Cheukting/mathqa huggingface dataset:
Question (general): if 5 x = 6 y and xy ≠ 0 , what is the ratio of 1 / 4 * x to 1 / 6 * y ?
Options: a ) 25 / 6 , b ) 36 / 25 , c ) 9 / 5 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 6 y = > x / y = 6 / 5 1 / 4 * x to 1 / 6 * y = x / y * 3 / 2 = ( 6 / 5 ) * ( 3 / 2 ) = 9 / 5 ans : c"
Answer: c
Question (other): the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 4 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 6 : 5 , d ) 3 : 6 , e ) 3 : 8
Rationale: "4 : 5 3 : 4 - - - - - - - 12 : 15 : 20 12 : 20 - - - - - - > 6 : 10 3 : 5 answer : b"
Answer: b
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1200 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 24,750 , c ) rs . 15,600 , d ) rs . 16,500 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1200 x 20.625 ) = rs . 24,750 . answer b"
Answer: b
Question (physics): a man sitting in a train which is travelling at 80 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 80 kmph . , e ) 32 kmph .
Rationale: solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 80 ) kmph = 32 kmph . answer e
Answer: e
Question (physics): three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 20 minutes . if a , b & c are kept open successively for 1 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 1 hour 30 min , d ) 5 hours , e ) 6 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 20 = 2 / 60 = 1 / 30 part is filled 3 min - - - - - - - - 1 / 30 parts x min - - - - - - - - - 1 part ( full ) x = 90 min = 1 hour 30 min answer : c"
Answer: c
Question (general): how many zeroes are there at the end of the number n , if n = 70 ! + 140 ! ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "the number of zeroes at the end of 70 ! will be less than the number of zeroes at the end of 140 ! hence it is sufficient to calculate the number of zeroes at the end of 70 ! the number of zeroes = [ 70 / 5 ] + [ 70 / 25 ] + [ 70 / 125 ] = 14 + 2 + 0 = 16 the answer is c ."
Answer: c
Question (physics): x can finish a work in 25 days . y can finish the same work in 20 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 25 work done by y in 1 day = 1 / 20 work done by y in 12 days = 12 / 20 = 3 / 5 remaining work = 1 – 3 / 5 = 2 / 5 number of days in which x can finish the remaining work = ( 2 / 5 ) / ( 1 / 20 ) = 8 e"
Answer: e
Question (gain): a , b and c invested rs . 6000 , rs . 7200 and rs . 10800 respectively , in a partnership business . find the share of c in profit of rs . 19000 after a year ?
Options: a ) 3630 , b ) 5580 , c ) 19000 , d ) 8550 , e ) 6000
Rationale: "explanation : 6000 : 7200 : 10800 5 : 6 : 9 9 / 20 * 19000 = 8550 answer : d"
Answer: d
Question (general): if 15 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 60
Rationale: "let x be the number of students in the school . 0.15 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.15 x / 0.25 = 0.6 x students went to the camping which is 60 % . the answer is e"
Answer: e
Question (general): an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 80 , b ) 88 , c ) 94 , d ) 112 , e ) 124
Rationale: "we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 150 = - 14 ( 4 ) + 150 = 94 the answer is c ."
Answer: c
Question (general): a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on convenience he has rs . 1400 left with him , find his expenditure on food and conveyance .
Options: a ) 1000 , b ) 3000 , c ) 4000 , d ) 2000 , e ) 5000
Rationale: "part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) let the monthly salary be rs . x then , 7 / 40 of x = 1400 x = ( 1400 * 40 / 7 ) = 8600 expenditure on food = rs . ( 3 / 10 * 800 ) = rs . 2400 expenditure on conveyance = rs . ( 1 / 8 * 8000 ) = rs . 1000 answer is a ."
Answer: a
Question (geometry): how many cones of radius 4 m , height 2 m can be formed from a cylinder of 12 m radius , 10 m height :
Options: a ) 135
b ) 125
c ) 145
d ) 115
e ) 155
Rationale: ( cylinder volume ) / ( cone volume ) ( π r ( power 2 ) h ) / ( 1 / 3 π r ( power 2 ) h ) = ( π × 12 × 12 × 10 ) / ( 1 / 3 π × 4 × 4 × 2 ) = 135 answer is a .
