Cheukting/mathqa huggingface dataset:
Question (general): of the families in city x in 1956 , 25 percent owned a personal computer . the number of families in city x owning a computer in 1960 was 15 percent greater than it was in 1956 , and the total number of families in city x was 5 percent greater in 1956 than it was in 1960 . what percent of the families in city x owned a personal computer in 1960 ?
Options: a ) 50 % , b ) 51.22 % , c ) 5.26 % , d ) 7.20 % , e ) 27.38 %
Rationale: "say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 number of families owning computer in 1960 = 25 * 115 / 100 = 28.75 number of families in 1960 = 105 the percentage = 28.75 / 105 * 100 = 27.38 % . option : e"
Answer: e
Question (gain): if the cost price is 91 % of sp then what is the profit %
Options: a ) 9.89 % , b ) 8.90 % , c ) 9.00 % , d ) 8.00 % , e ) 9.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 91 : profit = rs 9 . profit = { ( 9 / 91 ) * 100 } % = 9.89 % answer is a ."
Answer: a
Question (general): a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 24 , find the sum of money ?
Options: a ) 288 , b ) 262 , c ) 72 , d ) 123 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 24 41 - - - - ? = > rs . 123 answer : d"
Answer: d
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a girl sitting at window seat in the slower train in 32 seconds . find the length of the faster train ?
Options: a ) 170 m , b ) 100 m , c ) 270 m , d ) 320 m , e ) 350 m
Rationale: "explanation : relative speed = ( 72 - 36 ) x 5 / 18 = 2 x 5 = 10 mps . distance covered in 32 sec = 32 x 10 = 320 m . the length of the faster train = 320 m . answer is d"
Answer: d
Question (general): tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?
Options: a ) 6 , b ) 7 , c ) 12 , d ) 16 , e ) 24
Rationale: number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e
Answer: e
Question (gain): a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 44000 . what is the share of c ?
Options: a ) rs . 12000 , b ) rs . 13375 , c ) rs . 11750 , d ) rs . 11625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 44000 ] = rs . 12000 answer : option a"
Answer: a
Question (general): in a 400 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 ) 81 , b ) 147 , c ) 145 , d ) 143 , e ) 141
Rationale: "solution simple out of 400 20 % are male i . e 80 and 25 % are female i . e 100 , so total homeowner is 180 . now min number homeowner is 80 and max is 180 so question ask us to find least and 81 has least value among all option . so ans is 81 . answer : a"
Answer: a
Question (general): a sum of rs . 100 is lent at simple interest of 3 % p . a . for the first month , 9 % p . a . for the second month , 27 % p . a . for the third month and so on . what is the total amount of interest earned at the end of the year approximately
Options: a ) rs . 797160 , b ) rs . 791160 , c ) rs . 65930 , d ) rs . 66430 , e ) rs . 67430
Rationale: total amount of interest is i = p / 100 * 1 [ 3 / 12 + 9 / 12 + 27 / 12 … . 312 / 12 where p = 100 ; i = 1 / 12 ( 3 + 9 + … . . 312 ) i = 1 / 12 ( 3 ( 312 - 1 ) ) / 3 - 1 = 531440 * 3 / 12 * 2 = rs . 66430 answer : d
Answer: d
Question (geometry): suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 10 , e ) 12
Rationale: the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the “ back ” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b .
Answer: b
Question (geometry): the side of a square has the length of 6 . what is the area of the region shaded ?
Options: a ) 48 - 8 π
b ) 48 - 6 π
c ) 24 + 6 π
d ) 16 + 8 π
e ) 64 - 8 π
Rationale: the area of a square whose side is 6 – ( the area of a square whose side is 4 + the area of the semi - circle whose side is 4 ) = the area of the region shaded the correct answer is b .
Answer: b
Question (general): how many positive integer solutions does the equation 4 x + 5 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 5 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 4 * 5 ) = 5 answer : d"
Answer: d
Question (gain): a man bought 10 crates of mangoes for $ 40 total . if he lost 2 of the crates , at what price would he have to sell each of the remaining crates in order to earn a total profit of 20 percent of the total cost ?
Options: a ) $ 6 , b ) $ 8 , c ) $ 10 , d ) $ 12 , e ) $ 14
Rationale: as given , after lost , the remaining 8 crates total cost = $ 40 so , 1 crate cost = 40 / 8 = 5 to get 20 % profit , 1 crate cost should be = 5 + 5 * 20 / 100 = $ 6 answer : a
Answer: a
Question (physics): a train passes a station platform in 32 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 887 , d ) 166 , e ) 180
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 32 = 15 = > x = 180 m . answer : e"
Answer: e
Question (other): irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 170 cookies , what percent of the cookies did irin bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 12.5 % , d ) 53.5 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 170 cookies x = 170 / 16.4 = 10 ( approx ) so , irin baked 10 * 9.18 cookies or 91 cookies ( approx ) % share = 91 / 170 = 53.5 approx hence , answer is d ."
Answer: d
Question (general): how many four - digit numbers that do not contain the digits 3 or 6 are there ?
