regisss/math_qa huggingface dataset:
Problem: a box contains 12 pairs of shoes ( 24 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 23 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 24 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 23 ( as after taking one at random there are 23 shoes left and only one is the pair of the first one ) = 1 / 23 answer : b"
Answer: b
Problem: if 2 ^ 5 , 3 ^ 3 , and 10 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 120 , d ) 65 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 10 rest of them must be in w so w = 10 * 3 * 4 = 120 smash c"
Answer: c
Problem: how long does a train 130 m long running at the speed of 65 km / hr takes to cross a bridge 150 m length ?
Options: a ) 15.7 sec , b ) 15.1 sec , c ) 15.5 sec , d ) 17.1 sec , e ) 16.7 sec
Rationale: "speed = 65 * 5 / 18 = 18.1 m / sec total distance covered = 130 + 150 = 280 m . required time = 280 / 18.1 ' = 15.5 sec . answer : c"
Answer: c
Problem: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 60 days .
Options: a ) 36 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 60 * 6 / 10 = 36 days . answer : a"
Answer: a
Problem: in a school with 5 classes , each class has 2 students less then the previous class . how many students are there in the largest class if the total number of students at school is 95 ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 23 , e ) 25
Rationale: "total classes = 5 total students = 95 . average = 19 if the classes had average number of students : 19 19 19 19 19 given case = 23 21 19 17 15 hence number of students in the largest class = 23 correct option : d"
Answer: d
Problem: jane and thomas are among the 6 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 6 people if at least one of either jane or thomas is to be selected ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the total number of ways to choose 3 people from 6 is 6 c 3 = 20 . the number of committees without jane or thomas is 4 c 3 = 4 . there are 20 - 4 = 16 possible committees which include jane and / or thomas . the answer is c .
Answer: c
Problem: when 1 / 20 % of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 398 , e ) 400
Rationale: "( 1 / 10 ) * 4000 - ( 1 / 20 * 100 ) * 4000 = 400 - 2 = 398 answer d"
Answer: d
Problem: the average weight of a class is x pounds . when a new student weighing 60 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 30 / 5 = 6 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 80 = 6 ( x - 1 ) - - > x = 88 pounds . answer : c ."
Answer: c
Problem: if a train , travelling at a speed of 180 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 250 m , b ) 112 m , c ) 117 m , d ) 125 m , e ) 123 m
Rationale: "a a = 180 * 5 / 18 * 5 = 250 m"
Answer: a
Problem: if 6 < x < 10 < y < 17 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 6 , e ) 7
Rationale: "let x = 6.1 and y = 16.1 greatest possible difference = 16.1 - 6.1 = 10 answer c"
Answer: c
Problem: 9 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 12 cm height . what is the diameter of each sphere ?
Options: a ) 4 cm
b ) 6 cm
c ) 8 cm
d ) 10 cm
e ) 12 cm
Rationale: volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 9 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 12 = 64 cm ^ 3 r = 4 cm d = 8 cm the answer is c .
Answer: c
Problem: a survey was sent to 90 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 6 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 90 ) = x / 100 x = 8 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 8 ) % = 6 % answer is b"
Answer: b
Problem: a car started running at a speed of 29 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 41 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 41 km the total distance covered by the car in the first 10 hours = 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 = sum of 10 terms in ap whose first term is 32 and last term is 50 = 10 / 2 [ 32 + 50 ] = 410 km ."
Answer: a
Problem: q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years . what is definitely the difference between r and q ' s age ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 77 , e ) 23
Rationale: "r - q = r - t q = t . also r + t = 50 ; r + q = 50 so , ( r - q ) can not be determined . answer : d"
Answer: d
Problem: a deer passed a certain tree at a constant speed of 50 miles per hour while being chased by a cheetah . then , 2 minutes later , the cheetah passed the same tree at a constant speed of 60 miles per hour . if both animals maintained their speeds , how long after the cheetah passed the tree did the cheetah catch up with the deer ?
