Cheukting/mathqa huggingface dataset:
Question (general): an alloy of copper and zinc contains copper and zinc in the ratio 5 : 4 . another alloy of copper and zinc contains copper and zinc in the ratio 3 : 6 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 4 : 1 , b ) 6 : 1 , c ) 1 : 3 , d ) 2 : 1 , e ) 4 : 1
Rationale: let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 5 x / 9 , and fraction of zinc in alloy _ 1 = 4 x / 9 . similarly , fraction of copper in alloy _ 2 = 3 y / 9 , and fraction of zinc in alloy _ 2 = 6 y / 9 . mixing them , we get copper = 5 x / 9 + 3 y / 9 ; zinc = 4 x / 9 + 6 y / 9 so , 5 x + 3 y = 4 x + 6 y - > x = 3 y - > x / y = 1 / 3 so , they must be mixed in the ratio 1 : 3 answer : c
Answer: c
Question (geometry): find the area of a parallelogram with base 26 cm and height 14 cm ?
Options: a ) 287 cm 2 , b ) 887 cm 2 , c ) 364 cm 2 , d ) 368 cm 2 , e ) 668 cm 2
Rationale: "area of a parallelogram = base * height = 26 * 14 = 364 cm 2 answer : c"
Answer: c
Question (gain): after decreasing 24 % in the price of an article costs rs . 532 . find the actual cost of an article ?
Options: a ) 118 , b ) 677 , c ) 700 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 532 cp = 7 * 100 = > cp = 700 answer : c"
Answer: c
Question (physics): a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 25 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 108 , d ) 55 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 25 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 25 = 180 / 4 t t = 108 b - c = 108 mph answer c"
Answer: c
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 44.5 meters . how many times did the ball bounce ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "division of total diatance travelled will be 16 + 16 + 8 + 4 + 0.5 ans : 4"
Answer: a
Question (general): of 70 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 90 thrower = 37 rest = 90 - 37 = 33 left handed = 33 / 3 = 11 right handed = 22 if all thrower are right handed then total right handed is 37 + 22 = 59 so c . 59 is the right answer"
Answer: c
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 5 per sq m ?
Options: a ) 675 , rs . 3375 , b ) 575 , rs . 1350 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 5 = rs . 3375 answer : a"
Answer: a
Question (general): an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 4 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 1 ) to be divisible by 4 either n or n + 1 must be a multiples of 4 . in each following group of numbers : { 1 , 2 , 3 , 4 } , { 5 , 6 , 7 , 8 } , . . . , { 97 , 98 , 99 , 100 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 , 4 } n can be : 3 , or 4 . thus , the overall probability is 2 / 4 = 1 / 2 . answer : c ."
Answer: c
Question (general): the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 31 , e ) 35
Rationale: let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . option a
Answer: a
Question (general): an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 1400 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "since 70 % is accepted and figure will be 1400 therefore in last stage tested / interviewed no . candidates should be 2000 so from here i will work for those two steps of decrements of 100000 candidates . fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 . . . here we are done with total 5 steps and last step of accepting 70 % of 2000 = 1400 ( our target ) total 6 steps required . answer : c"
Answer: c
Question (physics): express a speed of 342 kmph in meters per second ?
Options: a ) 10 mps , b ) 59 mps , c ) 79 mps , d ) 90 mps , e ) 19 mps
Rationale: "342 * 5 / 18 = 90 mps answer : d"
Answer: d
Question (general): how many positive integers less than 50 are multiples of 3 but not multiples of 5 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "imo the answer is c ( 8 numbers ) the lcm of 3 and 5 is 15 . if x < 50 and x is divisible by 3 not by 5 - - > x is not divisible by 15 . from 1 - - > 50 , we have 3 numbers which is divisible by 15 : 15 , 30 , 45 . from 1 - - > 50 , we have ( 45 - 3 ) / 3 + 1 = 15 numbers divisible by 3 . therefore , our answer is 15 - 3 = 12 numbers . e"
Answer: e
Question (general): out of 9 persons , 8 persons spent rs . 30 each for their meals . the ninth one spent rs . 20 more than the average expenditure of all the 9 . the total money spent by all of them was
Options: a ) rs . 292.50 , b ) rs . 297.50 , c ) rs . 298 , d ) rs . 298.50 , e ) none of these
Rationale: explanation : let the average expenditure be rs . x then , 9 x = [ 8 × 30 + ( x + 20 ) ] ⇔ 9 x = x + 260 ⇔ x = 32.50 total money spent = 9 x = rs . ( 9 x 32.5 o ) = rs 292 . 50 answer : a
Answer: a
Question (general): a driver just filled the car ' s gas tank with 36 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 36 ) + x = 0.1 ( 36 + x ) 0.9 x = 3.6 - 1.8 = 1.8 x = 2 liters the answer is c ."
