regisss/math_qa huggingface dataset:
Problem: right triangle pqr is the base of the prism in the figure above . if pq = pr = â ˆ š 5 and the height of the prism is 10 , what is the volume of the prism ?
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 5 ) * ( square root of 5 ) * 10 = 25 answer : e
Answer: e
Problem: each of the positive integers a and c is a 4 - digit integer . if each of the digits 0 through 9 appears in one of these 3 integers , what is the maximum possible value of the sum of a and c ?
Options: a ) 18695 , b ) 18325 , c ) 18365 , d ) 18395 , e ) 18485
Rationale: according to the stem we should use the digits 0 through 9 to construct 2 four - digit integers , so that their sum is as big as possible . to maximize the sum , maximize the thousands digits of a and c , so make them 9 and 8 . next , maximize hundreds digits . make them 7 and 6 . next maximize 10 ' s digit place by 5 and 4 use the remaining digits ( 3 , and 2 ) for units digits . so , a would be 9753 , and c would be 8642 . 9753 + 8642 = 18395 answer : d .
Answer: d
Problem: the length of a rectangle is doubled while its width is doubled . what is the % change in area ?
Options: a ) 250 % , b ) 300 % , c ) 500 % , d ) 650 % , e ) 700 %
Rationale: "the original area is l * w the new area is 2 l * 2 w = 4 * l * w = l * w + 3 * l * w the area increased by 300 % . the answer is b ."
Answer: b
Problem: riya and priya set on a journey . riya moves eastward at a speed of 18 kmph and priya moves westward at a speed of 24 kmph . how far will be priya from riya after 15 minutes
Options: a ) 25 kms , b ) 11 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: total eastward distance = 18 kmph * 1 / 4 hr = 4.5 km total westward distance = 24 kmph * 1 / 4 hr = 6 km total distn betn them = 4.5 + 6 = 10.5 m ans 11 km answer : b
Answer: b
Problem: 36 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 12 , b ) 16 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 36 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 36 x 5 x 12 x = ( 36 x 5 x 12 ) / ( 30 x 6 ) x = 12 answer a"
Answer: a
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 10 % profit on the first article and 10 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 100 , d ) 202 , e ) 270
Rationale: profit on first article = 10 % of 1000 = 100 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : c
Answer: c
Problem: a can run 4 times as fast as b and gives b a start of 63 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 84 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 63 m he gains 63 * ( 4 / 3 ) i . e 84 m answer : e"
Answer: e
Problem: if c is 25 % of a and 10 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "c is 25 % of a - - > c = a / 4 ; c is 10 % of b - - > c = b / 10 ; thus a / 4 = b / 10 - - > b = 5 / 2 * a = 2.5 a . therefore , b is 250 % of a . answer : e"
Answer: e
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 40 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 205 , b ) 220 , c ) 240 , d ) 247 , e ) 294
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 40 t t = 8.4 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 8.4 = 294 miles answer : - e"
Answer: e
Problem: what is the ratio between perimeters of two squares one having 2.5 times the diagonal then the other ?
Options: a ) 4 : 5 , b ) 1 : 3 , c ) 2.5 : 1 , d ) 3.5 : 1 , e ) 3 : 2
Rationale: "d = 2.5 d d = d a √ 2 = 2.5 d a √ 2 = d a = 2.5 d / √ 2 a = d / √ 2 = > 2.5 : 1 answer : c"
Answer: c
Problem: a number when divided by 899 gives a remainder 63 . what remainder will be obtained by dividing the same number by 29
Options: a ) 8 , b ) 5 , c ) 7 , d ) 6 , e ) 9
Rationale: 63 / 29 , thereforerequired number is : 5 , correct answer ( b )
Answer: b
Problem: a and b can do a piece of work in 10 days , while b and c can do the same work in 15 days and c and a in 25 days . they started working together , after 4 days a left . after another 4 days b left . in how many days c can finish the remaining work ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 96 , e ) none of these
Rationale: "let the rates of a , b and c be a , b , and c respectively . a and b can do a piece of work in 10 days : a + b = 1 / 10 ; b and c can do the same work in 15 days : b + c = 1 / 15 ; c and a can do the same work in 25 days : c + a = 1 / 25 . sum the above 3 equations : 2 ( a + b + c ) = 31 / 150 - - > a + b + c = 31 / 300 subtract a + b = 1 / 10 from above to get c = 1 / 300 . for 4 days all 3 worked and completed 4 * ( a + b + a ) = 124 / 300 of the work . for the next 4 days b and c worked and they completed 4 ( b + c ) = 4 / 15 = 80 / 300 of the work . so , by the time c is left alone 1 - ( 124 / 300 + 80 / 300 ) = 96 / 300 of the work is left to be completed by c alone . time = job / rate = ( 96 / 300 ) / ( 1 / 300 ) = 96 days . answer : d"
Answer: d
Problem: 17 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 34 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 17 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 17 * 21 * 8 = 14 * x * 6 x = 34 answer : a"
Answer: a
Problem: if xy = 9 , x / y = 36 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
Rationale: very easy question . 2 variables and 2 easy equations . xy = 9 - - - > x = 9 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 9 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 9 / 36 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a .
