leaves a remainder of 6 when divided by 24 ) 3 n = 3 ( 6 ) = 18 , which leaves a remainder of 2 when divided by 8 . answer e"
Answer: e
Question (general): a certain debt will be paid in 40 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 442.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475
Rationale: "total number of installments = 40 payment per installment for the first 20 installments = 410 payment per installment for the remaining 20 installments = 410 + 65 = 475 average = ( 20 * 410 + 20 * 475 ) / 40 = 442.50 answer a"
Answer: a
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 20 % profit on the first article and 20 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 177 , c ) 188 , d ) 166 , e ) 129
Rationale: "profit on first article = 20 % of 1000 = 200 . answer : a"
Answer: a
Question (physics): 20 men do a work in 20 days . how many men are needed to finish the work in 4 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 100 , e ) 15
Rationale: "men required to finish the work in 4 days = 20 * 20 / 4 = 100 answer is d"
Answer: d
Question (gain): the cost of 20 articles is equal to selling price of 10 . find the gain or loss percent ?
Options: a ) 50 % , b ) 100 % , c ) 25 % , d ) 15 % , e ) 60 %
Rationale: c . p . of each article be $ 1 c . p . of 10 articles = 10 gain % = 10 / 10 * 100 = 100 % answer is b
Answer: b
Question (general): a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 6500 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 16000 , c ) 15000 , d ) 190000 , e ) 13000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 6500 - > x = 13000 answer : e"
Answer: e
Question (physics): johnny makes $ 7.35 per hour at his work . if he works 6 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 48.32 , d ) $ 44.10 , e ) $ 9.60
Rationale: 4.75 * 6 = 28.50 . answer is c .
Answer: c
Question (gain): find the 25 % of rs . 200 .
Options: a ) rs . 50 , b ) rs . 70 , c ) rs . 100 , d ) rs . 80 , e ) rs . 60
Rationale: explanation : 25 % of 200 = > 25 / 100 * 200 = rs . 50 answer : a
Answer: a
Question (general): what is the least common multiple of 15 , 16 , and 24 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 16 = 2 ^ 4 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 240 option c"
Answer: c
Question (general): how many integers from 101 to 800 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "first digit possibilities - 1 through 7 = 7 8 is not possible here because it would result in a number greater than 8 ( i . e 808 , 818 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 7 * 10 = 70 answer is c ."
Answer: c
Question (gain): a bowl of fruit contains 14 apples and 25 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 19
Rationale: "number of apples = 14 number of oranges = 25 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 25 - x ) = 39 - x 14 / ( 39 - x ) = 7 / 10 = > 20 = 39 - x = > x = 19 answer e"
Answer: e
Question (general): on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent r of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before r = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b
Answer: b
Question (general): 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 140 kg then find the average weight of all the 7 rounds ?
Options: a ) 98.5 kgs , b ) 80 kgs , c ) 76.5 kgs , d ) 67.5 kgs , e ) 58.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 140 / 7 = 80 kgs answer : b"
Answer: b
Question (geometry): the ratio of the volumes of two cubes is 8 : 27 what is the ratio of their total surface areas ?
Options: a ) 2 : 4 , b ) 3 : 6 , c ) 4 : 12 , d ) 4 : 9 , e ) 1 : 3
Rationale: "ratio of the sides = â ³ â ˆ š 8 : â ³ â ˆ š 27 = 2 : 3 ratio of surface areas = 4 : 9 answer : d"
Answer: d
Question (physics): what is the greatest of 3 consecutive integers whose sum is 21 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 21 ; = > 3 n = 18 ; = > n = 6 the greatest of the three numbers is therefore 6 + 2 = 8 answer : c"
Answer: c
Question (geometry): the measure of the side of a square is multiplied by 6 . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x , b ) 4 x , c ) 6 x , d ) 12 x , e ) 27 x
Rationale: "original perimeter = x hence original side = x / 4 new side = 6 x / 4 new perimeter = 4 * 6 x / 4 = 6 x correct option : c"
Answer: c
Question (other): x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 24000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 2
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 24000 × 9 = 45 × 12 : 24 × 9 = 15 × 12 : 8 × 9 = 5 : 2 answer is e ."
