regisss/math_qa huggingface dataset:
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is
Options: a ) 3220 , b ) 4830 , c ) 5120 , d ) 6420 , e ) none
Rationale: "solution clearly , l = ( 48 - 16 ) m = 32 m ‹ = › b = ( 36 - 16 ) m = 20 m , ‹ = › h = 8 m . . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer c"
Answer: c
Problem: 1,2 , 3,2 , 4,6 , 4,8 , _____
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "divide the series : 1 , 2,3 2 , 4,6 4,8 , ? so it is 12 answer : c"
Answer: c
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 312 votes . find the number of votes casted to the winning candidate ?
Options: a ) 806 , b ) 744 , c ) 912 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 312 62 % - - - - - - - - ? = > 806 answer : a"
Answer: a
Problem: 5358 x 52 = ?
Options: a ) 272258 , b ) 272358 , c ) 278616 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 2 ) = 5358 x 50 + 5358 x 2 = 267900 + 10716 = 278616 . c )"
Answer: c
Problem: if x / ( 9 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 54 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 9 p ) = odd prime number x = odd prime number * 9 p least value of x = lowest odd prime number * 9 * lowest value of p = 3 * 9 * 2 = 54 answer a"
Answer: a
Problem: rs . 900 is divided among maya , annie , saiji so that maya receives half as much as annie and annie half as much as saiji . then saiji ’ s share is :
Options: a ) rs . 200 , b ) rs . 300 , c ) rs . 400 , d ) rs . 600 , e ) rs . 500
Rationale: let saiji = x . then , annie = x / 2 and maya = x / 4 . therefore , maya : annie : saiji = x / 4 : x / 2 : x = 1 : 2 : 4 . therefore , saiji ’ s share = rs . 900 * 4 / 9 = rs . 400 . answer : c
Answer: c
Problem: a company has two models of computers , model m and model n . operating at a constant rate , a model m computer can complete a certain task in 24 minutes and a model n computer can complete the same task in 12 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model m computers were used ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 6
Rationale: let ' s say 1 work is processing 24 gb of data . model m : 1 gb per min model n : 2 gb per min working together , 1 m and 1 n = 3 gb per min so , 8 times as many computers would work at 18 gb per min . so no . of m = 8 answer is d
Answer: d
Problem: a and b together can do a work in 4 days . a alone can do it in 20 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 4 a alone can do 1 day ' s work = 1 / 20 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 4 ) - ( 1 / 20 ) = 5 days answer : option e"
Answer: e
Problem: in a kilometer race , a beats b by 200 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 180 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 40 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 200 = 50 sec . time taken by a = 50 - 10 = 40 sec . answer : e"
Answer: e
Problem: if a car went the first third of the distance at 80 kmh , the second third at 15 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 30 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 15 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 15 * t 2 = 16 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 24 hrs d = rt ( 240 * 3 ) = r * 24 r = 30 answer : a"
Answer: a
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 15,000 , e ) none
Rationale: solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d
Answer: d
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 100 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 100 5 x - 20 = 100 5 x = 120 x = 24 the answer is a .
Answer: a
Problem: an article is bought for rs . 600 and sold for rs . 900 , find the gain percent ?
Options: a ) 33 1 / 7 % , b ) 33 1 / 6 % , c ) 50 % , d ) 38 1 / 3 % , e ) 33 2 / 3 %
Rationale: "600 - - - - 300 100 - - - - ? = > 50 % answer : c"
Answer: c
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 7 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "if n = 8 mark sold 1 box and ann sold 6 boxes total 7 < 8 answer : e"
Answer: e
Problem: total 15 cows 5 cow gives each 2 liter milk 5 cow gives each 3 / 4 liter milk 5 cow gives each 1 / 4 liter milk this is split into 3 son per each 5 cows & 5 liter milk how ?