Answer: a
Problem: in one year , the population , of a village increased by 20 % and in the next year , it decreased by 20 % . if at the end of 2 nd year , the population was 9600 , what was it in the beginning ?
Options: a ) 10000 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 2081
Rationale: x * 120 / 100 * 80 / 100 = 9600 x * 0.96 = 9600 x = 9600 / 0.96 = > 10000 answer : a
Answer: a
Problem: two numbers are in the ratio of 15 : 11 . if their h . c . f . is 13 , find the numbers .
Options: a ) 195,143 , b ) 185,133 , c ) 175,123 , d ) 165,113 , e ) none of them
Rationale: let the required numbers be 15 . x and llx . then , their h . c . f . is x . so , x = 13 . the numbers are ( 15 x 13 and 11 x 13 ) i . e . , 195 and 143 . answer is a .
Answer: a
Problem: a bag contains 7 red , 5 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 7 / 40 , d ) 3 / 29 , e ) 4 / 27
Rationale: "p ( both are red ) , = 7 c 216 c 2 = 7 c 216 c 2 = 21 / 120 = 7 / 40 c"
Answer: c
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 216 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 8 hours
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 216 km time taken = distance / speed = 216 / 27 = 8 hours . answer : option e"
Answer: e
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio w of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Problem: in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 5 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 1.2 , d ) 3.1 , e ) 1.6
Rationale: "number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 2 = ~ 6.2 passengers using logan airport = 6.2 / 5 = ~ 1.24 so c"
Answer: c
Problem: the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 3 , the average of the numbers increases to 12.8 . what number is multiplied by 3 ?
Options: a ) 15.0 , b ) 13.0 , c ) 13.9 , d ) 10.0 , e ) 6.0
Rationale: "the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 3 is 12.8 the sum of the numbers will now be 12.8 x 5 = 64 so the sum has increased by 64 - 34 = 30 let the number multiplied by 3 be n then , 3 n = n + 30 or 2 n = 30 or n = 15 answer : - a"
Answer: a
Problem: in covering a distance of 18 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 3 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 7.8 kmph
Rationale: let abhay ' s speed be x km / hr . then , 18 / x - 18 / 2 x = 3 6 x = 18 x = 3 km / hr . answer : option a
Answer: a
Problem: a portion of the 50 % solution of chemicals was replaced with an equal amount of 60 % solution of chemicals . as a result , 55 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 5 , e ) 1 / 2
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.5 ( 1 - x ) + 0.6 * x = 0.55 - - > x = 1 / 2 . answer : e ."
Answer: e
Problem: ram get 450 marks in his exam which is 90 % of total marks . what is the total marks ?
Options: a ) 475 , b ) 600 , c ) 550 , d ) 500 , e ) 525
Rationale: x * ( 90 / 100 ) = 450 x = 5 * 100 x = 500 answer : d
Answer: d
Problem: all the faces of a cube are painted with blue colour . then it is cut into 125 small equal cubes . how many small cubes will be formed having only one face coloured ?
Options: a ) 54 , b ) 8 , c ) 16 , d ) 24 , e ) 34
Rationale: no . of small cubes will have only one face painted = ( x - 2 ) 2 * 6 here x = side of the small cube = 5 therfore ( x - 2 ) 2 * 6 = 54 answer : a
Answer: a
Problem: in a certain country 1 / 7 of 8 = 5 . assuming the same proportion , what would be the value of 1 / 5 of 40 ?
Options: a ) 54 , b ) 25 , c ) 45 , d ) 35 , e ) 52
Rationale: "d 35"
Answer: d
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 30 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 29 % , e ) 20 %
Rationale: let me try a simpler one . lets assume that candidate got 30 % votes and total votes is 100 . candidate won = 30 remaining = 70 to get 50 % , candidate requires 20 votes from 100 which is 20 % and 20 votes from 70 . 20 / 70 = 2 / 7 = . 285 = 28.5 % which is approx 29 % . hence the answer is d .
Answer: d
Problem: if f ( x ) = x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 5 x , then f ( - 1 ) =
Options: a ) - 4 , b ) - 2 , c ) - 1 , d ) 1 , e ) 2
Rationale: f ( - 1 ) = ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 2 ( - 1 ) ^ 2 + 5 ( - 1 ) = 1 + 4 - 2 - 5 = - 2 the answer is b .
Answer: b
Problem: in the junior basketball league there are 18 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 10
Rationale: otal teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . answer : e
Answer: e
Problem: working alone , john finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . john alone cleans the entire house in 6 hours . how many hours will it take nick and john to clean the entire house if they work together ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
Rationale: answer is 3.6 hours . john does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: e
Problem: the radius of a cylinder is 2 r units and height is 3 r units . find the curved surface ?