Options: a ) 30 min , b ) 3 min , c ) 1 hr , d ) 1 min , e ) 2 min
Rationale: when the cheetah is at the tree , the deer is 50 / 30 miles ahead on the highway . ( the distance covered in 2 min ) every hour , cheetah runs 10 miles more than the deer . how many hours will it takes it to cover 50 / 30 miles more ? the answer is ( 50 / 30 ) / 10 = 1 / 60 = 1 min answer d
Answer: d
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 150 per component . shipping costs for delivering the components are $ 1 per unit . further , the manufacturer has costs of $ 19,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 250 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 199 , b ) 249 , c ) 233 , d ) 215 , e ) 229
Rationale: "$ 19500 is a fixed cost each component is $ 151 ( $ 150 to produce , $ 1 to ship ) manufacturer will be producing and selling 250 components so therefore the equation to find price would be 250 * p = 19500 + ( 250 * 150 ) + ( 250 * 1 ) p = ( 19500 + 37500 + 250 ) / 250 p = 229 answer : e"
Answer: e
Problem: the minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is
Options: a ) 4 tiles
b ) 5 tiles
c ) 6 tiles
d ) 7 tiles
e ) 8 tiles
Rationale: lcm of 16,24 = 48 48 * 48 is the minimum size of square made with 16 by 24 tiles number of tiles required = area of square / area of one tile = 48 * 48 / ( 16 * 24 ) = 6 tiles answer : c
Answer: c
Problem: sandy bought 65 books for $ 1380 from one shop and 55 books for $ 900 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 13 , b ) $ 15 , c ) $ 17 , d ) $ 19 , e ) $ 21
Rationale: average price per book = ( 1380 + 900 ) / ( 65 + 55 ) = 2280 / 120 = $ 19 the answer is d .
Answer: d
Problem: the simple interest on rs . 23 for 3 months at the rate of 5 paise per rupeeper month is
Options: a ) 3.45 , b ) 4.5 , c ) 2.25 , d ) 3.21 , e ) none
Rationale: sol . s . i . = rs . [ 23 * 5 / 100 * 3 ] = rs . 3.45 answer a
Answer: a
Problem: the weight of a glass of jar is 15 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 9 / 17 , e ) 9 / 23
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 15 g weight of coffee beans = 85 g weight of jar and remaining beans = 60 g weight of remaining beans = 45 g fraction remaining = 45 / 85 = 9 / 17 answer is d ."
Answer: d
Problem: how many numbers from 10 to 1000 are exactly divisible by 9 ?
Options: a ) 100 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "10 / 9 = 1 and 1000 / 9 = 111 = = > 111 - 1 = 100 . therefore 100 answer : a"
Answer: a
Problem: in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 48 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 38 , e ) 59
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 48 - 25 x 50 = 190 ∴ average for last 5 days = 190 / 5 = 38 d"
Answer: d
Problem: pradeep has to obtain 40 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 550 , d ) 1000 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 40 % of x = 200 + 20 = > 40 / 100 x = 220 x = ( 22000 / 40 ) x = 550 . answer : c"
Answer: c
Problem: a batsman makes a score of 56 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 8 , c ) 27 , d ) 29 , e ) 39
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 56 = total runs scored in 17 innings = > 16 ( x - 3 ) + 56 = 17 x = > 16 x - 48 + 56 = 17 x = > x = 8 answer is b ."
Answer: b
Problem: if 2 x + y = 6 and x + 2 y = 5 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 11 / 9 , e ) 4
Rationale: we have two equations : 2 x + y = 6 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 11 divide both sides by 3 to get : x + y = 11 / 3 so , ( x + y ) / 3 = 11 / 9 answer : d
Answer: d
Problem: what is the value of ( 12 + 22 + 32 + 42 + - - - - - + 102 )
Options: a ) 295 , b ) 324 , c ) 385 , d ) 391 , e ) 399
Rationale: "explanation : ( 12 + 22 + … . . + n 2 ) = ( 1 / 6 ) n ( n + 1 ) ( 2 n + 1 ) here , n = 10 therefore , ( 12 + 22 + … . . + 102 ) = ( 1 / 6 ) 10 ( 10 + 1 ) ( 2 x 10 + 1 ) = ( 1 / 6 ) x 10 x 11 x 21 = 385 answer : c"
Answer: c
Problem: if m and n are positive integers and m = 15 n - 1 , what is the remainder when m is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that m and n are positive integers and m = 15 n - 1 . we ' re asked for the remainder when m is divided by 5 . if . . . . n = 1 m = 14 14 / 5 = 2 remainder 4 final answer : e
Answer: e
Problem: a man has $ 10,000 to invest . he invests $ 4000 at 5 % and $ 3500 at 4 % . in order to have a yearly income of $ 500 , he must invest the remainder at :
Options: a ) 4.6 % , b ) 3.6 % , c ) 6.4 % , d ) 7.8 % , e ) 8.9 %
Rationale: "c 6.4 % income from $ 4000 at 5 % in one year = $ 4000 of 5 % . = $ 4000 × 5 / 100 . = $ 4000 × 0.05 . = $ 200 . income from $ 3500 at 4 % in one year = $ 3500 of 4 % . = $ 3500 × 4 / 100 . = $ 3500 × 0.04 . = $ 140 . total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340 . remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340 . = $ 160 . total invested amount = $ 4000 + $ 3500 = $ 7500 . remaining invest amount = $ 10000 - $ 7500 = $ 2500 . we know that , interest = principal × rate × time interest = $ 160 , principal = $ 2500 , rate = r [ we need to find the value of r ] , time = 1 year . 160 = 2500 × r × 1 . 160 = 2500 r 160 / 2500 = 2500 r / 2500 [ divide both sides by 2500 ] 0.064 = r r = 0.064 change it to a percent by moving the decimal to the right two places r = 6.4 % therefore , he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year ."