Options: a ) 10 , b ) 5 , c ) 15 , d ) 7.5 , e ) 12.5
Rationale: "5 cow 2 liter each = 10 liter 5 cow 3 / 4 liter each = 3 / 4 = 0.75 * 5 = 3.75 5 cow 1 / 4 liter each = 1 / 4 = 0.25 * 5 = 1.25 add 10 + 3.75 + 1.25 = 15 milk split into 3 son each 5 liter then 15 / 3 = 5 answer : b"
Answer: b
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 19 = f ( x – 4 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 2 ( 3 x - 5 ) - 19 = 3 ( x - 4 ) - 5 3 x = 12 x = 4 the answer is b .
Answer: b
Problem: a committee is reviewing a total of 20 x black - and - white films and 8 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 40 / 41 , b ) 20 / 41 , c ) 30 / 41 , d ) 60 / 41 , e ) 80 / 41
Rationale: "say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 8 y = 80 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 80 color films , thus total of 82 films were selected . color films thus compose 80 / 82 = 40 / 41 of the selected films . answer : a"
Answer: a
Problem: if | 4 x + 2 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 1 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 2 = 46 or 4 x + 2 = - 46 = > x = 11 or x = - 12 sum of both the values will be - 12 + 11 = - 1 answer is b"
Answer: b
Problem: there are 780 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 130 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 780 . hence , we have m + f = 780 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 780 / 3 = 260 solving the three equations yields the solution f = 260 , m = 520 , and d = 260 . the number of female democratic participants equals half the female participants equals 260 / 2 = 130 . answer : a"
Answer: a
Problem: there are 680 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 425 , b ) 345 , c ) 375 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 680 . hence 3 x + 5 x = 680 solve for x 8 x = 680 x = 85 number of boys 3 x = 3 × 85 = 255 number of girls 5 x = 5 × 85 = 425 a"
Answer: a
Problem: in a clothing store , there are 6 different colored neckties ( orange , yellow , green , blue , and indigo ) and 5 different colored shirts ( orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?
Options: a ) 719 / 720 , b ) 1 / 120 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720
Rationale: 5 ties and 5 shirts . . . red tie can take any of 5 shirts . . orange can take any of the remaining 4 shirts yellow any of remaining 3 . . and so on till last indigo chooses the 1 remaining . . total ways = 5 * 4 * 3 * 2 * 1 = 120 out of this 120 , only 1 way will have same colour tie and shirt . . prob = 1 / 120 b
Answer: b
Problem: 325 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 13 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "26 trees have 25 gaps between them , required distance ( 325 / 25 ) = 13 a"
Answer: a
Problem: in the coordinate plane , points ( x , 1 ) and ( 4 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x + y =
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 1 ) = ( 4 , 1 ) and ( 4 , y ) = ( 4,1 ) - - > x + y = 4 + 1 = 5 . answer : d"
Answer: d
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 45 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 60
Rationale: "20 x + 45 = 21 ( x – 5 ) x = 60 answer : e"
Answer: e
Problem: q and f represent two distinct digits . if the number 457 q 89 f is divisible by 36 , what is the value of ( q + f ) ?
Options: a ) a ) 9 , b ) b ) 3 , c ) c ) 12 , d ) d ) 6 , e ) e ) 10
Rationale: a no . divisible by 36 means it is div by 49 . to be div by 4 last 2 digits to be multiple of 4 so , f could be either 2 or 6 only similarly for a number to be div by 9 its sum must be multiple of 9 first . filtering we find q could be either 1 , 47 only . to be divisible by 9 only 1 works . ( if we choose f = 6 then q have to be 6 but as per condition qf are distinct ) so q = 1 f = 2 ans : - 3 . b
Answer: b
Problem: the total population of dogs in a community is estimated to be 50 % male and 50 % female . the total number of black dogs is 20 % greater than the total number of male black dogs . if the total number of female dogs is 8 times more than the number of female black dogs what percentage of male dogs is black ?
