Cheukting/mathqa huggingface dataset:
Question (general): as a treat for her two crying children , a mother runs to the freezer in which she has 4 cherry ice pops , 3 orange ice pops , and 4 lemon - lime ice pops . if she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one invariably being jealous of the other and getting even more upset , what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?
Options: a ) 1 / 99 , b ) 1 / 6 , c ) 5 / 18 , d ) 13 / 18 , e ) 5 / 6
Rationale: probability of not getting the same flavor - > fouvarable - > cherry - orange [ 4 c 1 * 3 c 1 [ or simply 4 * 3 ] or cherry - lemon [ 4 * 4 ] or orange - lemon [ 3 * 4 ] prob = ( 4 * 3 + 4 * 4 + 3 * 4 ) / 9 c 2 = 40 / 3960 = 1 / 99 answer - > a
Answer: a
Question (physics): a and b together can complete a work in 12 days . a alone complete it in 20 days . if b does the work only for half a day daily , then in how many days a and b together will complete the work ?
Options: a ) 110 days , b ) 11 days , c ) 15 days , d ) 20 days , e ) 17 days
Rationale: b ' s one day work = ( 1 / 12 - 1 / 20 ) = 1 / 30 . now , ( a + b ) ' s one day work = ( 1 / 20 + 1 / 60 ) = 1 / 15 . [ ∵ b work for half day only ] . so , a and b together will complete the work in 15 days . correct answer : ` ` c ' ' .
Answer: c
Question (general): in a fuel station the service costs $ 1.65 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 448.8 $ , e ) 480 $
Rationale: "total cost = ( 1.65 * 12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 = > 448.8 hence answer will be ( d )"
Answer: d
Question (geometry): a certain rectangular crate measures 6 feet by 8 feet by 10 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 8 x 10 i . e . of radius 8 / 2 = 4 b"
Answer: b
Question (physics): the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 950 per sq . metre .
Options: a ) s . 20,550 , b ) s . 15,600 , c ) s . 20,900 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 950 ã — 22 ) = rs . 20900 answer : option c"
Answer: c
Question (general): the function f ( n ) is defined as the product of all the consecutive positive integers between 3 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 3 answer : c"
Answer: c
Question (physics): how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 136 m length ?
Options: a ) 82.1 sec . , b ) 12.3 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 136 = 246 m . required time = 246 / 20 = 12.3 sec . answer : b"
Answer: b
Question (general): by approximately what percent is x greater than 5 / 11 if ( 4 / 11 ) ( x ) = 1 ?
Options: a ) 730 % , b ) 560 % , c ) 410 % , d ) 505 % , e ) 209 %
Rationale: "what percent is x greater than 5 / 11 if ( 4 / 11 ) ( x ) = 1 ? = > x = 11 / 4 % change = [ ( 11 / 4 - 5 / 11 ) / ( 5 / 11 ) ] * 100 = 505 % ans , d"
Answer: d
Question (probability): two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability = ( 8 / 20 ) * 100 = 40 % . ans : : d
Answer: d
Question (general): a group of 7 teenagers recently visited the japanese restaurant . the total bill for the meal , including 20 % gratuity , came to $ 840 . on average , how much did the meal of each individual cost before gratuity ?
Options: a ) $ 160 , b ) $ 96 , c ) $ 90 , d ) $ 10 , e ) $ 55
Rationale: 7 teenagers - so total 7 people the bill $ 840 includes 20 % gratuity . . . so the actual cost of dinner was $ 700 now , the cost per person will be $ 700 / 7 which is $ 10 option d
Answer: d
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 65 % = 35 % of books that were loaned out are not returned . now , there are 68 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.35 = 7 - - > { loaned out } = 20 . answer : a ."
Answer: a
Question (gain): a shopkeeper forced to sell at cost price , uses a 950 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 11.11 % , d ) 5.26 % , e ) none of these
Rationale: "shopkeeper sells 950 g instead of 1000 g . so , his gain = 1000 - 950 = 50 g . thus , % gain = ( 50 * 100 ) / 950 = 5.26 % . answer : option d"
Answer: d
Question (general): if 7 ^ q is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of q ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: so the question just means that we have to find all the multiples q of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e
Answer: e
Question (physics): susan drove an average speed of 30 miles per hour for the first 60 miles of a tripthen at a average speed of 60 miles / hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 36 , c ) 45 , d ) 50 , e ) 55
Rationale: "avg . speed = total distance / total time total distance = 90 miles total time = 60 / 30 + 30 / 60 = 5 / 2 avg . speed = 36 answer - b"
Answer: b
Question (general): a 415 m long train is running at 63 km / hr . in how much time will it cross a tunnel 285 m long ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 60 , e ) 40
Rationale: "speed of the train = ( 63 * 5 / 18 ) m / sec = 35 / 2 m / sec . distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the tunnel = 415 + 285 = 700 m time = ( 700 / 35 / 2 ) = 40 sec answer : e"
Answer: e
Question (gain): the bankers discount of a certain sum of money is rs . 288 and the true discount on the same sum for the same time is rs . 240 . the sum due is :
Options: a ) 1400 , b ) 1420 , c ) 1440 , d ) 1460 , e ) 1480
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 288 * 240 ) / 288 - 240 ; 1440 answer : c"
Answer: c
Question (gain): a shopkeeper sold an article offering a discount of 4 % and earned a profit of 32 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24.5 , b ) 28.5 , c ) 30.5 , d ) 32.5 , e ) 37.5
Rationale: let c . p . be rs . 100 . then , s . p . = rs . 132 let marked price be rs . x . then , 96 / 100 x = 132 x = 13200 / 96 = rs . 137.5 now , s . p . = rs . 137.5 , c . p . = rs . 100 profit % = 37.5 % . answer : e
Answer: e
Question (geometry): the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?
