Cheukting/mathqa huggingface dataset:
Question (gain): population is 22000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 29282 , c ) 36620 , d ) 26620 , e ) 26820
Rationale: "population after 1 st year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24000 population after 2 nd year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26620 population after 3 rd year = 26620 * 10 / 100 = 2662 = = = > 26620 + 2662 = 29282 answer : b"
Answer: b
Question (physics): a 180 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 54 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 180 / 12 * 18 / 5 = 54 kmph answer : a"
Answer: a
Question (general): ( 26.3 * 12 * 20 ) / 3 + 125 = ?
Options: a ) 2339 , b ) 2229 , c ) 4429 , d ) 5529 , e ) 2669
Rationale: b 2229 ? = [ ( 26.3 * 12 * 20 ) / 3 ] + 125 ? = 2104 + 125 = 2229
Answer: b
Question (geometry): rectangular tile each of size 45 cm by 50 cm must be laid horizontally on a rectangular floor of size 250 cm by 180 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 35 , b ) 40 , c ) 25 , d ) 18 , e ) 20
Rationale: "area of tile = 45 * 50 = 2250 area of floor = 250 * 180 = 45000 no of tiles = 45000 / 2250 = 20 so , the no of tile = 20 answer : e"
Answer: e
Question (general): if 15 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 16 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "b for me 14 people with 1 $ each - > maximum = 16"
Answer: b
Question (geometry): a water tank , having the shape of a rectangular prism of base 100 square centimeters , is being filled at the rate of 1 liter per minute . find the rate at which the height of the water in the water tank increases . express your answer in centimeters per minute .
Options: a ) 30 cm
b ) 10 cm
c ) 50 cm
d ) 90 cm
e ) 70 cm
Rationale: the volume of a rectangular prism is given by area of base ? height the rate at which the tank is being filled is 1 liter per minute which we need to convert 1 liter = 1 dm 3 but 1 dm = 10 cm . hence 1 liter = ( 10 cm ) 3 = 1000 cm 3 the height h of the water is related to the volume by volume = area of base * h in one minute the volume increases by 1 liter or 1000 cm 3 and the height increases by h = volume / area of base = 1000 cm 3 / 100 cm 2 = 10 cm correct answer b
Answer: b
Question (general): the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 72 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 72 ⇔ 9 ( x - y ) = 72 ⇔ x - y = 8 answer d"
Answer: d
Question (physics): machine a can put caps on a set of bottles in 8 hours at a constant rate . if machine a does the job for 6 hours and machine b does the rest of the job , which works at 1 / 4 constant rate of machine a . how long will it take for machine b alone to do the rest of the job ?
Options: a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 10 hrs , e ) 16 hrs
Rationale: machine a will do 6 / 8 in 6 hrs , so a does 3 / 4 of the work . . therefore , b will do the remaining 1 / 4 th work alone . . as the speed of b is 1 / 4 rate of a , b will do the 1 / 4 th work in same time that a takes to complete full job . . . ans 8 c
Answer: c
Question (general): a ’ s speed is 16 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 15 , d ) 1 / 32 , e ) 1 / 31
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 16 v / 15 ) = xd / v ( 15 / 16 ) * d / v = x * d / v x = 15 / 16 b should have a head start of 1 / 16 of the full distance . the answer is b ."
Answer: b
Question (physics): 6 women can do 75 unit of work in 8 days by working 5 hr / day in how many days 4 women do 30 units of work by working 8 hr / day
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: ( 6 x 8 x 5 ) / 75 = ( ax 4 x 8 ) / 30 a = 3 answer : a
Answer: a
Question (gain): 50 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 640 , b ) 278 , c ) 800 , d ) 267 , e ) 121
Rationale: "( 50 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 2 x = 320 x = 640 answer : a"
Answer: a
Question (general): what is the units digit of the expression 14 ^ 7 − 16 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 8 , d ) 6 , e ) 4
Rationale: i think answer on this one should be c too . since we know that 14 ^ 7 > 16 ^ 4 , as will said one should always check if the number is positive .
Answer: c
Question (general): when xyz co discontinued an agency arrangement with john , management held his commission of rs . 25000 / - for one month . earlier john had availed an advance agency fees of 8280 / - from company . but robert forgot that . after one month john asked his fees and accountant gives rs . 18500 / - to him . what is the incentive amount given to john ?