Answer: a
Question (general): the denominator of a fraction is 7 greater than the numerator . if the numerator and the denominator are increased by 4 , the resulting fraction is equal to 5 â  „ 6 . what is the value of the original fraction ?
Options: a ) 23 / 30 , b ) 25 / 32 , c ) 31 / 38 , d ) 37 / 44 , e ) 47 / 54
Rationale: "let the numerator be x . then the denominator is x + 7 . x + 4 / x + 11 = 5 / 6 . 6 x + 24 = 5 x + 55 . x = 31 . the original fraction is 31 / 38 . the answer is c ."
Answer: c
Question (general): the average of 11 numbers is 500 . out of 11 numbers the average of first 6 no . is 50 , and last 6 numbers is 60 then find 6 th number ?
Options: a ) 95 , b ) 80 , c ) 110 , d ) 120 , e ) 72
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 50 + 6 * 60 - 11 * 50 = 110 answer is c"
Answer: c
Question (gain): 70 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 105 , d ) 30 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 70 + 50 % ( 70 ) = 70 + 35 = 105 . answer c"
Answer: c
Question (other): in a group of 8 semifinalists , all but 2 will advance to the final round . if in the final round only the top 3 will be awarded medals , then how many groups of medal winners are possible ?
Options: a ) 20 , b ) 56 , c ) 120 , d ) 560 , e ) 720
Rationale: 1 ) is it important here that how many go into finals . . . no . . . . what is important is how many get medals . . 3 finally these 3 can be any of the 8 - 8 c 3 = 8 ! 5 ! 3 ! = 8 ∗ 7 ∗ 63 ∗ 2 = 568 c 3 = 8 ! 5 ! 3 ! = 8 ∗ 7 ∗ 63 ∗ 2 = 56 2 ) is order important . . . no we are looking for groups only . . ans 56 answer : b
Answer: b
Question (gain): martha has the unique talent of being able to guess other people ’ s height and weight . for every 6 people that martha meets , she consistently guesses the people ’ s correct height 5 times , and for every 8 people that she meets , she consistently guesses the people ’ s correct weight 6 times . if martha meets 3 people and her success rate remains constant , what is the probability that martha correctly guesses a person ’ s weight and height at least once ?
Options: a ) 8 / 27 , b ) 2 / 5 , c ) 485 / 512 , d ) 98 / 125 , e ) 625 / 952
Rationale: probability that she guesses the height correctly p ( h ) = 5 / 6 probability that she guesses the weight correctlyp ( w ) = 6 / 8 probability that she guesses both weight and height correctly ( p ( h ) * p ( w ) ) = 5 / 6 * 6 / 8 = 30 / 48 now the q asks about the probability of this happening atleast once . we calculate it by finding the probability of not being able to guess in any of the three occasions . probability of not being able to guess any no . of times = 1 - 30 / 48 = 18 / 48 = 3 / 8 for all three occasions p ( a ) = 3 / 8 * 3 / 8 * 3 / 8 = 27 / 512 probability of the event happening atleast once = 1 - p ( a ) = 1 - 27 / 512 = 485 / 512 ans should be c
Answer: c
Question (other): the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 90 black cars in the lot , how many red cars are there in the lot ?
Options: a ) 11 , b ) 33 , c ) 24 , d ) 27 , e ) 32
Rationale: b is correct r / b = 3 / 8 and b = 90 r = 90 * 3 / 8 = 33
Answer: b
Question (general): ages of two persons differ by 20 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 16,36 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 20 ) = > 3 ( x - 6 ) = ( x + 20 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 14 = > x = 16 so other person age is x + 20 = 36 answer : option c"
Answer: c
Question (other): a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 25 / 36 . how many marbles are in the bag ?
Options: a ) 24 , b ) 48 , c ) 60 , d ) 72 , e ) 84
Rationale: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 25 / 36 - - > ( x - 12 ) ^ 2 = 25 / 36 x ^ 2 square rooting u have x - 12 / x = 5 / 6 or 6 x - 72 = 5 x therefore x = 72 b"
Answer: b
Question (gain): a bowl was filled with 10 ounces of water , and 0.004 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 2 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 004 * 50 = . 004 * 100 / 2 = . 4 / 2 = . 2 percent of the original amount of water evaporated during this period = ( . 2 / 10 ) * 100 % = 2 % answer d"
Answer: d
Question (general): of the families in city x in 1994 , 35 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 20 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . what percent of the families in city x owned a personal computer in 1998 ?