Answer: c
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.25 lacs . how many workers were they ?
Options: a ) 350 , b ) 400 , c ) 500 , d ) 550 , e ) 590
Rationale: "n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 c"
Answer: c
Problem: in the xy - coordinate system , if ( m , n ) and ( m 1 2 , n 1 k ) are two points on the line with the equation x 5 2 y 1 5 , then k 5
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: step 1 : analyze the question for any question involving the equation of a line , a good place to start is the slope - intercept form of the line , y = mx 1 b . remember that if you have two points on a line , you can derive the entire equation , and if you have an equation of the line , you can calculate any points on that line . step 2 : state the task we are solving for k , which is the amount by which the y - coordinate increases when the x - coordinate increases by 2 . step 3 : approach strategically the slope of a line is the ratio between the change in y and the change in x . in other words , every time the x - coordinate increases by 1 , the y - coordinate increases by the amount of the slope . the equation of the line in the question stem is defined as x = 2 y + 5 . we must isolate y to have slope - intercept form : so the slope of this line is 1 / 2 . this means that for every change of + 1 in the x direction , there is a change of + 1 / 2 in the y direction . then we know that , because there is an increase in 2 units in the x direction when moving from m to m + 2 , there must be a change of 1 unit in the y direction when moving from n to n + k . so k = 1 . since there are variables that eventually cancel ( m and n are not part of the answers ) , we can pick numbers . let ’ s say that you choose the y - coordinate of the point ( m , n ) to be 0 to allow for easier calculations . using the equation we ’ re given to relate x - and y - coordinates , we can calculate the x - coordinate : so ( m , n ) is the point ( 5 , 0 ) . now we ’ ll plug our values of m and n into the next point : ( m + 2 , n + k ) . that yields ( 7 , k ) . all we have to do is plug an x - coordinate of 7 into the equation to solve for k , the y - coordinate : answer is b
Answer: b
Problem: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 11 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d
Answer: d
Problem: find √ ? / 13 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 2704 , e ) none
Rationale: "answer let √ n / 13 = 4 then √ n = 13 x 4 = 52 ∴ n = 52 x 52 = 2704 . correct option : d"
Answer: d
Problem: an athlete runs 200 metres race in 25 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 37 , d ) 30 , e ) 28.8
Rationale: "speed = distance / time = 200 / 25 = 8 m / s = 8 * 18 / 5 = 28.8 km / hr answer : e"
Answer: e
Problem: how many odd prime numbers are there less than 125 ?
Options: a ) 29 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: odd prime number less than 125 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 there is 29 the odd prime number answer is a
Answer: a
Problem: the radius of a semi circle is 3.1 cm then its perimeter is ?
Options: a ) 15.94 , b ) 12.41 , c ) 16.1 , d ) 32.92 , e ) 32.3
Rationale: "36 / 7 r = 6.3 = 15.94 answer : a"
Answer: a
Problem: a , band c can do a piece of work in 11 days , 5 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 5 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: ( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 5 = 16 / 55 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 16 / 55 + 6 / 55 = 2 / 5 2 / 5 th work done in 2 days work done = 5 / 2 * 2 = 5 days answer : a
Answer: a
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8200 / 20.5 = 400 answer : c"
Answer: c
Problem: two trains 300 m and 400 m long run at the speed of 36 kmph and 18 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 46.67 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 36 + 18 = 54 kmph * 5 / 18 = 15 m / s distance covered in crossing each other = 300 + 400 = 700 m required time = 700 * 1 / 15 = 46.67 sec answer is b"
Answer: b
Problem: if 1 / ( x + 2 ) + 1 / ( x - 2 ) = 1 / ( x + 2 ) , what is the value of x ?