Options: a ) a ) 1780 , b ) b ) 1250 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600
Rationale: total fees = rs . 25000 / - advance fees = 8280 / - balance fees = 25000 - 8280 = 16720 paid amount = 18500 / - incentive amount = 18500 - 16720 = 1780 / - answer is a
Answer: a
Question (general): if | 5 x - 5 | = 150 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 6 , d ) - 3 , e ) 5
Rationale: "there will be two cases 5 x - 5 = 150 or 5 x - 5 = - 150 = > x = 31 or x = - 29 sum of both the values will be - 29 + 31 = 2 answer is a"
Answer: a
Question (general): x is the product of each integer from 1 to 100 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 100 = 100 ! no . of trailing zeros in 100 ! = 100 / 5 + 100 / 5 ^ 2 = 20 + 4 = 24 100 ^ k = 10 ^ 2 k → k = 24 / 2 = 12 e"
Answer: e
Question (general): jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 9 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 9 / 49 = ( 3 / 7 ) * ( 3 / 7 ) therefore probability that the next one she draws is pink = 4 / 7 option ( b )
Answer: b
Question (gain): a sum was put a simple interest at a certain rate for 2 years . had it been put at 4 % higher rate , it would have fetched rs . 60 more . the sum is :
Options: a ) rs . 750 , b ) rs . 700 , c ) rs . 820 , d ) rs . 940 , e ) rs . 900
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x × ( r + 4 ) × 2 / 100 − x × r × 2 / 100 = 60 ⇒ x × 4 × 2 / 100 = 60 ⇒ x × 2 / 100 = 15 ⇒ 2 x = 1500 ⇒ x = 750 answer : option a"
Answer: a
Question (probability): three coins are tossed . find the probability of at least 2 tails ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 3 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 let e is the event of getting at least 2 tails n ( e ) = ttt , tth , htt , tht = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 ans - a"
Answer: a
Question (physics): a train can travel 50 % faster than a car . both start from point a at the same time and reach point b at 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is ?
Options: a ) 2387 , b ) 267 , c ) 120 , d ) 277 , e ) 271
Rationale: "let speed of the car be x km / hr . then , speed of the train = 150 / 100 x = 3 / 2 x km / hr . 75 / x - 75 / ( 3 / 2 x ) = 125 / ( 10 * 60 ) 75 / x - 50 / x = 5 / 24 = 120 km / hr . answer : c"
Answer: c
Question (physics): tom traveled the entire 60 miles trip . if he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 40 mph , e ) 42 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 12 + 48 ) / ( ( 12 / 24 ) + ( 48 / 48 ) ) = 60 * 2 / 3 = 40 mph d"
Answer: d
Question (general): a grocer has a sale of rs . 2435 , rs . 2920 , rs . 2855 , rs . 3230 and rs . 2560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 2500 ?
Options: a ) 5000 , b ) 4000 , c ) 1000 , d ) 6000 , e ) 8000
Rationale: "total sale for 5 months = rs . ( 2435 + 2920 + 2855 + 3230 + 2560 ) = rs . 14000 . required sale = rs . [ ( 2500 x 6 ) - 14000 ] = rs . ( 15000 - 14000 ) = rs . 1000 answer : option c"
Answer: c
Question (general): a mixture contains alcohol and water in the ratio 4 : 3 . if 5 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 10 litres , b ) 20 litres , c ) 30 litres , d ) 5 litres , e ) 14 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 5 ) = 4 / 5  20 x = 4 ( 3 x + 5 )  8 x = 20  x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer a 10 litres"
Answer: a
Question (gain): evaluate 28 % of 550 + 45 % of 280
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 280
Rationale: "explanation : = ( 28 / 100 ) * 550 + ( 45 / 100 ) * 280 = 154 + 126 = 280 answer : option e"
Answer: e
Question (general): what sum of money put at c . i amounts in 2 years to rs . 8840 and in 3 years to rs . 9261 ?