Options: a ) 84.4 , b ) 70.2 , c ) 80.1 , d ) 60.8 , e ) 62.5
Rationale: since we are dealing in percentage let us pick 100 as the number of black male dogs . that means that the total number of black dogs is = 120 ( 20 % more ) , therefore the number of black female dogs is 20 . the total number of female dogs is 8 x the number of black female = 20 * 8 = 160 female dogs . male dogs are 50 % of the dogs , and because there are 160 female dogs , then there must also be 160 male dogs therefore percentage of male dogs that are black = 100 / 160 * 100 = 62.5 correct option is e
Answer: e
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d"
Answer: d
Problem: the ratio 25 : 50 expressed as percent equals to
Options: a ) 50 % , b ) 85 % , c ) 25 % , d ) 75 % , e ) none of above
Rationale: "explanation : actually it means 25 is what percent of 50 , which can be calculated as , ( 25 / 50 ) * 100 = 25 * 2 = 50 answer : option a"
Answer: a
Problem: a man is 22 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 22 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 22 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 20 answer : d"
Answer: d
Problem: 18 beavers , working together in a constant pace , can build a dam in 8 hours . how many hours will it take 36 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .
Rationale: "total work = 18 * 8 = 144 beaver hours 36 beaver * x = 144 beaver hours x = 144 / 36 = 4 answer : b"
Answer: b
Problem: 2 + 4
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: d
Answer: d
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 30 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 30 / 10 = 3 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 3 = 18 kms . . . answer - b"
Answer: b
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 6 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 26 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 6 ) = 1 / 26 leak will empty the tank in 26 hrs . answer : e"
Answer: e
Problem: 10 people went to a hotel for combine dinner party 5 of them spent rs . 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 240 , e ) none of these
Rationale: "solution : let average expenditure of 10 people be x . then , 10 x = 20 * 5 + 5 * ( x + 4 ) ; or , 10 x = 20 * 5 + 5 x + 20 ; or , x = 24 ; so , total money spent = 24 * 10 = rs . 240 . answer : option d"
Answer: d
Problem: a sum is divided among w , x and y in such a way that for each rupee w gets , x gets 30 paisa and y gets 20 paisa . if the share of w is rs . 10 , what is the total amount ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: w : x : y = 100 : 30 : 20 20 : 6 : 4 20 - - - 10 30 - - - ? = > 15 answer : d
Answer: d
Problem: a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 4 new workers . how many different ways can she assign the new workers ?
Options: a ) 1485 , b ) 2700 , c ) 3300 , d ) 4860 , e ) 5400
Rationale: whatever : my take selecting team of 4 out of 12 to assign to the shifts = 12 c 4 = 495 ways . now 4 out of 12 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 4 out of 12 ) * arranging those teams in shifts = 495 * 3 = 1485 ans : a
Answer: a
Problem: a car was driving at 66 km / h for 30 minutes , and then at 100 km / h for another 45 minutes . what was its average speed ?
Options: a ) 84 . , b ) 75 . , c ) 70 . , d ) 65 . , e ) 54 .
Rationale: "driving at 66 km / h for 30 minutes , distance covered = 60 * 1 / 2 = 30 km driving at 100 km / h for 45 minutes , distance covered = 100 * 3 / 4 = 75 km average speed = total distance / total time = 105 / 1.25 = 84 km / h answer : a"
Answer: a
Problem: if the price of a book is first decreased by 30 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 16 , c ) 37 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 20 % on rs 70 = 70 + 14 = 84 net change in price = 100 - 84 = 16 answer : b"
Answer: b
Problem: what is theleast number should be added to 519 , so the sum of the number is completely divisible by 25 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "( 519 / 25 ) gives remainder 19 19 + 6 = 25 , so we need to add 6 answer : d"
Answer: d
Problem: a man can do a piece of work in 10 days , but with the help of his son , he can do it in 4 days . in what time can the son do it alone ?
Options: a ) 13 / 2 , b ) 17 / 3 , c ) 15 / 2 , d ) 20 / 3 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 10 ) = 3 / 20 the son alone can do the work in 20 / 3 days answer is d"
Answer: d
Problem: find the next term 88 , 62 , . . ?
Options: a ) - 2 , b ) - 4 , c ) - 6 , d ) - 8 , e ) - 9
Rationale: 8 , 8 , 6 , 2 , x i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - x should be ` ` 6 ' ' 2 - x = 6 x = - 4 answer : b
Answer: b
Problem: the cash difference between the selling prices of an book at a profit of 2 % and 4 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 51 : 52 , d ) 45 : 53 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 102 % of x / 104 % of x = 102 / 104 = 51 / 52 = 51 : 52 c"
Answer: c
Problem: how long does a train 100 m long running at the speed of 75 km / hr takes to cross a bridge 135 m length ?