Options: a ) - 1 , b ) 2 , c ) 1 , d ) - 2 , e ) 0
Rationale: "if we solve the question , we get x = - 2 . option : d"
Answer: d
Problem: find the compound interest on $ 1200 for 1 year at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 240 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 1 = 1200 * 6 / 5 = $ 1440 ci = a - p = 1440 - 1200 = $ 240 answer is c"
Answer: c
Problem: find the perimeter and area of a square of side 12 cm .
Options: a ) 144 , b ) 121 , c ) 169 , d ) 196 , e ) 100
Rationale: "we know that the perimeter of square = 4 ã — side side = 12 cm therefore , perimeter = 4 ã — 12 cm = 48 cm now , area of the square = ( side ã — side ) sq . units = 12 ã — 12 cm â ² = 144 cm â ² answer : a"
Answer: a
Problem: if the sides of a cube are in the ratio 5 : 4 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 5 : 4 , c ) 4 : 7 , d ) 3 : 4 , e ) 4 : 5
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 4 d 1 : d 2 = 5 : 4 where √ 3 cancelled both side answer : b"
Answer: b
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 9 minutes 17 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 13 %
Rationale: bob ' s time = 640 secs . his sis ' time = 557 secs . percent increase needed = ( 640 - 557 / 640 ) * 100 = 83 / 640 * 100 = 13 % . ans ( e ) .
Answer: e
Problem: a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 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 ) 7 : 00 , b ) 8 : 00 , c ) 9 : 00 , d ) 10 : 00 , e ) 11 : 00
Rationale: in one hour and thirty minutes the first train travels 105 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 105 / 10 = 10.5 hours , so at 9 : 00 pm . the answer is c .
Answer: c
Problem: working together , jose and jane can complete an assigned task in 15 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 26 days , b ) 31 days , c ) 50 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 15 15 ( x + y ) = xy next , we ' re told 1 job takes 45 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 45 x + y = 90 so xy = 1350 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 50 days for jose and 27 days for jane . answer : c"
Answer: c
Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 6 ohms ?
Options: a ) 5 / 12 , b ) 7 / 12 , c ) 12 / 5 , d ) 7 / 5 , e ) 11 / 5
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 6 = 5 / 12 r = 12 / 5 the answer is c ."
Answer: c
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 87 , b ) 27 , c ) 25 , d ) 26 , e ) 24
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c"
Answer: c
Problem: when x is multiplied by 3 , the result is 16 more than the result of subtracting x from 36 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 16 = 36 - x or , 4 x = 52 or , x = 13 . answer : d"
Answer: d
Problem: a goods train leaves a station at a certain time and at a fixed speed . after 6 hours , an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph . this train catches up the goods train in 4 hours . find the speed of the goods train .
Options: a ) 36 kmph , b ) 40 kmph , c ) 30 kmph , d ) 42 kmph , e ) none of these
Rationale: let the speed of the goods train be x kmph . distance covered by goods train in 10 hours = distance covered by express train in 4 hours . ∴ 10 x = 4 × 90 or x = 36 . so , speed of goods train = 36 kmph . answer a
Answer: a
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 4 people to do 4 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 7
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 4 people can do 4 / 3 of the work in one day . 4 people can do 4 times the work in 3 days . the answer is c ."
Answer: c
Problem: 5 ! / ( 5 - 3 ) ! = ?
Options: a ) 36 , b ) 46 , c ) 56 , d ) 59 , e ) 60
Rationale: 5 ! / ( 5 - 3 ) ! = 5 ! / 2 ! = 5 * 4 * 3 = 60 . hence , the correct answer is e .