Options: a ) 8054 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8840 - - - - 421 100 - - - - ? = > 4.76 % x * 104.76 / 100 * 104.76 / 100 = 8840 x * 1.0975 = 8840 x = 8840 / 1.0975 = > 8054.54 answer : a"
Answer: a
Question (general): if square - root of 15 is 3.87 . then find the value of square - root of ( 5 / 3 )
Options: a ) 1.29 , b ) 1.39 , c ) 1.49 , d ) 1.59 , e ) 1.69
Rationale: = > root 5 / root 3 = ( root 5 / root 3 ) * ( root 3 / root 3 ) = root 15 / root 9 = 3.87 / 3 = 1.29 answer : a
Answer: a
Question (other): a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 480 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "3 x = 480 x = 160 therefore , the salesman sold 160 kg in the morning and 2 ⋅ 160 = 320 kg in the afternoon . so answer is e ."
Answer: e
Question (general): 0.004 × 0.5 = ?
Options: a ) none of these , b ) 0.02 , c ) 0.002 , d ) 0.0002 , e ) 2
Rationale: "explanation : 0.004 × 0.5 = 0.002 . answer : option c"
Answer: c
Question (general): on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 20 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: t = the number of cups of tea c = the number of cups of hot chocolate t + c = 20 t - c = 10 - > t = 15 . c = 5 . mo drinks 3 cups of tea a day then number of days that are not rainy = 15 / 3 = 5 so number of rainy days = 7 - 5 = 2 a is the answer .
Answer: a
Question (gain): how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 10 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 72 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / sec distance = 50 * 4 = 200 m time taken = 200 * 9 / 25 = 72 sec answer is c"
Answer: c
Question (geometry): the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 675 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 30 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 3 x = 675 x ^ 2 = 225 x = 15 length = 3 * 15 = 45 difference = 45 - 15 = 30 b is the answer"
Answer: b
Question (general): a grocery shop has a sale of rs . 6235 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 5191 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6235 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6235 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 33809 + x = 39000 = > x = 39000 − 33809 = 5191 answer : d"
Answer: d
Question (physics): a train 225 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 ) 86 , b ) 50 , c ) 12 , d ) 13 , e ) 67
Rationale: "speed of the train relative to man = ( 225 / 10 ) m / sec = ( 45 / 2 ) m / sec . [ ( 45 / 2 ) * ( 18 / 5 ) ] km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 81 = = > x = 86 km / hr . answer : option a"
Answer: a
Question (general): 0.0006688 / 0.0000120 x 17.05 = ?
Options: a ) 450.1 , b ) 910.1 , c ) 930.1 , d ) 920.1 , e ) 950.1
Rationale: "explanation : ? = 0.0006688 / 0.0000120 x 17.05 = 950.1 answer : option e"
Answer: e
Question (general): the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 45 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 15 , e ) 14
Rationale: initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 45 + q = > q = 15 answer : d
Answer: d
Question (general): a car traveled 75 % of the way from town a to town b at an average speed of 75 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 40 , e ) 45
Rationale: "assume total distance = 100 miles time taken for 75 miles = 75 / 75 = 1 hour time taken for the rest of the 25 miles = 25 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 25 / v hence v = 25 mph answer : c"
Answer: c
Question (physics): if 20 men can build a wall 66 metres long in 15 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 151.36 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 15 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 15 * 20 ) = 151.36 mtrs answer : a"
Answer: a
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "we are given that orangeade is made on day 1 with an equal amount of water and orange juice . we can set this information up into a ratio using a variable multiplier : w : oj = x : x thus , orangeade quantity = amount of water + amount of oj = x + x = 2 x we are next given that orangeade on day 2 was made by mixing the same amount of orange juice with twice the amount of water . we can set this information up into a ratio using a variable multiplier : w : oj = 2 x : x thus , orangeade quantity = amount of water + amount of oj = 2 x + x = 3 x we also know that all orangeade made was sold and that the revenue on both days was the same . we can therefore set up the following equation : day 1 revenue = day 2 revenue that is , ( quantity sold day 1 ) ( price per glass day 1 ) = ( quantity sold day 2 ) ( price per glass day 2 ) let a be the amount of orangeade a glass can hold , then quantity sold day 1 = the number of glasses of orangeade sold on day 1 = 2 x / a similarly , quantity sold day 2 = the number of glasses of orangeade sold on day 2 = 3 x / a we also know that the price per glass on day 1 = $ 0.6 but we don ’ t know the price per glass on day 2 , so let ’ s label it as variable p . we now have : ( 2 x / a ) ( 0.6 ) = ( 3 x / a ) ( p ) multiplying both sides by a , we have : ( 2 x ) ( 0.6 ) = ( 3 x ) ( p ) 1.2 x = 3 xp 1.2 = 3 p p = 0.4 thus , each glass of orangeade was sold for $ 0.40 on day 2 . answer d ."