Options: a ) 11.3 sec , b ) 12.1 sec , c ) 13.1 sec , d ) 16.5 sec , e ) 12.7 sec
Rationale: "speed = 75 * 5 / 18 = 20.8 m / sec total distance covered = 100 + 135 = 235 m . required time = 235 / 20.8 ' = 11.3 sec . answer : a"
Answer: a
Problem: what is the smallest positive integer x , such that 7000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: "take out the factors of 7000 x that will come 10 ^ 3 * 7 . for perfect cube you need every no . raise to the power 3 . for 7000 x to be a perfect cube , need two 7 that means 49 . e is the answer ."
Answer: d
Problem: if x = 1 - 5 t and y = 2 t - 1 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 2 / 3 , d ) 2 / 7 , e ) 0
Rationale: "we are given x = 1 – 5 t and y = 2 t – 1 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 5 t for x and 2 t – 1 for y in the equation x = y . this gives us : 1 – 5 t = 2 t – 1 2 = 7 t 2 / 7 = t the answer is d ."
Answer: d
Problem: a person buys an article at $ 1200 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 1670 , b ) 1600 , c ) 1680 , d ) 1900 , e ) 1230
Rationale: c 1680 cost price = $ 1200 profit = 40 % of 1200 = $ 480 selling price = cost price + profit = 1200 + 480 = 1680
Answer: c
Problem: there is a 75 % chance that tigers will not win at all during the whole season . there is a 25 % chance that germany will not play at all in the whole season . what is the greatest possible probability that the tigers will win and germany will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: there is a 75 % chance that tigers will not win at all during the whole season we can infer that there is 25 % chance tigers will win . similarly there is a 25 % chance that germany will not play at all in the whole season we can also infer that there is 75 % chance that germany will play . answer d
Answer: d
Problem: in the coordinate plane , points ( x , 8 ) and ( 20 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x * y =
Options: a ) 120 , b ) 100 , c ) 135 , d ) 140 , e ) 160
Rationale: line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 8 ) = ( 32 , 8 ) and ( 20 , y ) = ( 20,5 ) - - > x * y = 32 * 5 = 160 . answer : e
Answer: e
Problem: find the sum of first 35 odd numbers
Options: a ) 4900 , b ) 3000 , c ) 1250 , d ) 1200 , e ) 1225
Rationale: "explanation : n 2 = 352 = 1225 answer : option e"
Answer: e
Problem: bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ?
Options: a ) 16 , b ) 10 , c ) 28 , d ) 4 , e ) 2
Rationale: at least 20 golf tees for each member of his foursome = total of at least 4 * 20 = 80 tees . 2 packages of the generic golf tees , that are packaged by the dozen = 2 * 12 = 24 tees . so , bill must by at least 16 aero tees . they come by the pair , hence he must by at least 56 / 2 = 28 packages of aero flight tees . answer : c .
Answer: c
Problem: a man ' s speed with the current is 20 kmph and speed of the current is 3 kmph . the man ' s speed against the current will be
Options: a ) 11 kmph , b ) 12 kmph , c ) 14 kmph , d ) 17 kmph , e ) none of these
Rationale: "explanation : if you solved this question yourself , then trust me you have a all very clear with the basics of this chapter . if not then lets solve this together . speed with current is 20 , speed of the man + it is speed of the current speed in still water = 20 - 3 = 17 now speed against the current will be speed of the man - speed of the current = 17 - 3 = 14 kmph option c"
Answer: c
Problem: country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 888 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 388 mill / 2 month i . e . $ 194 mill / month difference / month = 194 - 120 = 74 difference / year = $ 74 mill * 12 = $ 988 mill answer : e"
Answer: e
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 70 % of the total school population of x students , what is x ?
Options: a ) 113 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 70 / 100 * x = > x ^ 2 = 9 * 10000 / 7 = > x = 113 a"
Answer: a
Problem: what is the remainder when 43 ^ 88 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 88 has the form 4 k so the units digit of 43 ^ 88 is 1 . the remainder when dividing by 5 is 1 . the answer is b ."