Answer: e
Question (gain): if a and b get profits of rs . 4,000 and rs . 2,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 1
Rationale: "ratio = 4000 / 2000 = 2 : 1 answer : e"
Answer: e
Question (general): a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 45 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,360 , e ) $ 29,160
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.45 * 12000 = 12000 - 5400 x = 6600 earning becomes 9360 + 3 x = 9360 + 3 * 6600 = 29160 ans : e"
Answer: e
Question (physics): speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 48 hours , b ) 51 hours , c ) 36 hours , d ) 56 hours , e ) none
Rationale: "sol . speed upstream = 6 kmph ; speed downstream = 10 kmph . ∴ total time taken = [ 210 / 6 + 210 / 10 ] hours = 56 hours . answer d"
Answer: d
Question (gain): find the annual income derived by investing $ 6800 in 20 % stock at 136 .
Options: a ) 550 , b ) 1000 , c ) 2500 , d ) 300 , e ) 4000
Rationale: "by investing $ 136 , income obtained = $ 20 . by investing $ 6800 , income obtained = $ [ ( 20 / 136 ) * 6800 ] = $ 1000 . answer b ."
Answer: b
Question (general): if x = - 12 / 5 and y = - 6 / 7 , what is the value of the expression - 2 x – y ^ 2 ?
Options: a ) 741 / 357 , b ) 456 / 789 , c ) 636 / 735 , d ) 564 / 263 , e ) - 636 / 735
Rationale: "x = - 12 / 15 and y = - 6 / 7 = = > - 2 ( - 12 / 15 ) - ( - 6 / 7 ) ^ 2 = 24 / 15 - 36 / 49 = 636 / 735 ans : c"
Answer: c
Question (gain): a man can row his boat with the stream at 16 km / h and against the stream in 6 km / h . the man ' s rate is ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 16 us = 6 s = ? s = ( 16 - 6 ) / 2 = 5 kmph answer : a"
Answer: a
Question (gain): if the compound interest on a certain sum of money for 4 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 1200 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 4 yrs = ( 3000 x 10 x 4 ) / 100 = 1200 / - answer : c ."
Answer: c
Question (general): when n is divided by 27 , the remainder is 4 . what is the remainder when n + 16 is divided by 7 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 23 remainder ( n / 27 ) = 4 n + 16 = 39 remainder ( 39 / 7 ) = 4 option c"
Answer: c
Question (gain): jar a has 16 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 13 %
Rationale: an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 116 marbles . now , for both jars to have equal marbles we should move 8 marbles from a to b , which is 8 / 116 = ~ 7 % of a . answer : b .
Answer: b
Question (gain): a and b started a business investing rs . 21,000 and rs . 28,000 respectively . out of a total profit of rs . 14,000 , b ’ s share is :
Options: a ) 7600 , b ) 7700 , c ) 7800 , d ) 7900 , e ) 8000
Rationale: "ratio of their shares = 21000 : 28000 = 3 : 4 . b ’ s share = rs . 14000 * 4 / 7 = rs . 8000 answer : e"
Answer: e
Question (gain): a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 5 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.05 p x = 1.05 / 1.75 = 0.6 which is a discount of 40 % . the answer is d ."
Answer: d
Question (physics): find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 17 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1683 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 17 = 1683 answer : d"
Answer: d
Question (general): 1370 , 1320 , 1070 , x , - 6430
Options: a ) - 180 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ."
Answer: a
Question (general): if ( 27 / 4 ) x - 18 = 3 x + 27 what is the value of x ?