Answer: d
Question (physics): two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many r hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many r hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Question (general): the number 1254 is divisible by which number ?
Options: a ) 8 , b ) 7 , c ) 4 , d ) 5 , e ) 6
Rationale: last 3 digit can not divisible by 8 so , reject option a 1254 is not divisible by 7 last number is not 0 or 5 , so neglect 4 is not divide 1254 divisibility rule of 6 is a number divisible both by 3 and 2 . 1254 attains both divisible . so the number is divisible by 6 option e
Answer: e
Question (physics): what is the cost of leveling the field in the form of parallelogram at the rate of rs . 40 / 10 sq . metre , whose base & perpendicular distance from the other side being 24 m & 34 m respectively ?
Options: a ) s . 600 , b ) s . 630 , c ) s . 640 , d ) s . 648 , e ) s . 816
Rationale: "area of the parallelogram = length of the base * perpendicular height = 24 * 34 = 816 m . total cost of levelling = rs . 816 e"
Answer: e
Question (general): a certain no . when divided by 35 leaves aremainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) c
Answer: c
Question (gain): on a certain road , 40 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 50 %
Rationale: "suppose there are x motorists . 40 % of them exceeded the speed limit and received the ticket , i . e . 2 x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = 2 x / 5 or y / x = 1 / 2 or y / x * 100 = 1 / 2 * 100 = 50 % e"
Answer: e
Question (general): if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 56 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 280 , b ) $ 800 , c ) $ 892 , d ) $ 1,108 , e ) $ 1,200
Rationale: "( a ) $ 280 ( b ) $ 800 ( c ) $ 892 ( d ) $ 1,108 ( e ) $ 1,200 y = 2000 - x . 1 x - . 08 ( 2000 - x ) = 56 . - 160 + . 18 x = 56 x = 1200 and y = 800 answer : b"
Answer: b
Question (general): if a mixture is 1 ⁄ 2 alcohol by volume and 3 ⁄ 2 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 3 ⁄ 7 , b ) 4 ⁄ 7 , c ) 3 ⁄ 4 , d ) 4 ⁄ 3 , e ) 7 ⁄ 4
Rationale: "should be a sub - 600 level q . . volume = { 1 / 2 } / { 3 / 2 } = 1 / 3 c"
Answer: c
Question (general): a number when divided by 342 gives a remainder 38 , what remainder will be obtained by dividing the same number 21 ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 342 + 38 = 380 / 21 = 2 ( remainder ) answer : d"
Answer: d
Question (general): at the beginning of 1992 , maria ' s stock portfolio was worth $ 600000 . during 1992 , the portfolio ' s value increased by 95 % . during the next year , the portfolio increased its worth by only 5 % . what was maria ' s portfolio worth , in dollars , by the end of 1993 ?
Options: a ) 1 , 180000 , b ) 1 , 200000 , c ) 1 , 200300 , d ) 1 , 228500 , e ) 1 , 330,000
Rationale: by the end of 1992 , the port folio worth is 1.95 * ( $ 600 k ) by 1993 , the portfolio is 1.05 * ( 1.95 * $ 600 k ) = $ 1 , 228,500 answer : d
Answer: d
Question (physics): amit and ananthu can do a work in 15 days and 45 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 30 days , c ) 33 days , d ) 35 days , e ) 39 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 45 ananthu can do work in = 4 / 5 * 45 = 36 days so total days = 36 + 3 = 39 days answer : e"
Answer: e
Question (other): a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 5 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 20 : 25 , c ) 1 : 5 , d ) 2 : 5 , e ) 4 : 6
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 5 - - > x ( a - b ) = 5 . since 5 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 5 . the above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 5 * 4 = 20 and dogs = 5 * 5 = 25 . answer : b ."
Answer: b