Answer: c
Question (geometry): a cylinder and a cone have the same height and same radius of base . the ratio between the volumes of the cylinder and the cone is :
Options: a ) 4 : 1
b ) 2 : 1
c ) 7 : 1
d ) 5 : 1
e ) 3 : 1
Rationale: volume of the cylinder = π r ( power 2 ) h volume of the cone = 1 / 3 π r ( power 2 ) h ( π r ( power 2 ) h ) / ( 1 / 3 π r ( power 2 ) h ) = 3 / 1 = 3 : 1 answer is e .
Answer: e
Question (physics): when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in f hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of f ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * f = 1 = > x = 1 / f when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / f = 4 / 3 = > 1 / f = ( 8 - 3 ) / 6 = 5 / 6 = > f = 6 / 5 = 1 [ 1 / 5 ] answer b
Answer: b
Question (gain): a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,054 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1054 / 1000 ) - 1 = 0.054 = 5.4 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.054 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.054 - 0.01 x = - 0.006 x = - 0.006 / - 0.01 = 6 / 10 = 60 % so x = 60 % of the 1000 which is 600 answer : b
Answer: b
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 192 in 4 years ?
Options: a ) 5 % , b ) 6 % , c ) 3 % , d ) 9 % , e ) 1 %
Rationale: "192 = ( 800 * 4 * r ) / 100 r = 6 % answer : b"
Answer: b
Question (general): the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 45 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 17 , b ) 18 , c ) 22 , d ) 26 , e ) 36
Rationale: "the total sum of the numbers should be increased by 20 . then the average will increase by 20 / 10 = 2 . the correct average is 18 . the answer is b ."
Answer: b
Question (gain): what percent of 15 is 15 percent of 1 ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 1 , e ) 101
Rationale: "15 % of 1 = ( 15 / 100 ) * 1 = 15 / 100 to determine what percentage of 15 this is : [ 15 ] [ / 100 * 15 ] * 100 = 1 % ans : d"
Answer: d
Question (physics): two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 70 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 120 , d ) 80 , e ) 105
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 80 kmph , speed of b must be 70 * ( 3 / 2 ) = 105 kmph e"
Answer: e
Question (general): 7528 : 5306 : : 4673 : ?
Options: a ) 2351 , b ) 2451 , c ) 2551 , d ) 2651 , e ) 2751
Rationale: "as there is a difference of 2222 . 7528 - 2222 = 5306 . so 4673 - 2222 = 2451 answer : b"
Answer: b
Question (general): in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 90 % people got computers and 85 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 20 %
Rationale: "e 10 % 100 - [ ( 100 - 85 ) + ( 100 - 90 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 10 + 15 ) = 100 - 80"
Answer: e
Question (general): a merchant has selected two items to be placed on sale , one of which currently sells for 20 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 23 % , b ) 24 % , c ) 25 % , d ) 26 % , e ) 27 %
Rationale: expensive item = $ 100 ; cheap item = $ 80 ; we must increase $ 80 to $ 100 , so by $ 20 , which is 25 % increase : ( 100 - 80 ) / 80 = 1 / 4 = 0.25 answer : c .
Answer: c
Question (geometry): what is the ratio between perimeters of two squares one having 5 times the diagonal then the other ?
Options: a ) 5 : 1 , b ) 3 : 1 , c ) 5 : 8 , d ) 3 : 2 , e ) 8 : 3
Rationale: "d = 5 d d = d a √ 2 = 5 d a √ 2 = d a = 5 d / √ 2 a = d / √ 2 = > 5 : 1 answer : a"
Answer: a
Question (geometry): find the area of a parallelogram with base 48 cm and height 36 cm ?