Answer: b
Problem: how many factors of 990 are odd numbers greater than 1 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: when factorized , 990 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option c )
Answer: c
Problem: square a has an area of 25 square centimeters . square b has a perimeter of 12 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 25 , d ) 3 / 5 , e ) 6 / 25
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 12 , then its side is 12 / 4 = 3 and the area is 3 ^ 2 = 9 empty space between the squares is 25 - 9 = 16 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 16 / 25 . answer : c"
Answer: c
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 40
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 / 26.50 m = 200 m . 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m . answer : c
Answer: c
Problem: two trains 150 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 ) 7.18 , b ) 7.12 , c ) 7.16 , d ) 7.55 , e ) 7.82
Rationale: "t = ( 150 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.82 answer : e"
Answer: e
Problem: a train running at the speed of 50 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 125 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 197 m
Rationale: "speed = 50 * 5 / 18 = 125 / 9 m / sec length of the train = speed * time = 125 / 9 * 9 = 125 m answer : a"
Answer: a
Problem: two - third of a positive number and 25 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25
Rationale: "let the number be x . then , 2 / 3 x = 25 / 216 * 1 / x x 2 = 25 / 216 * 3 / 2 = 25 / 144 x = 5 / 12 answer : a"
Answer: a
Problem: if 50 % of ( x - y ) = 40 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 11 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 40 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 40 / 100 ) ( x + y ) 5 ( x - y ) = 4 ( x + y ) x = 9 y x = 9 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 9 y ) x 100 ) = 11 % answer is b ."
Answer: b
Problem: a certain quantity of 60 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 60 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 60 ml and 25 ml is 35 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 35 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 25 % . therefore , 25 out of 35 is 5 / 7 and e is the answer ."
Answer: e
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team t . if team a ' s average speed was 5 mph greater than team t ' s , what was team t ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team t ' s speed was s . then team t ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team t . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team t is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Problem: a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is :
Options: a ) 4 mph , b ) 2.5 mph , c ) 3 mph , d ) 2 mph , e ) none of these
Rationale: explanation : speed of the boat in still water = 10 mph let speed of the stream be x mph then , speed downstream = ( 10 + x ) mph speed upstream = ( 10 - x ) mph time taken to travel 36 miles upstream - time taken to travel 36 miles downstream = 90 / 60 hours = > 36 / ( 10 − x ) − 36 / ( 10 + x ) = 3 / 2 = > 12 / ( 10 − x ) − 12 / ( 10 + x ) = 1 / 2 = > 24 ( 10 + x ) − 24 ( 10 − x ) = ( 10 + x ) ( 10 − x ) = > 240 + 24 x − 240 + 24 x = ( 100 − x 2 ) = > 48 x = 100 − x 2 = > x 2 + 48 x − 100 = 0 = > ( x + 50 ) ( x − 2 ) = 0 = > x = - 50 or 2 . answer : option d
Answer: d
Problem: ) a cube is painted blue on all of its surfaces . it is then cut in to 27 smaller cubes of equal size . find how many smaller cubes have no color ?
Options: a ) 1
b ) 3
c ) 8
d ) 5
e ) 7
Rationale: if the cube is cut in to 27 smaller cubes , then number of separations made = n = 3 ( since 3 × 3 × 3 = 27 ) . number of smaller cubes with no color = ( n – 2 ) 3 = ( 3 – 2 ) 3 = 13 = 1 answer : a
Answer: a
Problem: a rectangular field has to be fenced on three sides leaving a side of 25 feet uncovered . if the area of the field is 880 sq . feet , how many feet of fencing will be required ?