Options: a ) 12 , b ) - 12 , c ) 1 / 12 , d ) - 1 / 12 , e ) 3
Rationale: ( 27 / 4 ) x - 18 = 3 x + 27 = > 27 x - 72 = 12 x + 108 = > 15 x = 180 = > x = 12 answer : a
Answer: a
Question (general): if the average marks of 3 classes of 55 , 60 and 45 students respectively is 50 , 55 , 60 , then find the average marksof all the students is
Options: a ) 53 , b ) 53.5 , c ) 54.68 , d ) 55.6 , e ) 67.2
Rationale: required average = 55 x 50 + 60 x 55 + 45 x 60 55 + 60 + 45 = 2750 + 3300 + 2700 160 = 8750 160 = 54.68 c
Answer: c
Question (general): the batting average of a particular batsman is 63 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 248
Rationale: explanation : total runs scored by the batsman = 63 * 46 = 2898 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2898 – 2552 = 346 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 346 2 x = 496 x = 248 runs answer e
Answer: e
Question (geometry): a lady builds 10 cm length , 13 cm width , and 5 cm height box using 5 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 108 , c ) 130 , d ) 150 , e ) 145
Rationale: "number of cubes required = volume of box / volume of cube = 10 * 13 * 5 / 5 = 130 cubes answer : c"
Answer: c
Question (physics): a train 275 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 8 , b ) 6 , c ) 5 , d ) 15 , e ) 1
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 275 * 3 / 55 = 15 sec . answer : d"
Answer: d
Question (general): when 2 + 3 = 65 , 3 + 4 = 125 , 4 + 5 = 205 , then 5 + 6 = ?
Options: a ) 285 , b ) 305 , c ) 315 , d ) 350 , e ) 245
Rationale: "2 + 3 = > 2 ã — 3 = 6 = > 6 ã — 10 + 5 = 65 3 + 4 = > 3 ã — 4 = 12 = > 12 ã — 10 + 5 = 125 4 + 5 = > 4 ã — 5 = 20 = > 20 ã — 10 + 5 = 205 then 5 + 6 = > 5 ã — 6 = 30 = > 30 ã — 10 + 5 = 305 answer : b"
Answer: b
Question (general): a certain experimental mathematics program was tried out in 2 classes in each of 22 elementary schools and involved 31 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 6 , e ) 2 and 8
Rationale: "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 22 * 2 = 44 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 44 - 31 = 13 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 13 / 2 = 6.5 . so the greatest possible value of the # of teachers who had 3 classes is 6 . only answer d has this option ."
Answer: d
Question (physics): a is twice as good a work man as b and together they finish a piece of work in 24 days . the number of days taken by a alone to finish the work is :
Options: a ) 28 days . , b ) 16 days . , c ) 12 days . , d ) 24 days . , e ) 36 days .
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 24 divide 1 / 14 in the ratio 2 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 24 x 2 / 3 ) = 1 / 36 hence , a alone can finish the work in 36 days . answer e"
Answer: e
Question (gain): what will be the difference between simple and compound interest at 12 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 94.19 , b ) 94.12 , c ) 93.5 , d ) 64.1 , e ) 64.11
Rationale: "s . i . = ( 1000 * 12 * 4 ) / 100 = rs . 480 c . i . = [ 1000 * ( 1 + 12 / 100 ) 4 - 1000 ] = rs . 573.5 difference = ( 573.5 - 480 ) = rs . 93.5 answer : c"
Answer: c
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 290 m long ?
Options: a ) 40 sec , b ) 52 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 290 = 650 m required time = 650 * 2 / 25 = 52 sec answer : b"
Answer: b
Question (general): q ' = 3 q - 3 , what is the value of ( 7 ' ) ' ?
Options: a ) 6 , b ) 106 , c ) 206 , d ) 306 , e ) 406
Rationale: "( 7 ' ) ' = ( 3 * 7 - 3 ) ' = 18 ' = 18 * 18 - 18 = 306 answer d"
Answer: d
Question (other): find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.50 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 2 : 1 , d ) 8 : 9 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 80 : 90 = 8 : 9 answer : d"
Answer: d
Question (general): a grocer has a sale of rs . 5400 , rs . 9000 , rs . 6300 , rs . 7200 and rs . 4500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?
Options: a ) s . 1200 , b ) s . 5400 , c ) s . 5400 , d ) s . 4999 , e ) s . 5000
Rationale: "total sale for 5 months = rs . ( 5400 + 9000 + 6300 + 7200 + 4500 ) = rs . 32400 . required sale = rs . [ ( 5600 x 6 ) - 32400 ] = rs . ( 33600 - 32400 ) = rs . 1200 . option a"
Answer: a
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 $ 12000 and the marginal cost is $ 200 , and the total cost is $ 16000 , what is the value of n ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a .