Answer: e
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.99 , d ) $ 1.00 , e ) $ 1.20
Rationale: assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90 x - 80 = 9.6 90 x = 89.6 x = 89.6 / 90 = 0.995 x is slightly under 0.9955 = 0.99 answer : c
Answer: c
Problem: what is the remainder when 4 ^ 8707 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "4 ^ 0 = 1 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ 5 = . . . . . 4 4 ^ 6 = . . . . . . . 6 and so on in a distinct last - digit pattern of 4,6 , 4,6 . . . after ignoring the first last - digit of 1 8707 / 2 = 4353 ( with a remainder of 1 ) so the last number is a 4 . alternatively , 8707 is an odd number and hence the last digit is a 4 when 4 ^ 8707 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Problem: if 5 % more is gained by selling an article for rs . 220 than by selling it for rs . 160 , the cost of the article is ?
Options: a ) 127 , b ) 1200 , c ) 1600 , d ) 1400 , e ) 1202
Rationale: "let c . p . be rs . x . then , 5 % of x = 220 - 160 = 60 x / 20 = 60 = > x = 1200 answer : b"
Answer: b
Problem: how many integers between 100 and 170 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "the total numbers between 100 and 170 , inclusive , is 71 . 3 * 34 = 102 and 3 * 56 = 168 so the number of multiples of 3 is 23 . 5 * 20 = 100 and 5 * 34 = 170 so the number of multiples of 5 is 15 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 11 = 165 so the number of multiples of 15 is 5 . thus the total number is 71 - 23 - 15 + 5 = 38 . the answer is b ."
Answer: b
Problem: two persons a and b can complete a piece of work in 20 days and 40 days respectively . if they work together , what part of the work will be completed in 5 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 3 / 6 , d ) 3 / 8 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 20 b ' s one day ' s work = 1 / 40 ( a + b ) ' s one day ' s work = 1 / 20 + 1 / 40 = 3 / 40 the part of the work completed in 5 days = 5 ( 3 / 40 ) = 3 / 8 . answer : d"
Answer: d
Problem: there are x persons and y chocolates . if each person is given 1 chocolate then 1 chocolate is left , if each person is given 2 chocolates then 1 person will be left . so how many persons and chocolates are there ? ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 45 , e ) 44
Rationale: x person , y chocolates 1 st equation = = > ( y - 1 ) / x = 1 2 nd equation = = > y / ( x - 1 ) = 2 solving we get x = 3 , y = 4 answer : c
Answer: c
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 3 days at a time . if a starts they finish the task in exactly 9 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 5 , e ) 9 / 2
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 3 → 6 x + 3 y = 1 when b starts : no . of days when a works = 4 no . of days when a works = 5 → 5 x + 4 y = 1 solving the above two equations for xy x = 1 / 9 y = 1 / 9 → total work done by ab in a day = 1 / 9 + 1 / 9 = 2 / 9 → no . of days to complete the work when both work together = 9 / 2 ; answer : e"
Answer: e
Problem: find out the square of a number which when doubled exceeds its one seventh by 13 ?
Options: a ) 16 , b ) 49 , c ) 19 , d ) 26 , e ) 17
Rationale: "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 7 ) + 13 = > 14 p = p + 91 = > p = 7 p ^ 2 = 7 ^ 2 = 49 . answer : b"
Answer: b
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 20 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 244 , e ) 312
Rationale: "so 12.2 * 20 = 244 . . imo option d is correct answer . ."
Answer: d
Problem: an engineering student has to secure 36 % marks to pass . he gets 130 marks and fails by 14 marks . the maximum number of marks obtained by him is ?
Options: a ) 337 , b ) 400 , c ) 298 , d ) 2798 , e ) 271
Rationale: 130 14 - - - - - - - 361 - - - - - - 144 100 % - - - - - - ? = > 400 answer : b
Answer: b
Problem: united telephone charges a base rate of $ 9.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes
Rationale: lets take number of minutesx . given that , 9 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 60 minutes ans e
Answer: e
Problem: the cost of carpeting a room 18 m long with a carpet 75 cm wide at 45 paise per meter is rs . 81 . the breadth of the room is :
Options: a ) 7 m , b ) 7.5 m , c ) 5.5 m , d ) 6.5 m , e ) 8.5 m
Rationale: "length of the carpet = total cost / rate / m = 8100 / 45 = 180 m area of the carpet = 180 * 75 / 100 = 135 m 2 breadth of the room = ( area / length ) = 135 / 18 = 7.5 m answer : b"
Answer: b
Problem: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 7 km ?