Options: a ) 75.4 feet , b ) 98.4 feet , c ) 95.4 feet , d ) 85.4 feet , e ) 92.4 feet
Rationale: "area of the field = 880 sq . feet . length of the adjacent sides are 25 feet and 880 / 25 = 35.2 feet . required length of the fencing = 25 + 35.2 + 35.2 = 95.4 feet answer : c"
Answer: c
Problem: x + ( 1 / x ) = 2.5 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 2.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 6.25 - 2 x ^ 2 + 1 / x ^ 2 = 4.25 answer : c"
Answer: c
Problem: a = { 0 , 1 , - 3 , 6 , - 8 , - 10 } b = { - 1 , 2 , - 4 , 7 , 6 , - 9 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab < 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 13 , d ) 5 / 12 , e ) 1 / 2
Rationale: for the product of 2 numbers to be negative either of them must be positive or negative : p ( positive , negative ) = 2 / 6 * 3 / 6 = 6 / 36 ; p ( negative , positive ) = 3 / 6 * 3 / 6 = 9 / 36 p = 6 / 36 + 9 / 36 p = 15 / 36 p = 5 / 12 answer : d
Answer: d
Problem: which number need to add to 172835 to get a number exactly divisible by 136 ?
Options: a ) 27 , b ) 25 , c ) 26 , d ) 21 , e ) 24
Rationale: "172835 / 136 = 1270 and reminder = 115 . 136 - 115 = 21 so , the next number divisible by 115 is 21 places in front of 172835 which means 21 + 172835 = 172856 21 should be added to 172835 d"
Answer: d
Problem: simplify : 99 ^ 48 / 49 * 245 .
Options: a ) 23345 , b ) 26695 , c ) 24495 , d ) 25575 , e ) none of them
Rationale: "given expression = ( 100 - 1 / 49 ) * 245 = ( 4899 / 49 ) * 245 = 4899 * 5 = 24495 . answer is c ."
Answer: c
Problem: a boy swims downstream 91 km and upstream 21 km taking 7 hours each time , what is the speed of the boy in still water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 91 - - - 7 ds = 13 ? - - - - 1 21 - - - - 7 us = 3 ? - - - - 1 m = ? m = ( 13 + 3 ) / 2 = 8 answer : c
Answer: c
Problem: speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4664 km and comes back to the starting point . the total time taken by him is :
Options: a ) 784 hours , b ) 794 hours , c ) 780 hours , d ) 684 hours , e ) 884 hours
Rationale: "speed downstream = ( 12 + 1.2 ) = 13.2 kmph speed upstream = ( 12 - 1.2 ) = 10.8 kmph total time taken = 4664 / 13.2 + 4664 / 10.8 = 353 + 431 = 784 hours answer : a"
Answer: a
Problem: the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 15 / 2 , e ) 24
Rationale: after passing the hiker the cyclist travels for 5 minutes at a rate of 10 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 6 miles . in those 5 mins the hiker travels a distance of 1 / 2 miles . so the hiker still has to cover 1 / 2 miles to meet the waiting cyclist . the hiker will need 15 / 2 mins to cover the remaining 1 / 2 miles . so the answer is d .
Answer: d
Problem: the average of first five multiples of 2 is :
Options: a ) 3 , b ) 9 , c ) 12 , d ) 15 , e ) e
Rationale: "solution average = 2 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 30 / 5 = 6 answer e"
Answer: e
Problem: find the amount on rs . 9000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 5568 , b ) 9828 , c ) 5460 , d ) 5635 , e ) 6734
Rationale: "9000 * 104 / 100 * 105 / 100 = > 9828 answer : b"
Answer: b
Problem: what decimal fraction is 40 ml of a litre ?
Options: a ) . 4 , b ) . 04 , c ) . 05 , d ) 0.04 , e ) none of these
Rationale: "answer required fraction = 40 / 1000 = 4 / 100 = . 04 correct option : b"
Answer: b
Problem: how many even integers n , such that 20 < = n < = 180 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36
Rationale: the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 278 = 16 + 6 ( 27 ) there are 27 numbers in the list . the answer is b .
Answer: b
Problem: two numbers n and 12 have lcm = 48 and gcf = 8 . find n .
