Cheukting/mathqa huggingface dataset:
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 90 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 4 sec , d ) 2.8 , e ) 2.1
Rationale: "speed = 90 * 5 / 18 = 25 m / sec time taken = 100 / 25 = 4 sec . answer : c"
Answer: c
Question (general): if the number is divided by 3 , it reduced by 34 . the number is
Options: a ) 51 , b ) 50 , c ) 45 , d ) 40 , e ) 36
Rationale: explanation : let the number be x . then , x - ( x / 3 ) = 34 = > 2 x / 3 = 34 = > x = 51 answer : option a
Answer: a
Question (general): if a train runs at 40 kmph , it reach its destination late by 11 minutes but if it runs at 50 kmph it is late by 5 minutes only . the correct time for a train to complete its journey is ? let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min
Options: a ) 19 min , b ) 19 hrs , c ) 52 min , d ) 126 min , e ) 52 min
Rationale: let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )
Answer: a
Question (probability): how many cubes of 8 cm edge can be cut out of a cube of 16 cm edge
Options: a ) 36 , b ) 2 , c ) 8 , d ) 48 , e ) none of these
Rationale: "explanation : number of cubes = ( 16 x 16 x 16 ) / ( 8 x 8 x 8 ) = 8 answer : c"
Answer: c
Question (other): share rs . 5400 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 1800 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400
Rationale: "amount received by sanjay . 4 / 12 x 5400 = 1800 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1800 . a"
Answer: a
Question (geometry): a room is a square of side 50 feet . a second room is of area 100 square yards . a third room is of area 200 square feet . which of these can seat maximum people ? ( hint : 1 yard = 3 feet )
Options: a ) 200 sq feet , b ) 300 sq feet , c ) 400 sq feet , d ) 500 sq feet , e ) 600 sq feet
Rationale: first room because area 50 * 50 = 2500 sq feet second room area 100 sq yard in feet 300 sq feet third room area 200 sq feet answer : a
Answer: a
Question (gain): alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ?
Options: a ) 5 : 4 , b ) 4 : 3 , c ) 18 : 11 , d ) 3 : 2 , e ) 18 : 13
Rationale: alex invests rs . 7000 for 18 months , but brian invests rs . 7000 for the first 8 months and then withdraws rs . 3500 . so , the investment of brian for remaining 10 months is rs . 3500 only . alex : brian 7000 * 18 : ( 7000 * 8 ) + ( 3500 * 10 ) 126000 : 91000 alex : brian = 18 : 13 answer : e
Answer: e
Question (other): of the people who responded to a market survey , 240 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 6 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 280 , d ) 360 , e ) 480
Rationale: "ratio = 6 : 1 = > 6 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 240 = > 6 x = 240 = > x = 40 hence total no . of respondents = 240 + 40 = 280 hence c is the answer ."
Answer: c
Question (geometry): a block of wood has dimensions 10 cm x 10 cm x 40 cm . the block is painted red and then cut evenly at the 20 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "the area of each half is 100 + 4 ( 200 ) + 100 = 1000 the area that is not painted is 100 . the fraction that is not painted is 100 / 1000 = 1 / 10 = 10 % the answer is b ."
Answer: b
Question (physics): two trains 119 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.17 , c ) 7.2 , d ) 7.15 , e ) 7.05
Rationale: "t = ( 119 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.05 answer : e"
Answer: e
Question (general): if an integer e is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that e ( e + 1 ) ( e + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: for e total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d
Answer: d
Question (physics): if 20 men can build a wall 66 metres long in 10 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 227.04 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 10 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 10 * 20 ) = 227.04 mtrs answer : a"
Answer: a
Question (general): if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 9 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 9 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 9 hence x = 11 . answer is b"
Answer: b
Question (physics): by travelling at 60 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 30 kmph , b ) 28 kmph , c ) 26 kmph , d ) 24 kmph , e ) 22 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 60 * 3 x = 180 x km he covered 2 / 3 * 180 x = 120 x km in 1 / 3 * 3 x = x hours so , the remaining 60 x km , he has to cover in 2 x hours . required speed = 60 x / 2 x = 30 kmph . answer : a"
Answer: a
Question (gain): a candidate got 35 % of the votes polled and he lost to his rival by 2430 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 8100 , d ) 2888 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2430 100 % - - - - - - - - - ? = > 8100 answer : c"
Answer: c
Question (general): if the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 52 , c ) 59 , d ) 68 , e ) 73
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 65 = 325 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 325 i . e . 5 a = 315 i . e . a = 63 i . e . largest e = 63 + 10 = 73 answer : option e"
Answer: e
Question (physics): p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 20 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 22 , c ) 25 , d ) 27 , e ) 40
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 20 work done by p , q and r in 1 day = 1 / 10 + 1 / 20 = 3 / 20 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 3 / 20 = > work done by p in 1 day = 3 / 40 = > work done by q and r in 1 day = 3 / 40 hence work done by q in 1 day = 3 / 40 â € “ 1 / 20 = 1 / 40 so q alone can do the work in 40 days answer is e ."