Options: a ) 3.0 , b ) 3.25 , c ) 3.5 , d ) 3.75 , e ) 4.0
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 7 / 2 = 3.5 hours . the answer is c ."
Answer: c
Problem: ratio between 2 numbers is 5 : 7 and their product is 560 . what is the difference between 2 numbers ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2
Rationale: "explanation : x / y = 5 / 7 x × y = 560 ⇒ x = 560 / y substituting this value in first equation , we get 560 / yy = 57560 / yy = 57 ⇒ 560 y 2 = 57560 y 2 = 57 ⇒ y = 28 x = 20 so difference between the numbers could be x – y = – 8 y – x = 8 answer : c"
Answer: c
Problem: the edges of three metal cubes are 1 cm , 2 cm , and 3 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 3.3 , b ) 3.5 , c ) 3.7 , d ) 3.9 , e ) 4.1
Rationale: "the total volume is 1 ^ 3 + 2 ^ 3 + 3 ^ 3 = 36 the edge of the new cube is the cube root of 36 which is about 3.3 cm . the answer is a ."
Answer: a
Problem: a scale 6 ft . 8 inches long is divided into 2 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 40 inches
Rationale: explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 2 parts = 80 / 2 = 40 inches answer : e
Answer: e
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 11 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 120 , c ) $ 183.3 , d ) $ 220 , e ) $ 260
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 11 * ( a + e ) = = > 10 a = 12 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 a = 220 + 10 a = = > a = 220 ; e = 183.3 c"
Answer: c
Problem: if 11 oranges bought 10 r and 10 oranges sold 11 r . what is the profit
Options: a ) 11 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 23 %
Rationale: suppose he bought 110 apples . cp = rs 100 sp = rs 121 % profit = 100 * ( 121 - 100 ) / 100 = 21 % answer : d
Answer: d
Problem: the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 110 meters ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 28
Rationale: "the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 110 meters = 110 / 5 = 22 seconds . the answer is b ."
Answer: b
Problem: find the simple interest on rs . 567 for 7 months at 9 paisa per month ?
Options: a ) s . 357.21 , b ) s . 322.12 , c ) s . 400 , d ) s . 278.9 , e ) s . 300
Rationale: "explanation : i = ( 567 * 7 * 9 ) / 100 = 357.21 answer : option a"
Answer: a
Problem: the least number which when divided by 4 , 6 , 7 and 8 leaves a remainder 6 , but when divided by 9 leaves no remainder , is
Options: a ) 340 , b ) 342 , c ) 523 , d ) 363 , e ) none of these
Rationale: "explanation : l . c . m of 4 , 6 , 7 , 8 = 168 therefore required number is of the form 168 k + 6 . least value of k for which ( 168 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 168 x 2 + 6 ) = 342 . answer : b"
Answer: b
Problem: if 0.6 : 1.4 : : 2 : 4 : x , then x = ?
Options: a ) 56 , b ) 5.6 , c ) 0.56 , d ) 0.056 , e ) none of these
Rationale: "explanation : 0.6 × x = 2.4 × 1.4 x = ( 2.4 × 1.4 ) / 0.6 = 24 / 10 × 17 / 10 × 1 / ( 6 / 10 ) 24 / 10 × 14 / 10 × 10 / 6 2 / 5 × 14 = 28 / 5 = 5.6 answer : option b"
Answer: b
Problem: the tax on a commodity is diminished by 10 % and its consumption increases by 10 % . find the effects on revenue ?
Options: a ) 1 % decrease , b ) 2 % increase , c ) 3 % decrease , d ) 4 % decrease , e ) none of these
Rationale: "since tax consumption = revenue . therefore , net % change in revenue = ( x + y + xy / 100 ) % = [ - 10 + 10 + ( - 10 x 10 ) / 100 ] % or - 1 % . therefore , revenue decreased by 1 % . answer : a"
Answer: a
Problem: at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 4 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d"
Answer: d
Problem: ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the maximum and minimum possible values of ' a + b ' ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 9 , e ) 11
Rationale: a = 4 , b = 5 as they have to co - primes ( hcf being 1 and lcm = 20 ) so a + b = 9 is their max and min value hence difference = 0 answer - a
Answer: a
Problem: if a , b and c together can finish a piece of work in 4 days . a alone in 6 days and b in 18 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 36
Rationale: "c = 1 / 4 - 1 / 6 – 1 / 18 = 1 / 36 = > 36 days ' answer : e"
Answer: e
Problem: wo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 227 , b ) 444 , c ) 277 , d ) 298 , e ) 212
Rationale: 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b
Answer: b
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 3135 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 1000 , d ) 3000 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 3135 x * ( 11 / 10 ) * ( 1 / 100 ) = 33 x = 3000 answer : d"
Answer: d
Problem: a train speeds past a pole in 15 sec and a platform 130 m long in 25 sec , its length is ?