Options: a ) 24 , b ) 34 , c ) 44 , d ) 54 , e ) 32
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 12 × n = 48 × 8 n = 48 × 8 / 12 = 32 correct answer e"
Answer: e
Problem: in a hostel , the number of students decreased by 9 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 8.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.91 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.91 * 1.2 ) = > f ( new ) = 0.915 f therefore the new cost of food must be 91.5 % of the old cost , or the cost of food must decrease by 8.4 % ( option e )"
Answer: e
Problem: a company produces on an average 4000 items per month for the first 3 months . how many items it must produce on an average per month over the next 9 months , to average of 4375 items per month over the whole ?
Options: a ) 4500 , b ) 4600 , c ) 4680 , d ) 4710 , e ) none
Rationale: sol . required average = ( 4375 x 12 ) - ( 4000 x 3 ) / 9 ⇔ 52500 - 12000 / 9 ⇔ 40500 / 9 = 4500 . answer a
Answer: a
Problem: pat , kate and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 80 , d ) 90 , e ) 108
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 144 - total hours charged for , x = 16 . mat charged 6 x - x or 5 x for more hours than kate , or for 80 hours . c is correct"
Answer: c
Problem: 69 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 8 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: "69 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 69 = 70 , 48 = 50 , 25,075 = 25,000 are derived , which makes ( 69 ) ( 48 ) ( 25,075 ) = ( 70 ) ( 50 ) ( 25,000 ) = 10 ^ 7 . the answer is a ."
Answer: a
Problem: divide $ 5000 among x , y in the ratio 2 : 8 . how many $ that x get ?
Options: a ) $ 1000 , b ) $ 1050 , c ) $ 1100 , d ) $ 1150 , e ) $ 1200
Rationale: sum of ratio terms = 2 + 8 = 10 x = 5000 * 2 / 10 = $ 1000 answer is a
Answer: a
Problem: a teacher gave the same test to 3 history classes : u , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 80 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?
Options: a ) 74 , b ) 75 , c ) 76 , d ) 77 , e ) 78
Rationale: ans : b ( 75 ) lets say class u indeed has 4 children , b has 6 children and c has 5 children . now , if the average of class u is 65 , hence total marks awarded in the class = 65 * 4 = 260 similarly , class b = 80 * 6 = 480 class c = 77 * 5 = 385 total marks provided = u + b + c = 260 + 480 + 385 = 1125 avg . marks = 1125 / 15 ( total no . of students ) = 75 = b
Answer: b
Problem: a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 15 = 11.25 cm answer is c"
Answer: c
Problem: how many positive integers less than 28 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 11 - 1 = 22 . answer : d ."
Answer: d
Problem: what are the last two digits of 63 * 35 * 37 * 82 * 71 * 41 * 53 ?
Options: a ) 10 , b ) 30 , c ) 40 , d ) 70 , e ) 80
Rationale: we know that to find the last two digits , we need to find the remainder we get when we divide the product by 100 . remainder of ( 63 * 35 * 37 * 82 * 71 * 41 ) / 100 note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator . but before we do that , here is an important note : note : we can not just cancel off the common terms in the numerator and denominator to get the remainder . but , if we want to cancel off to simplify the question , we can do it , provided we remember to multiply it back again . so say , we want to find the remainder when 14 is divided by 10 i . e . 14 / 10 ( remainder 4 ) . but we cancel off the common 2 to get 7 / 5 . the remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10 . but if we multiply 2 back by 2 ( the number we canceled off ) , the remainder will become 2 * 2 = 4 which is correct . take another example to reinforce this – what is the remainder when 85 is divided by 20 ? it is 5 . we might rephrase it as – what is the remainder when 17 is divided by 4 ( cancel off 5 from the numerator and the denominator ) . the remainder in this case is 1 . we multiply the 5 back to 1 to get the remainder as 5 which is correct . so keeping this very important point in mind , let ’ s go ahead and cancel the common 5 and 2 . we need the remainder of ( 63 * 7 * 37 * 41 * 71 * 41 * 5 * 2 ) / 10 * 5 * 2 remainder of ( 63 * 7 * 37 * 41 * 71 * 41 ) / 10 now using concept 2 , let ’ s write the numbers in form of multiples of 10 remainder of ( 60 + 3 ) * 7 * ( 30 + 7 ) * ( 40 + 1 ) * ( 70 + 1 ) * ( 40 + 1 ) / 10 remainder of 3 * 7 * 7 * 1 * 1 * 1 / 10 remainder of 147 / 10 = 7 now remember , we had canceled off 10 so to get the actual remainder so we need to multiply by 10 : 7 * 10 = 70 . when 63 * 35 * 37 * 82 * 71 * 41 is divided by 100 , the remainder is 70 . so the last two digits of 63 * 35 * 37 * 82 * 71 * 41 must be 80 . answer ( e )
Answer: e
Problem: in n is a positive integer less than 200 , and 27 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 27 n / 60 must be an integer . = > 9 n / 20 must be an integer . hence n must be a multiple of 2 * 5 . = > n has 2 different prime integers ."