Options: a ) 2401 , b ) 3584 , c ) 4096 , d ) 5040 , e ) 7200
Rationale: "1 st digit can be filled up by the numbers - { 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 7 ways 2 nd digit can be filled up by the numbers - { 0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways 3 rd digit can be filled up by the numbers - { 0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways so , total no of ways is 7 * 8 * 8 = > 3584 hence answer will be ( b )"
Answer: b
Question (gain): a number increased by 30 % gives 650 . the number is ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 650 ( 130 ã — 5 = 650 ) 100 % - - - - - - - > 400 ( 100 ã — 5 = 500 ) option ' d '"
Answer: d
Question (general): the positive numbers w , x , y , and z are such that x is 25 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.2 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16.2 - answer b"
Answer: b
Question (physics): arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 20 days .
Options: a ) 12 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 20 * 6 / 10 = 12 days . answer : a"
Answer: a
Question (general): if ' x ' is a positive integer exactly divisible by 6 or 15 but not divisible by 12 . what could possibly be the value of ' x ' ?
Options: a ) 120 , b ) 60 , c ) 36 , d ) 90 , e ) 54
Rationale: 120 and 60 are both divisible by 6 and 15 but also by 12 . so they are not the right answer . 36 and 54 are both clearly not divisible by 15 ( not correct ) 90 is both divisible by 6 and 15 but not by 12 . answer : ( d ) 90
Answer: d
Question (gain): if rs . 450 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) 227 , b ) 299 , c ) 270 , d ) 585 , e ) 271
Rationale: "90 = ( 450 * 4 * r ) / 100 r = 5 % i = ( 450 * 6 * 5 ) / 100 = 135 450 + 135 = 585 answer : c"
Answer: c
Question (gain): on a sum of money , the simple interest for 2 years is rs . 324 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 9.87 % , d ) 10.5 % , e ) 11.5 %
Rationale: "the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 324 = 16 ( r ã — si ) / ( 2 ã — 100 ) = 16 ( r ã — 324 ) / ( 2 ã — 100 ) = 16 r = 9.87 % answer : option c"
Answer: c
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 10 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.10 t + 0.08 ( p - t ) = 1440 - - - - > t = 1600 . a is the correct answer ."
Answer: a
Question (physics): a taxi leaves point a 2 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .
Options: a ) 42 , b ) 48 , c ) 44 , d ) 50 , e ) 40
Rationale: "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 4 hrs and taxi a total of 2 hrs . hence 4 * ( v - 20 ) = 2 v 4 v - 80 = 2 v 2 v = 80 v = 40 mph e"
Answer: e
Question (physics): a man walking at a constant rate of 12 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 24 miles per hour . the woman stops to wait for the man 10 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 13 , b ) 10 , c ) 15 , d ) 11 , e ) 9
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 10 * 24 / 60 = 4 miles and the man walks the distance mm , which is 10 * 12 / 60 = 2 mile . the difference of 4 - 2 = 2 miles ( mw ) will be covered by the man in ( 2 ) / 9 = 2 / 9 of an hour , which is ~ 13 minutes . answer a ."
Answer: a
Question (general): if | 5 x - 5 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 2 , d ) - 3 , e ) 4
Rationale: "| 5 x - 5 | = 100 5 x - 5 = 100 or 5 x - 5 = - 100 5 x = 105 or 5 x = - 95 x = 21 or x = - 19 sum = 21 - 19 = 2 answer is c"
Answer: c
Question (general): a bag of potatoes weighs 39 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 13 lb , e ) 5 lb
Rationale: "sol . 39 ÷ 3 = 13 . answer : d"
Answer: d
Question (general): a person saved $ 50 in buying an item on sale . if he spent $ 500 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 1.8 %
Rationale: "actual price = 500 + 50 = $ 550 saving = 10 / 550 * 100 = 100 / 55 = 1.8 % approximately answer is e"
Answer: e
Question (general): the difference between a number and its two - fifth is 510 . what is 20 % of that number ?
Options: a ) 58 , b ) 170 , c ) 95 , d ) 100 , e ) 120
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 20 % of 850 = 170 . answer : b"
Answer: b
Question (general): monica planned her birthday party . she prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra . after the party , it turned out that one of the guests did n ' t come but every one of the guests that did come ate 6 muffins and 6 muffins remained . how many guests did monica plan on ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 7 .
Rationale: let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a
Answer: a
Question (general): a boy rides his bicycle 10 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately ?
Options: a ) 10.7 km / hr , b ) 10.8 km / hr , c ) 17.8 km / hr , d ) 10.5 km / hr , e ) 30.8 km / hr
Rationale: total distance traveled = 10 + 12 = 22 km / hr . total time taken = 10 / 12 + 12 / 10 = 61 / 30 hrs . average speed = 22 * 30 / 61 = 10.8 km / hr . answer : b
Answer: b
Question (general): if 3 ^ x = 2 , then 3 ^ ( 4 x + 3 ) =
Options: a ) 429 , b ) 454 , c ) 432 , d ) 438 , e ) 108
Rationale: 3 ^ x = 2 3 ^ 4 x = 2 ^ 4 3 ^ 4 x = 16 3 ^ ( 4 x + 3 ) = 3 ^ 4 x * 3 ^ 3 = 16 * 27 = 432 answer : c
Answer: c
Question (physics): two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 360 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 24 sec , e ) 1 min
Rationale: "they meet every 360 / 7 + 8 = 24 sec answer is d"
Answer: d
Question (general): carol spends 1 / 3 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 9 , d ) 1 / 2 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 3 ) s amount spent on television = ( 1 - 1 / 3 ) ( 1 / 3 ) s = ( 2 / 3 ) * ( 1 / 3 ) * s = ( 2 / 9 ) s ( stereo + tv ) / total savings = s ( 1 / 3 + 2 / 9 ) / s = 5 / 9 answer : c"
Answer: c
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 36 . what is the value of x ?