Options: a ) 195 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 130 ) / 25 = x / 15 = > x = 195 m . answer : option a"
Answer: a
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 35 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 35 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 35 pm + 2 hrs = 6 : 35 pm answer : d . 6 : 35"
Answer: d
Problem: if - 11 a and - 8 b are negative integers , then ( - 11 a ) * ( - 8 b ) + ab is
Options: a ) 88 ab , b ) - 89 ab , c ) 89 ab , d ) - 88 a , e ) - 88 b
Rationale: answer : c
Answer: c
Problem: what is the thousandths digit in the decimal equivalent of 43 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 8
Rationale: "43 / 5000 = 43 / ( 5 * 10 ^ 3 ) = ( 43 / 5 ) * 10 ^ - 3 = 8.6 * 10 ^ - 3 = . 0086 thousandths digit = 8 answer e"
Answer: e
Problem: what is the difference between the largest number and the least number written with the digits 5 , 3 , 1 , 4 ?
Options: a ) 6084 , b ) 3788 , c ) 4086 , d ) 2721 , e ) 1812
Rationale: explanation : 1345 5431 - - - - - - - - - - - - 4086 answer : c
Answer: c
Problem: if ( a – b ) is 9 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( a – b ) – ( c + d ) = 9 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 9 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 9 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 9 = ( c – a ) – 3 = > 2 ( a – c ) = 6 = > ( a – c ) = 3 answer : c
Answer: c
Problem: the population of a town increased from 1 , 75,000 to 2 , 10,000 in a decade . the average percent increase of population per year is
Options: a ) 2 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 210000 - 175000 ) = 35000 . increase % = ( 35000 / 175000 ã — 100 ) % = 20 % . required average = ( 20 / 10 ) % = 2 % . answer a"
Answer: a
Problem: there are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 27 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 240 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 240 / 24 = 17 + 10 = 27 answer : a"
Answer: a
Problem: an alloy weighing 20 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 76 , e ) 48
Rationale: "in 24 ounces , gold is 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 90 / 100 = > x = 76 . answer is d ."
Answer: d
Problem: the cost of the paint is rs . 20 per kg . if 1 kg of paint covers 15 sq . ft , how much will it cost to paint outside of a cube having 5 feet each side
Options: a ) rs . 200
b ) rs . 672
c ) rs . 546
d ) rs . 876
e ) none of these
Rationale: explanation : surface area of a cube = 6 x 5 ^ 2 = 150 sq . ft quantity of paint required = ( 150 / 15 ) = 10 kg cost of painting = 20 x 10 = rs . 200 answer : a
Answer: a
Problem: a student committee on academic integrity has 30 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 11
Rationale: "xc 1 * ( x - 1 ) c 1 = 30 x ^ 2 - x - 30 = 0 ( x - 6 ) ( x + 5 ) = 0 x = 6 , - 5 - 5 ca n ' t possible . d"
Answer: d
Problem: what is the difference between the largest number and the least number written with the digits 9 , 3 , 5 , 7 ?
Options: a ) 6084 , b ) 3788 , c ) 2077 , d ) 2721 , e ) 6174
Rationale: "explanation : 3579 9753 - - - - - - - - - - - - 6174 answer : e"
Answer: e
Problem: a bag contains 4 red , 3 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 1 / 6 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , = 4 c 29 c 2 = 4 c 29 c 2 = 6 / 36 = 1 / 6 c"
Answer: c
Problem: what is the value of 8 1 / 3 % of 600 + 37 ½ of 400
Options: a ) 100 , b ) 300 , c ) 150 , d ) 200 , e ) 250
Rationale: "25 * 600 / 300 + 75 * 400 / 200 = 50 + 150 = 200 answer : d"
Answer: d
Problem: there is a 30 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ?