Answer: a
Problem: the ratio of the adjacent angles of a parallelogram is 5 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 144 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 5 x + 10 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 60 ° and 120 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 60 ° + 84 ° = 144 ° answer : c"
Answer: c
Problem: the population of a city increases by 5 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 27 % , d ) 12.48 % , e ) none of these
Rationale: "actual increase in population = 4 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 4 / 100 ) ^ 3 = 112.4864 ∴ required percentage = 12.48 % answer : d"
Answer: d
Problem: the sum of the present age of henry and jill is 33 . what is their present ages if 6 years ago henry was twice the age of jill ?
Options: a ) and 20 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 6 years ago be x , age of henry be 2 x x + 6 + 2 x + 6 = 33 x = 7 present ages will be 13 and 20 answer : a"
Answer: a
Problem: in a division sum , the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :
Options: a ) 72 , b ) 76 , c ) 100 , d ) 113 , e ) 112
Rationale: "diver = ( 5 * 3 ) + 3 = 18 3 * quotient = 18 quotient = 6 dividend = ( divisor * quotient ) + remainder dividend = ( 18 * 6 ) + 5 = 113 d"
Answer: d
Problem: what is the sum of the multiples of 4 between 34 and 135 inclusive ?
Options: a ) 2000 , b ) 2100 , c ) 2150 , d ) 2200 , e ) 2500
Rationale: the fastest way in an ap is to find the average and multiply with total integers . . between 34 and 135 , the smallest multiple of 4 is 36 and largest = 132 . . average = ( 36 + 132 ) / 2 = 84 . . total numbers = ( 132 - 36 ) / 4 + 1 = 24 + 1 = 25 . . sum = 25 * 84 = 2100 ans b
Answer: b
Problem: a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 9 : 30 am in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ?
Options: a ) 12 : 30 , b ) 1 : 00 , c ) 1 : 30 , d ) 2 : 00 , e ) 2 : 30
Rationale: "in thirty minutes the first train travels 35 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 35 / 10 = 3.5 hours , so at 1 : 00 pm . the answer is b ."
Answer: b
Problem: the area of a rectangular plot is 21 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 5 metres , c ) 11 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 21 × b ∴ l = 21 m and l – b = 10 ∴ b = 21 – 10 = 11 m answer c"
Answer: c
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 3600 interest . the principal amount borrowed by him was .
Options: a ) rs 10000 , b ) rs 15000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 3600 â ˆ — 100 / 12 â ˆ — 3 = rs 10000 option a"
Answer: a
Problem: a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find c ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 8 / 24 ) ã — 8640 ] = rs . 2880 answer : option c"
Answer: c
Problem: ( 3 x + 2 ) ( 2 x - 3 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: "expanding we have 6 x ^ 2 - 9 x + 4 x - 6 6 x ^ 2 - 5 x - 6 taking coefficients , a = 6 , k = - 5 , n = - 6 therefore a - n + k = 6 - ( - 6 ) - 5 = 12 - 5 = 7 the answer is b ."
Answer: b
Problem: a vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.5 ) x = 0.1 x . the remaining apples are ( 0.8 ) ( 0.5 ) x = 0.4 x . on day two , the vendor throws away ( 0.5 ) ( 0.4 ) x = 0.2 x . the vendor throws away a total of 0.1 x + 0.2 x = 0.3 x . the vendor throws away 30 percent of the apples . the answer is a ."
Answer: a