Options: a ) 50 %
b ) 60 %
c ) 75 %
d ) 80 %
e ) 89 %
Rationale: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c
Answer: c
Question (geometry): what will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of rs . 10 per square meter ?
Options: a ) rs . 3430
b ) rs . 3440
c ) rs . 3450
d ) rs . 3460
e ) rs . 3490
Rationale: explanation : in this question , we are having perimeter . we know perimeter = 2 ( l + b ) , right so , 2 ( l + b ) = 340 as we have to make 1 meter boundary around this , so area of boundary = ( ( l + 2 ) + ( b + 2 ) - lb ) = 2 ( l + b ) + 4 = 340 + 4 = 344 so required cost will be = 344 * 10 = 3440 answer : option b
Answer: b
Question (physics): a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 18 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 27 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 18 x = 27 days answer : option c"
Answer: c
Question (other): the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 25 and 24 . the larger of the two numbers is
Options: a ) 276 , b ) 799 , c ) 712 , d ) 750 , e ) none
Rationale: "solution clearly , the numbers are ( 30 x 25 ) and ( 30 x 24 ) . larger number = ( 30 x 25 ) = 750 . answer d"
Answer: d
Question (gain): by investing in 1623 % stock at 64 , one earns rs . 1800 . the investment made is
Options: a ) s . 6500 , b ) s . 7500 , c ) s . 5640 , d ) s . 5760 , e ) s . 6912
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1800 , investment needed = 64 × 3 × 1800 / 50 = 6912 answer : option e"
Answer: e
Question (gain): arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 15 % profit ?
Options: a ) 14.49 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 115 % of rs . 630 = 115 / 100 * 630 = rs . 724.5 s . p . per kg = 724.5 / 50 = 14.49 a"
Answer: a
Question (physics): one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in :
Options: a ) 180 min , b ) 144 min . , c ) 126 min , d ) 114 min , e ) 124 min
Rationale: explanation : let time taken by the faster pipe to fill the tank = x minutes . then , time taken by the slower pipe to fill the tank = 4 x minutes . time taken by both pipes together to fill the tank = x x 4 x / x + 4 x = 4 x / 5 4 x / 5 = 36 ⇒ x = 45 time taken by the slower pipe to fill the tank = 4 x = 180 minutes . answer : option a
Answer: a
Question (gain): carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 8 % . what is the approximate interest he pays annually ?
Options: a ) 1500 , b ) 1750 , c ) 2000 , d ) 3500 , e ) 2500
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 8 % of 10,000 which is $ 800 . so for the four quarters in the year , he will approximately play 800 * 4 = 3200 over the entire year . because of compound interest it will be more than 3200 . approx . option d is correct . answer : d"
Answer: d
Question (gain): a patient is given exactly 750 milliliters of a mixture of two medications daily . medication a contains 40 % pain killer and medication b contains 20 % pain killer . if the patient receives exactly 215 milliliters of pain killer daily , how many milliliters of medication b are in the mixture ?
Options: a ) 150 , b ) 225 , c ) 325 , d ) 425 , e ) 550
Rationale: let there be a milliliters of medication a and b milliliters of medication b a + b = 750 - - 1 medication a contains 40 % pain killer and medication b contains 20 % pain killer . ( 40 / 100 ) * a + ( 20 / 100 ) * b = 215 = > ( 2 / 5 ) * a + ( 1 / 5 ) * b = 215 multiplying by 5 , we get 2 a + b = 1075 - - 2 equation 2 - equation 1 , we get a = 325 b = 425 answer d
Answer: d
Question (physics): a train passes a platform in 18 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 120 , b ) 250 , c ) 260 , d ) 230 , e ) 220
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 18 = > 300 + l = 15 × 18 = 270 = > l = 390 - 270 = 120 meter answer is a ."
Answer: a
Question (general): let s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . find the sum of all elements in s ?