Options: a ) 25.0 % , b ) 37.5 % , c ) 50.0 % , d ) 62.5 % , e ) 75 %
Rationale: p ( chile and not madagascar ) = 0.3 * 0.5 = 0.15 p ( madagascar and not chile ) = 0.5 * 0.7 = 0.35 total probability = 0.15 + 0.35 = 0.5 = 50 % the answer is c .
Answer: c
Problem: how much 45 % of 60 is greater than 35 % of 40 ?
Options: a ) 18 , b ) 13 , c ) 15 , d ) 17 , e ) 71
Rationale: "( 45 / 100 ) * 60 – ( 35 / 100 ) * 40 27 - 14 = 13 answer : b"
Answer: b
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 180 . what is their h . c . f . ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 60 , e ) 70
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 180 x = 15 hcf of 2 x , 3 x and 4 x = x = 15 the answer is a ."
Answer: a
Problem: the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 5 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 7.27 , e ) 7.63
Rationale: "area of circle is pi * r ^ 2 but in 5 minutes area covered is ( 5 / 60 ) * 360 = 30 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 30 / 360 ) = 7.63 cm ^ 2 answer : e"
Answer: e
Problem: donovan and michael are racing around a circular 600 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 8 , b ) 7 , c ) 9 , d ) 6 , e ) 5
Rationale: one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 600 / 45 = > 40 / 3 2 . speed / rate of michael = distance / time = > 600 / 40 = > 15 relative speed between them = 15 - 40 / 3 = > 5 / 3 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 600 , relative rate = 5 / 3 total time taken by micheal to surpass donovan = distance / rate = > 600 * 3 / 5 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . c
Answer: c
Problem: if the function q is defined by the formula q = 5 w / ( 4 m ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , m is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: we just need to find the factor thats all , w - > quadrupled - > 4 w m - > doubled - > 2 m z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and m * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b
Answer: b
Problem: carol spends 1 / 4 of her savings on a stereo and 2 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12
Rationale: total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 2 / 3 ) ( 1 / 4 ) s = ( 1 / 3 ) * ( 1 / 4 ) * s = ( 1 / 12 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 12 ) / s = 1 / 4 answer : a
Answer: a
Problem: one week , a certain truck rental lot had a total of 18 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 12 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 8 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 18 n + r / 2 = 12 r = 12 c"
Answer: c
Problem: a grocer has 400 pounds of coffee in stock , 25 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: 1 . 25 % of 400 = 100 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 160 pounds of decaffeinated out of 500 pounds , that means 160 / 500 * 100 % = 32 % . the correct answer is c .
Answer: c
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 6 / 8 of its own speed and got to its destination in 11 hours ?
Options: a ) 2.5 hrs , b ) 2.9 hrs , c ) 4.5 hrs , d ) 3.5 hrs , e ) 1.5 hrs
Rationale: new speed = 6 / 8 of usual speed new time = 6 / 8 of usual time 6 / 8 of usual time = 10 hrs usual time = 10 * 6 / 8 = 7.5 hrs time saved = 10 - 7.5 = 2.5 hrs answer is a
Answer: a
Problem: a person spent rs . 7,540 from his salary on food and 5,690 on house rent . after that he was left with 60 % of his monthly salary . what is his monthly salary ?
Options: a ) 73,075 , b ) 34,075 , c ) 23,075 , d ) 33,075 , e ) 32,075
Rationale: "total money spent on food and house rent = 7,540 + 5,690 = 13,230 which is 100 - 60 = 40 % of his monthly salary ∴ his salary = 13230 x 100 / 40 = 33075 answer : d"
Answer: d
Problem: a survey was sent to 80 customers , 9 of whom responded . then the survey was redesigned and sent to another 63 customers , 12 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 69 %
Rationale: "rate of first survey = 9 / 80 rate of second survey = 12 / 63 % response rate increase ( 12 / 63 - 9 / 80 ) / ( 9 / 80 ) = 69 % answer is e = 69 %"
Answer: e
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is
Options: a ) 1.2 km , b ) 1.8 km , c ) 2.4 km , d ) 3.6 km , e ) 1.6 km
Rationale: "b = 15 km / hr , s = 3 km / hr , downstream b + s = 15 + 3 = 18 km / hr down stream time t = 12 min , we have to change it to hours so t = 12 / 60 = 1 / 5 hrs . distance = speed * time = 18 * 1 / 5 = 3.6 km . answer : d"
Answer: d