Answer: e
Question (general): sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6500 ?
Options: a ) 4966 , b ) 2477 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4966 answer : a
Answer: a
Question (geometry): find the area of a parallelogram with base 15 cm and height 40 cm ?
Options: a ) 200 cm 2 , b ) 100 cm 2 , c ) 42 cm 2 , d ) 600 cm 2 , e ) 230 cm 2
Rationale: "area of a parallelogram = base * height = 15 * 40 = 600 cm 2 answer : d"
Answer: d
Question (geometry): the number 70 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 70 : 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 . now , 70 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 70 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 60 equals to 9 + 25 + 36 = 3 ^ 2 + 5 ^ 2 + 6 ^ 2 = 70 - - > 3 + 5 + 6 = 14 . answer : d ."
Answer: d
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 25 to produce 100 units ?
Options: a ) 5 , b ) 9 , c ) 6 , d ) 10 , e ) 2
Rationale: "5 machines would produce 100 units in 50 hours . increasing the amount of machines by 5 would mean dividing 50 hours by 5 . 50 / 5 = 10 answer : d"
Answer: d
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 1034355 , b ) 1035677 , c ) 1045778 , d ) 1067675 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1083875 e"
Answer: e
Question (general): a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?
Options: a ) $ 450 , b ) $ 500 , c ) $ 750 , d ) $ 800 , e ) $ 840
Rationale: let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c
Answer: c
Question (geometry): the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 507 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 13 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 507 3 b 2 = 507 b 2 = 169 b = 13 m . answer : option c"
Answer: c
Question (general): the number 341 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 21 , d ) 30 , e ) 39
Rationale: 5 ^ 3 + 6 ^ 3 = 341 number is 5 * 6 = 30 d
Answer: d
Question (general): what is the sum of the multiples of 7 from 77 to 91 , inclusive ?
Options: a ) 260 , b ) 452 , c ) 352 , d ) 260 , e ) 252
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 91 / 7 ) - ( 77 / 7 ) + 1 = 3 multiply these together so what we show average * total numbers = sum ( 91 + 77 ) / 2 * 3 = sum 84 * 3 = 252 e"
Answer: e
Question (general): 45 x ? = 25 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) none
Rationale: "answer let 45 x a = ( 25 x 900 ) / 100 ∴ a = ( 25 x 9 ) / 45 = 5 correct option : c"
Answer: c
Question (general): if there are thrice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ?
Options: a ) 3 ⁄ 20 , b ) 11 ⁄ 60 , c ) 9 ⁄ 40 , d ) 1 ⁄ 10 , e ) 11 ⁄ 20
Rationale: consider a group of 100 men and 300 women , a total of 400 people . 30 % of them , which is 120 , form a group of people who do n ' t own a car . half of them are men , and the other half are women , more precisely 60 . it means that there are 100 - 60 = 40 men who own a car , and this represents 40 / 400 = 1 / 10 of the total . answer d
Answer: d
Question (general): | x + 3 | – | 4 - x | = | 7 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , s ố x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , s ố í t becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 c
Answer: c
Question (general): a man is 24 years older than his son . in three years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 21 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 3 = 2 ( x + 3 ) â € ¹ = â € º x + 27 = 2 x + 6 x = 21 . answer d"
Answer: d
Question (general): an auction house charges a commission of 17 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 205,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.17 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 205,000 ( 17 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c ."
Answer: c
Question (general): a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ?
Options: a ) 200 km , b ) 50 km , c ) 20 km , d ) 60 km , e ) 80 km
Rationale: not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d
Answer: d
Question (gain): if the a radio is sold for rs 490 and sold for rs 465.50 . find loss % .