Options: a ) 1584 , b ) 7640 , c ) 5640 , d ) 7240 , e ) 6780
Rationale: s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . such numbers are , s = { 1 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 } sum of s = 1584 . answer : a
Answer: a
Question (physics): a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 5 km ?
Options: a ) 2.0 , b ) 2.5 , c ) 3.0 , d ) 3.5 , e ) 4.0
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 5 / 2 = 2.5 hours . the answer is b ."
Answer: b
Question (physics): if a tire rotates at 400 revolutions per minute when the car is traveling 48 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 2 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 48,000 m : c is the circumference c = 2 meters correct answer d"
Answer: d
Question (geometry): a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 200 , b ) 276 , c ) 230 , d ) 240 , e ) 250
Rationale: let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b
Answer: b
Question (general): find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1160 ?
Options: a ) rs . 1000 , b ) rs . 1100 , c ) rs . 1010 , d ) rs . 10000 , e ) none of these
Rationale: "explanation : 1160 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1000 answer : option a"
Answer: a
Question (general): 4 balls of different colors are to be placed in 3 different boxes such that any box contains at least 1 ball . what is the maximum number of different ways in which this can be done ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 180
Rationale: since the balls are all of different colors , let ' s permute them and then decide how many balls we put in each box . for example , arrange in a row the balls , then decide : two balls go into the first box , next two in the second box , and the last ball goes to the third box . since in each box there must be at least one ball , we have the possibilities of ( 2 , 2,1 ) , ( 2 , 1,2 ) , ( 1 , 2,2 ) or ( 3 , 1,1 ) , ( 1 , 3,1 ) , ( 1 , 1,3 ) balls in the three boxes . for the 2 , 2,1 type arrangements , we have [ 6 ! / ( 2 ! 2 ! 1 ! ) ] * 3 = 100 possibilities . inside a box , it does n ' t matter the order of the balls . for the 3 , 1,1 type arrangements , we have [ 6 ! / ( 3 ! 1 ! 1 ! ) ] * 3 = 80 possibilities . total of 100 + 80 = 180 possibilities . answer e .
Answer: e
Question (probability): if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 6 answer : a"
Answer: a
Question (general): find the ones digit of 73 ^ 300
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 330 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer e ."
Answer: e
Question (general): find the value of ( 0.75 * 0.75 * 0.75 - 0.001 ) / ( 0.75 * 0.75 - 0.075 + 0.01 )
Options: a ) 0.845 , b ) 0.849 , c ) 0.842 , d ) 0.828 , e ) 0.8419
Rationale: "0.845 answer : a"
Answer: a
Question (physics): a train passes a station platform in 36 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 ) 120 m , b ) 240 m , c ) 300 m , d ) 500 m , e ) 550 m
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 ) / 36 = 15 = > x = 240 m . answer b"
Answer: b
Question (physics): the length of the bridge , which a train 140 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 255 , b ) 267 , c ) 235 , d ) 277 , e ) 211
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 140 + x ) / 30 = 25 / 2 = > 2 ( 140 + x ) = 750 = > x = 235 m . answer : c"
Answer: c
Question (physics): working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 10 pages a minute more than printer a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1500
Rationale: answer : d .
Answer: d
Question (general): the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 183.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"
Answer: b
Question (general): whats the reminder when 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 is divided by 16
Options: a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 = 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 450,000 + 4,889 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 16 . 4889 / 16 gives remainder 9 . answer ( e )
Answer: e
Question (gain): you enter a weight loss challenge game and manage to lose 12 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 10.24 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 12 % ) * ( 100 % + 2 % ) = 0.88 * 1.02 = 10.24 % the weigh in records your weight loss at 10.24 % ! the answer is a"
Answer: a
Question (physics): if 20 men can build a water fountain 56 metres long in 14 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 21 m , b ) 24 m , c ) 27 m , d ) 29 m , e ) 30 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 14 : 3 : : 56 : x therefore ( 20 x 14 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 280 = 49 hence , the required length is 21 m . answer : a"
Answer: a
Question (general): if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , r will receive
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 * ( 6 / 31 ) = 150 * 6 = 900 . answer : option d"
Answer: d
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years , the age of the 15 th student is
Options: a ) 17 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 8 + 16 * 6 ) ] = 17 years . answer : a"
Answer: a
Question (other): if log 2 = 0.3010 and log 3 = 0.4771 then the value of log 4.5 is :
Options: a ) 0.6532 , b ) 0.7727 , c ) 0.3266 , d ) 0.3796 , e ) none of these
Rationale: "log 3 + log 3 = log ( 3 * 3 ) - > log 9 = 0.4771 + 0.4771 = 0.9542 now log 9 - log 2 = log ( 9 / 2 ) = log 4.5 - > log 4.5 = 0.9542 - 0.3010 = 0.6532 answer : a"
Answer: a