Options: a ) 1730 cm 2 , b ) 1728 cm 2 , c ) 1870 cm 2 , d ) 1890 cm 2 , e ) 668 cm 2
Rationale: "area of a parallelogram = base * height = 48 * 36 = 1728 cm 2 answer : b"
Answer: b
Question (physics): a and b complete a work in 3 days . a alone can do it in 9 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 4.75 days , c ) 3.25 days , d ) 3.15 days , e ) 2.75 days
Rationale: "1 / 3 + 1 / 9 = 4 / 9 9 / 4 = 4.75 days answer : b"
Answer: b
Question (probability): a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 8 from part a & 5 from part b , in how many ways can he choose the questions ?
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 1140
Rationale: there 10 questions in part a out of which 8 question can be chosen as = 10 c 8 . similarly , 5 questions can be chosen from 10 questions of part b as = 10 c 5 . hence , total number of ways , = 10 c 8 * 10 c 5 = [ 10 ! / ( 2 ! 8 ! ) ] * [ 10 ! / ( 5 ! * 5 ) ] = { 10 * 9 / 2 } * { 10 * 9 * 8 * 7 * 6 / ( 5 * 4 * 3 * 2 * 1 ) } = 1140 . e
Answer: e
Question (general): what must be added to each term of the ratio 4 : 15 , so that it may become equal to 3 : 4 ?
Options: a ) 18 , b ) 29 , c ) 39 , d ) 49 , e ) 59
Rationale: "let x be added to each term of the ratio 4 : 15 . new ratio becomes ( 4 + x ) / ( 15 + x ) , which is given to be equal to 3 : 4 . this means , ( 4 + x ) / ( 15 + x ) = 3 / 4 solving we get , x = 29 . ans b"
Answer: b
Question (general): what is the greatest prime factor of ( 11 ! × 10 !   + 10 ! × 9 ! ) / 111 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: ( 11 ! × 10 !   + 10 ! × 9 ! ) / 111 in numerator take out 10 ! * 9 ! as common term 10 ! ∗ 9 ! ( 11 × 10   + 1 ) / 111 10 ! ∗ 9 ! ∗ 111 / 111 10 ! ∗ 9 ! 10 ! has 7 as the greatest prime factor , so ans is 7 answer : d
Answer: d
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1000 more than d , what is b ' s share ?
Options: a ) 4000 , b ) 5000 , c ) 2000 , d ) 1000 , e ) 6000
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1000 x = 1000 . b ' s share = rs . 2 x = rs . ( 2 x 1000 ) = rs . 2000 . answer is c ."
Answer: c
Question (general): there are 11 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "11 c 2 = 55 the answer is d ."
Answer: d
Question (general): the average of 10 numbers was calculated as 17 . it is discovered later on that while calculating the average , one number , namely 56 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: 10 * 17 - 26 + 56 = 200 200 / 10 = 20 the answer is b .
Answer: b
Question (general): the average of 6 observations is 15 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 8 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 90 + x ) / 7 = 14 = > x = 8 hence , the seventh observation is 8 answer : b"
Answer: b
Question (other): a bag holds 4 red marbles and 4 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 3 / 14 , d ) 2 / 7 , e ) 1 / 2
Rationale: "probability of selecting first red marble = 4 / 8 probability of selecting second red marble without replacement = 3 / 7 final probability = 4 / 8 * 3 / 7 = 3 / 14 the correct answer is c ."
Answer: c
Question (physics): a motorcyclist goes from bombay to pune , a distance of 288 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 1 : 4 , d ) 2 : 3 , e ) 1 : 8
Rationale: "t = 288 / 32 = 9 h t = 9 - 3 = 6 time ratio = 9 : 6 = 3 : 2 speed ratio = 2 : 3 answer : d"
Answer: d
Question (geometry): what is the area of square field whose side of length 5 m ?
Options: a ) 80 sq m , b ) 26 sq m , c ) 25 sq m , d ) 45 sq m , e ) 96 sq m
Rationale: "5 * 5 = 25 sq m answer : c"
Answer: c
Question (general): if 25 % of x is 30 less than 15 % of 1500 , then x is ?
Options: a ) 872 , b ) 738 , c ) 837 , d ) 780 , e ) 83
Rationale: "25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 30 = > x / 4 = 195 = > x = 780 . answer : d"
Answer: d
Question (gain): by selling an article at rs . 1000 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 500 , d ) s . 450 , e ) s . 550
Rationale: "sp = 1000 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 1000 * [ 100 / 125 ] = 800 loss = 25 % = 25 % of 800 = rs . 200 sp = cp - loss = 800 - 200 = rs . 600 answer : a"
Answer: a
Question (physics): if the population of a certain country increases at the rate of one person every 20 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 180 , e ) 160
Rationale: "answer = 3 * 60 = 180 answer is d"
Answer: d
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 40 , and 50 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 11 , b ) 1 / 2 , c ) 15 / 22 , d ) 200 / 9 , e ) 11 / 4
Rationale: "p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 40 + 1 / 50 = 9 / 200 therefore they take 200 / 9 ratio = 200 / 9 = d"
Answer: d
Question (probability): jane and thomas are among the 9 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 9 people if at least one of either jane or thomas is to be selected ?