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 3 % , e ) 5.5 %
Rationale: "sol . cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b ."
Answer: b
Question (physics): eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 6 hours ?
Options: a ) 675 , b ) 750 , c ) 1,800 , d ) 1,350 , e ) 7,500
Rationale: 8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 6 hours ) = 1350 cans . the answer is d .
Answer: d
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1160 , find the gain percent ?
Options: a ) 11 , b ) 29 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 260 100 - - - - ? = > 29 % answer : b"
Answer: b
Question (geometry): the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?
Options: a ) 8
b ) 1
c ) 3
d ) 4
e ) 6
Rationale: perimeter of rectangular yard = 2 ( l + b ) = 12 - - > l + b = 6 area = l * b = 9 b = 6 - l l ( 6 - l ) = 9 6 l - l ^ 2 = 9 l ^ 2 - 6 l + 9 = 0 upon simplifying we get l = 3 . answer : b
Answer: b
Question (general): x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 7 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 49
Rationale: explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 7 ^ 2 = 9 / 49 answer : e
Answer: e
Question (general): each machine of type a has 3 steel parts and 3 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 60 steel parts and 44 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "look at the below representation of the problem : steel chrome total a 3 3 60 > > no . of type a machines = 60 / 6 = 10 b 6 5 44 > > no . of type b machines = 44 / 11 = 4 so the answer is 14 i . e c . hope its clear ."
Answer: c
Question (geometry): a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 275 , c ) 360 , d ) 440 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 50 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 50 = 225 . total area = 50 + 225 = 275 . answer : b ."
Answer: b
Question (general): a clothing store purchased a pair of pants for $ 90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 5 , c ) $ 10 , d ) $ 6 , e ) $ 8
Rationale: sale price ( sp ) = 90 + markup ( mp ) - - > mp = sp - 90 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 90 3 sp / 4 = 90 sp = 120 now a discount of 20 % is given so new sp is . 8 * 120 = 96 profit = 96 - 90 = 6.0 $ answer is d
Answer: d
Question (general): a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 60 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 23,760 , e ) $ 27,360
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.6 * 12000 = 12000 - 7200 x = 4800 earning becomes 9360 + 3 x = 9360 + 3 * 4800 = 23760 ans : d"
Answer: d
Question (geometry): the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 6 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 8915
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 6 ) = rs . 8915 . answer : option e"
Answer: e
Question (general): the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) q = 20 , b ) q = 25 , c ) q = 30 , d ) q = 35 , e ) 40
Rationale: suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d
Answer: d
Question (physics): a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in .
Options: a ) 24 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 27 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : a"
Answer: a
Question (general): 5 n + 2 > 12 and 7 n - 5 < 23 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 4 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: "5 n > 10 - - > n > 2 7 n < 28 - - > n < 4 2 < n < 4 answer : b"
Answer: b
Question (general): how many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 7 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 70 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 and 65 = 7 ans b"
Answer: b
Question (general): find the value of 201834 x 99999 = m ?
Options: a ) 20183198166 , b ) 20194181766 , c ) 20175292556 , d ) 20132191166 , e ) 20153198166
Rationale: "201834 x 99999 = 201834 x ( 100000 - 1 ) = 201834 x 100000 - 201834 x 1 = 20183400000 - 201834 = 20183198166 a"
Answer: a
Question (general): if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 70 , how much more remains to be paid ?
Options: a ) $ 1120 , b ) $ 1190 , c ) $ 1260 , d ) $ 1330 , e ) $ 1400
Rationale: "95 % remains to be paid so the remaining amount is 19 * 70 = $ 1330 . the answer is d ."
Answer: d
Question (general): for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 3 , b ) 1.8 , c ) 6 , d ) 18 , e ) 60
Rationale: concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 4 + 18 ) / 2 ] * 8 = 88 h ( 10 ) = ( 4 + 10 ) / 2 ] * 4 = 28 h ( 18 ) / h ( 10 ) = ( 88 ) / ( 28 ) ~ 3 answer : a
Answer: a
Question (physics): due to construction , the speed limit along an 5 - mile section of highway is reduced from 60 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 2.5 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 60 = 5 * 1 / 1 = 5 new time in minutes to cross 5 miles stretch = 5 * 60 / 40 = 5 * 3 / 2 = 7.5 time difference = 2.5 ans : b"
Answer: b