Answer: a
Question (general): $ 392 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 212 , b ) $ 216 , c ) $ 220 , d ) $ 224 , e ) $ 228
Rationale: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 392 x = 56 4 x = 224 the answer is d ."
Answer: d
Question (physics): the cyclist walking at a constant rate of 15 miles per hour is passed by a car traveling in the same direction along the same path at 60 miles per hour . the car stops to wait for the cyclist for 6 minutes after passing her , while the cyclist continues to go at her constant rate , how many minutes must the car wait until the cyclist catches up ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 15 , e ) 18
Rationale: for the 6 minutes the car continues to overtake the cyclist , she is going at 45 miles per hour faster than the cyclist . once the car stops , the cyclist is going at 15 miles per hour while the car is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 45 / 15 * 6 or 18 minutes answer is ( e )
Answer: e
Question (general): the value for d = ( 0.889 × 55 ) / 9.97 to the nearest tenth is
Options: a ) 0.5 , b ) 4.63 , c ) 4.9 , d ) 7.7 , e ) 49.1
Rationale: if we read the q , we can easily home on to the answer , , the numerator is clearly between 40 and 50 . . denomiator is close to 10 . . so d = ( 0.889 × 55 ) / 9.97 is between 4 and 5 . . it may tempt us to solve it since ther are two values between 4 and 5 . . but the catch is innearest tenth 4.63 can be called nearest to hundreth and no tenth , so can be eliminated . . 4.9 is our answer . . . c
Answer: c
Question (general): find the least number which when divided by 37 and 7 leaves a remainder of 2 in each case .
Options: a ) 259 , b ) 261 , c ) 263 , d ) 265 , e ) 267
Rationale: the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 37 , 7 ) + 2 = 261 . answer : b
Answer: b
Question (physics): a cubical tank is filled with water to a level of 1 foot . if the water in the tank occupies 16 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2
b ) 1 / 3
c ) 1 / 4
d ) 1 / 5
e ) 1 / 6
Rationale: the volume of water in the tank is h * l * b = 16 cubic feet . since h = 1 , then l * b = 16 and l = b = 4 . since the tank is cubical , the capacity of the tank is 4 * 4 * 4 = 64 . the ratio of the water in the tank to the capacity is 16 / 64 = 1 / 4 the answer is c .
Answer: c
Question (general): by approximately what percent is x greater than 2 / 5 if ( 3 / 5 ) ( x ) = 1 ?
Options: a ) 723 % , b ) 156 % , c ) 316 % , d ) 37 % , e ) 29 %
Rationale: "what percent is x greater than 2 / 5 if ( 3 / 5 ) ( x ) = 1 ? = > x = 5 / 3 % change = [ ( 5 / 3 - 2 / 5 ) / ( 2 / 5 ) ] * 100 = 316.5 % = 316 % approx ans , c"
Answer: c
Question (general): a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 60 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 28 % , e ) 50 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 60 % more ie . , 160 recliners hence her sales tields 160 * 80 = $ 12800 increase in sales = 12800 - 10000 = $ 2800 so % increase = 2800 * 100 / 10000 = 28 % d is the answer"
Answer: d
Question (general): 10 play kabadi , 25 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 25 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 25 + 5 = 30 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 30 - 5 = 35 answer : b"
Answer: b
Question (general): on dividing a number by 5 , we get 5 as quotient and 0 as remainder . on dividing the same number by 11 , what will be the remainder ?
Options: a ) 5 , b ) 2 , c ) 7 , d ) 9 , e ) 3
Rationale: "number = 5 * 5 + 0 = 25 11 ) 25 ( 2 22 - - - - - - - - 3 required number = 0 . answer : e"
Answer: e
Question (geometry): if the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 8 ^ 2 = l * 4 = > l = 64 / 4 = 16 answer d"
Answer: d