Options: a ) 50.12 % , b ) 40.52 % , c ) 40.56 % , d ) 40.38 % , e ) 40.14 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 35 * 120 / 100 = 42 number of families in 1998 = 104 the percentage = 42 / 104 * 100 = 40.38 % . option : d"
Answer: d
Question (geometry): the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none
Rationale: "solution 4 π r 2 = 2 π 6 x 12 ⇒ r 2 = ( 6 x 12 / 2 ) ⇒ 36 ⇒ r = 6 cm . answer c"
Answer: c
Question (geometry): the area of a parallelogram is 72 sq m and its base is 12 m . then the length of the height is ?
Options: a ) 6 m , b ) 7 m , c ) 60 m , d ) 13 m , e ) none
Rationale: b * h = 72 . h * 12 = 72 = > h = 6 m . answer : ( a )
Answer: a
Question (physics): a fort had provision of food for 150 men for 45 days . after 15 days , 10 men left the fort . the number of days for which the remaining food will last , is :
Options: a ) 32 , b ) 37 1 / 4 , c ) 42 , d ) 54 , e ) 45
Rationale: "we have food for 150 men for 45 days . after 15 days food left for 150 men for 30 days . so 150 : 30 now we have 140 men and x days 140 : 150 : : 30 : x x = ( 150 * 30 ) / 140 = 32 days . answer : a"
Answer: a
Question (general): the sum of the ages of 5 children born at the intervals of 3 year each is 60 year . what is the age of the youngest child ?
Options: a ) 4 year , b ) 6 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 â ‡ ” 5 x = 30 â ‡ ” x = 6 . â ˆ ´ age of the youngest child = x = 6 years . answer b"
Answer: b
Question (other): a set of pictures of butterflies contains 10 pictures . jim bought 3 of the pictures . if 2 pictures are to be picked out from the 10 pictures , what is the probability that both pictures are not those that were already bought by jim ?
Options: a ) 14 / 15 , b ) 3 / 5 , c ) 6 / 13 , d ) 7 / 15 , e ) 7 / 10
Rationale: probability of first pick not one of the jim ' s picture is = 7 / 10 ( except for 3 which jim purchased ) probability of second pick not one of the jim ' s picture is = 6 / 9 total = 7 / 10 ∗ 6 / 9 = 7 / 15 answer is d option d
Answer: d
Question (general): maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability q , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , q = 9 provide the desired outcome , making the answer e .
Answer: e
Question (physics): a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 15 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 1650 , b ) 2750 , c ) 3850 , d ) 4950 , e ) 6050
Rationale: "the distance the sound traveled to the man is 15 * 330 = 4950 meters the answer is d ."
Answer: d
Question (physics): eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 510 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 34 / 15
Rationale: distance traveled by eddy = 510 km time taken by eddy = 3 hours average speed of eddy = 510 / 3 = 170 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 170 / 75 = 34 / 15 answer e
Answer: e
Question (general): two brothers ram and ravi appeared for an exam . the probability of selection of ram is 4 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 4 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 4 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 4 / 7 x 1 / 5 = 4 / 35 answer : a
Answer: a
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 12 m wide at the top and 2 m wide at the bottom and the area of cross - section is 4200 sq m , the depth of cannel is ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "1 / 2 * d ( 12 + 2 ) = 4200 d = 600 answer : b"
Answer: b
Question (other): 120 kg of an alloy a is mixed with 180 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 120.3 kg , c ) 139.5 kg , d ) 140.8 kg , e ) 114.5 kg
Rationale: "quantity of tin in 120 kg of a = 120 * 3 / 5 = 72 kg quantity of tin in 180 kg of b = 180 * 3 / 8 = 67.5 kg quantity of tin in the new alloy = 72 + 67.5 = 139.5 kg answer is c"
Answer: c
Question (physics): how many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 17 sec , b ) 21 sec , c ) 25 sec , d ) 27 sec , e ) 29 sec
Rationale: "d = 120 + 150 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec"
Answer: d
Question (general): 3 / 4 of a number is 19 less than the original number . the number is ?