Options: a ) 67 , b ) 73 , c ) 79 , d ) 85 , e ) 91
Rationale: "the total number of ways to choose 4 people from 9 is 9 c 4 = 126 . the number of committees without jane or thomas is 7 c 4 = 35 . there are 126 - 35 = 91 possible committees which include jane and / or thomas . the answer is e ."
Answer: e
Question (general): albert is 2 times mary ’ s age and 4 times as old as betty . mary is 22 years younger than albert . how old is betty ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 15 , e ) 18
Rationale: "a = 2 m = m + 22 m = 22 a = 44 a = 4 b , and so b = 11 the answer is c ."
Answer: c
Question (physics): a train speeds past a pole in 10 seconds and a platform 150 m long in 25 seconds . its length is :
Options: a ) 300 m . , b ) 250 m . , c ) 100 m . , d ) 200 m . , e ) 150 m .
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 150 / 25 = x / 10 x = 100 m . answer : option c"
Answer: c
Question (geometry): the perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 40 , b ) b ) 828 , c ) c ) 729 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 32 / 2 = 40 cm 2 answer : option a"
Answer: a
Question (general): two brother x and y appeared for an exam . the probability of selection of x is 1 / 5 and that of b is 2 / 3 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 20 , c ) 2 / 18 , d ) 2 / 29 , e ) 2 / 15
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 5 , p ( b ) = 2 / 3 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 5 ) ã — ( 2 / 3 ) = 2 / 15 answer : e ) 2 / 15"
Answer: e
Question (general): what is the smallest number which when increased by 7 is divisible by 25 , 49 , 15 , and 21 ?
Options: a ) 3,551 , b ) 3,668 , c ) 3,733 , d ) 3,822 , e ) 3,957
Rationale: "first factor each of 25 , 49 , 15 , and 21 into primes : 25 = 5 * 5 ; 49 = 7 * 7 ; 15 = 3 * 5 ; 21 = 3 * 7 the smallest number divisible by each of the numbers is 3 * 5 * 5 * 7 * 7 = 3,675 3,675 - 7 = 3,668 thus 3,668 + 7 is the smallest number divisible by 25 , 49 , 15 , and 21 b"
Answer: b
Question (general): at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 10 . if the price per share of stock k was $ 15 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 50 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %
Rationale: opening = 10 closing = 15 rise in price = 5 so , percent increase = 5 / 10 * 100 = 50 % answer : b
Answer: b
Question (general): find the least number which when divided by 5 , 6,7 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder .
Options: a ) 1638 , b ) 1863 , c ) 1683 , d ) 1836 , e ) none of them
Rationale: "l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is c ."
Answer: c
Question (physics): a can give b 100 meters start and c 150 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 10.55 meters , b ) 11.55 meters , c ) 33.55 meters , d ) 55.55 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 850 meters . therefore , b runs 900 meters while c runs 850 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 850 ) / 900 = 944.44 meters thus , b can give c ( 1000 - 944.44 ) = 55.55 meters start answer : d"
Answer: d
Question (general): if 213 × 16 = 3408 , then 1.6 × 2.13 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 1.6 × 2.13 = ( 16 / 10 x 213 / 100 ) = ( 16 x 213 / 1000 ) = 3408 / 100 = 3.408 . answer b"
Answer: b
Question (general): in how many no . between 100 and 1000 exactly one of the digits is 3 ?
Options: a ) 648 , b ) 512 , c ) 252 , d ) 225 , e ) 26
Rationale: "3 scenarios possible 3 xy = 1 * 9 * 9 = 81 x 3 y ( with x ≠ ≠ 3 or 0 ) = 8 * 1 * 9 = 72 y 3 x ( with y ≠ ≠ 3 or 0 ) = 8 * 1 * 9 = 72 total cases possible = 144 + 81 = 225 d is the correct answer"
Answer: d