Options: a ) 80 , b ) 96 , c ) 100 , d ) 108 , e ) 120
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 36 ( y / 100 ) * x = 36 ( x / 400 ) * x = 36 x ^ 2 = 36 * 400 x = 120 the answer is e ."
Answer: e
Question (physics): a van takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 40 kmph , b ) 50 kmph , c ) 60 kmph , d ) 75 kmph , e ) 860 kmph
Rationale: "time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )"
Answer: c
Question (probability): on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ?
Options: a ) 1 / 3 , b ) 5 / 9 , c ) 7 / 9 , d ) 19 / 27 , e ) 23 / 27
Rationale: "p ( missing all 3 ) = ( 2 / 3 ) ^ 3 = 8 / 27 p ( success on at least one attempt ) = 1 - 8 / 27 = 19 / 27 the answer is d ."
Answer: d
Question (physics): if an object travels 90 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 30.68 , b ) 32.34 , c ) 34.56 , d ) 36.72 , e ) 38.95
Rationale: "90 feet / 2 seconds = 45 feet / second ( 45 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 30.68 ( approximately ) the answer is a ."
Answer: a
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25 % . find his false weight age ?
Options: a ) 338 , b ) 278 , c ) 800 , d ) 269 , e ) 112
Rationale: "25 = e / ( 1000 - e ) * 100 1000 - e = 4 e 1000 = 5 e = > e = 200 1000 - 200 = 800 answer : c"
Answer: c
Question (general): 16.02 ã — 0.1 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.1 = 1.602 the answer is c ."
Answer: c
Question (gain): the population of a village is 13400 . it increases annually at the rate of 21 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 19619 , d ) 18989 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 13400 × 121 / 100 × 121 / 100 = 19619 c"
Answer: c
Question (gain): if the cost price is 90 % of sp then what is the profit %
Options: a ) 1.10 % , b ) 1.11 % , c ) 1.15 % , d ) 1.17 % , e ) 1.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 90 : profit = rs 10 . profit = { ( 10 / 90 ) * 100 } % = 1.11 % answer is b ."
Answer: b
Question (geometry): a box measuring 49 inches long by 21 inches wide by 14 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 ) 42 , c ) 54 , d ) 108 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is ."
Answer: b
Question (gain): a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 5,500 meters of fabric ?
Options: a ) $ 7,360 , b ) $ 8,540 , c ) $ 9,720 , d ) $ 10,570 , e ) $ 11,680
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 2000 = $ 3720 the total price is $ 4000 + $ 2850 + $ 3720 = $ 10,570 the answer is d ."
Answer: d
Question (gain): sonika deposited rs . 7000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 2277 , c ) 9620 , d ) 2774 , e ) 1212
Rationale: "( 7000 * 3 * 2 ) / 100 = 420 9200 - - - - - - - - 9620 answer : c"
Answer: c
Question (general): a ’ s speed is 20 / 13 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 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 7 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 13 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 13 meters ) to reach the finish line . so b should get a head start of 7 / 20 th of the race . answer ( d )"
Answer: d
Question (physics): if 4 spiders make 3 webs in 9 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 9 , b ) 12 , c ) 27 , d ) 24 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 4 : 1 ( webs ) 1 : 9 } : : x : 3 â ‡ ’ 4 ã — 1 ã — 9 = 1 ã — 3 ã — x â ‡ ’ x = 12 answer : option b"
Answer: b
Question (general): what is the largest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?
Options: a ) 9600 , b ) 5200 , c ) 362 , d ) 958 , e ) 258
Rationale: explanation : largest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , largest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : a
Answer: a
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 64 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2882 , c ) 2999 , d ) 1856 , e ) 2121
Rationale: "let the side of the square plot be a ft . a 2 = 64 = > a = 8 length of the fence = perimeter of the plot = 4 a = 32 ft . cost of building the fence = 32 * 58 = rs . 1856 . answer : d"
Answer: d
Question (gain): a 6 litre sol is 20 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3.6 , e ) e . 5.4
Rationale: "20 % of 6 = 1.2 50 % of 6 = 3 shortage is 1.8 so we need to have 1.8 / 50 % to get 50 % alcohol content . = 3.6 d"
Answer: d
Question (gain): if 45 % of z is 60 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 60 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 60 / 100 ) * ( 3 / 4 ) x i . e . z = ( 60 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1 ) x = ( 100 / 100 ) x i . e . z is 100 % of x answer : option c"
Answer: c