Options: a ) 84 , b ) 64 , c ) 76 , d ) 72 , e ) none
Rationale: answer let the original number be n . so from question n - 3 n / 4 = 19 ⇒ 4 n - 3 n = 76 ∴ n = 76 option : c
Answer: c
Question (gain): the cost price of 40 articles is the same as the selling price of x articles . if the profit is 25 % , what is x ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "let the cost price = y the cost price of 40 articles = 40 y the selling price of x articles = 1.25 y * x 1.25 y * x = 40 y x = 40 / 1.25 = 32 the answer is d ."
Answer: d
Question (physics): a man can row 6 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 4.5 , c ) 5.76 , d ) 5.74 , e ) 5.71
Rationale: "m = 6 s = 3 ds = 9 us = 3 x / 9 + x / 3 = 1 x = 2.25 d = 2.25 * 2 = 4.5 answer : b"
Answer: b
Question (gain): the interest on a certain deposit at 4.5 % p . a . is rs . 202.50 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a ?
Options: a ) rs . 20.25 , b ) rs . 22.50 , c ) rs . 25 , d ) rs . 42.75 , e ) none
Rationale: "solution s . i = rs . 202.50 , r = 4.5 % , t = 1 year principal = rs ( 100 * 202.50 / 4.5 * 1 ) = rs . 4500 now p = rs . 4500 , r = 5 % , t = 1 year s . i = ( 4500 * 5 * 1 / 100 ) = rs . 225 different in interest = rs . ( 225 - 202.50 ) = rs . 22.50 answer b"
Answer: b
Question (general): ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 5.0 = ?
Options: a ) - 0.852 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.852 answer a"
Answer: a
Question (general): what is the remainder when 12987 ^ ( 65987036 ) is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 65987036 has the form 4 a , the units digit is 1 . then the remainder when dividing by 5 is 1 . the answer is b ."
Answer: b
Question (physics): if the wheel is 12 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 26 , c ) 14 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 12 * x = 1056 = > x = 14 answer : c"
Answer: c
Question (geometry): if the length and breadth of a rectangular room are each increased by 1 m , then the area of floor is increased by 21 sq . m . if the length is creased by 1 m and breadth is decreased by 1 m , then the area is decreased by 5 sq . m . the perimeter of the floor is :
Options: a ) 27
b ) 35
c ) 40
d ) 49
e ) 38
Rationale: let length = x meters and breadth = y meters . then , ( x + 1 ) ( y + 1 ) - xy = 21 x + y = 20 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ 1 and , xy - [ ( x + 1 ) ( y - 1 ) ] = 5 x - y = 6 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ . . 2 solving ( i ) and ( ii ) , we get : x = 13 and y = 7 so , length = 13 m and breadth = 7 m . perimeter = [ 2 ( 13 + 7 ) ] m = 40 m . answer : c
Answer: c
Question (physics): a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :
Options: a ) 30 minutes , b ) 1 hour , c ) 2 hours , d ) 3 hours , e ) none of these
Rationale: explanation : new speed = 4 / 5 th of its actual speed new time = 5 / 4 th of its actual time = > 5 / 4 t - t = 15 / 60 = 1 / 4 = > 1 / 4 t = 1 / 4 = > t = 1 hour answer : b
Answer: b
Question (general): the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 36.67 , c ) 88 , d ) 13 , e ) 12
Rationale: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 30 matches = 1100 . average score of the batsman = 1100 / 30 = 36.67 . answer : b"
Answer: b
Question (probability): the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability t that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . t = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Question (general): anne bought doughnuts for a class breakfast party . she bought 6 chocolate doughnuts , 8 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 6 + 8 + 8 = 22 . answer is a ."
Answer: a
Question (gain): i sold a book at a profit of 10 % . had i sold it for $ 110 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2200 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: 115 % of cost - 110 % of cost = $ 110 5 % of cost = $ 110 cost = 110 * 100 / 5 = $ 2200 answer is b
Answer: b
Question (geometry): find the perimeter and area of the rectangle of length 19 cm and breadth 13 cm .
Options: a ) 71 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 171 cm 2 , e ) 247 cm 2
Rationale: "length = 19 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 19 + 13 ) cm = 2 × 32 cm = 64 cm we know that the area of rectangle = length × breadth = ( 19 × 13 ) cm 22 = 247 cm 2 answer : e"
Answer: e
Question (general): 90 % of the population of a village is 36000 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 40000
Rationale: "x * ( 90 / 100 ) = 36000 x = 400 * 100 x = 40000 answer : e"
Answer: e