Options: a ) 18 π r 2 , b ) 12 π r 2 , c ) 3 π r 2 , d ) 6 π r 2 , e ) 9 π r 2
Rationale: "explanation : 2 * π * 2 r * 3 r = 12 π r 2 answer : b"
Answer: b
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 5 ?
Options: a ) 10 ^ 2 , b ) 10 ^ 3 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 so it will from 5 to 7 i . e 6,7 = 10 * 10 = 10 ^ 2 answer is a"
Answer: a
Problem: the total of 344 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 277 , c ) 278 , d ) 200 , e ) 300
Rationale: explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 344 - x ) . 0.20 * ( x ) + 0.25 ( 344 - x ) = 71 = > x = 300 . . answer : e ) 300
Answer: e
Problem: a man buys a cycle for rs . 800 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 680 , d ) s . 520 , e ) s . 700
Rationale: "s . p . = 85 % of rs . 800 = rs . 85 / 100 x 800 = rs . 680 answer : c"
Answer: c
Problem: a math teacher has 26 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 26 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 26 - 17 = 9 answer ( a )"
Answer: a
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 7 .
Options: a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 1.5
Rationale: "6 * 15 * 3 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 7 + 1 ) = ( √ 8 * 18 ) / 8 = ( √ 144 ) / 8 = 12 / 8 = 1.5 answer is e"
Answer: e
Problem: if 3 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 3 z / 5 , e ) z / 9
Rationale: "3 x = 6 y = z x = z / 3 and y = z / 6 x + y = z / 3 + z / 6 = z / 2 answer is a"
Answer: a
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1400 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 20000 , d ) 12197 , e ) 12012
Rationale: "[ 1400 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 20000 answer : c"
Answer: c
Problem: how many bricks each measuring 21 cm x 10 cm x 8 cm , will be needed to build a wall 9 m x 5 m x 18.5 m
Options: a ) 4955 , b ) 4899 , c ) 4650 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 900 x 500 x 18.5 ) / ( 21 x 10 x 8 ) = 4955 answer : a"
Answer: a
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 62.8 , c ) 62.1 , d ) 62.9 , e ) 32.5
Rationale: "explanation : cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5 answer : a"
Answer: a
Problem: during a certain two - week period , 64 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 10 a , b ) 12 a , c ) 14 a , d ) 16 a , e ) 18 a
Rationale: total movies = 100 . comedies = 64 . action + drama = 36 . since there were 5 times as many dramas as action movies , then action + 5 * action = 36 - - > action = a = 6 . comedies = 60 = 10 a . a
Answer: a
Problem: find the greatest 4 digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24 . a . 9974
Options: a ) 388 , b ) 282 , c ) 378 , d ) 292 , e ) 281
Rationale: explanation : since the difference between the divisors and the respective remainders is not constant , back substitution is the convenient method . none of the given numbers is satisfying the condition . answer : e
Answer: e
Problem: p has $ 35 more than what q and r together would have had if both b and c had 1 / 7 of what p has . how much does p have ?
Options: a ) $ 45 , b ) $ 47 , c ) $ 49 , d ) $ 51 , e ) $ 53
Rationale: "p = ( 2 / 7 ) * p + 35 ( 5 / 7 ) * p = 35 p = 49 the answer is c ."
Answer: c
Problem: a can do a work in 20 days and b in 30 days . if they work on it together for 4 days , then the fraction of the work that is left is :
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3
Rationale: "ans is : b a ' s 1 day ' s work = 1 / 20 b ' s 1 day ' s work = 1 / 30 ( a + b ) ' s 1 day ' s work = ( 1 / 20 + 1 / 30 ) = 1 / 12 ( a + b ) ' s 4 day ' s work = ( 1 / 12 * 4 ) = 1 / 3 therefore , remaining work = ( 1 - 1 / 3 ) = 2 / 3"
Answer: b
Problem: 3 candidates in an election and received 1136 , 7636 and 10628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 54.8 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 7636 + 10628 ) = 19400 so , required percentage = 10628 / 19400 * 100 = 54.8 % c"
Answer: c
Problem: a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 4 a = 2 b = c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
Options: a ) 124 , b ) 297 , c ) 394 , d ) 421 , e ) 842
Rationale: ratio of a : b : c = 1 : 2 : 4 two possible greatest single digit values for c are 8 and 4 if c is 8 , then x = 248 if c is 4 , then x = 124 difference = 248 - 124 = 124 a is the answer
Answer: a
Problem: if albert ’ s monthly earnings rise by 27 % , he would earn $ 567 . if , instead , his earnings rise by only 26 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 562 , d ) 578 , e ) 693
Rationale: "= 567 / 1.27 ∗ 1.26 = 562 = 562 answer is c"
Answer: c
Problem: indu gave bindu rs . 1250 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 5 , b ) 2 , c ) 9 , d ) 5 , e ) 1
Rationale: "1250 = d ( 100 / 4 ) 2 d = 2 answer : b"
Answer: b
Problem: when n is divided by 24 , the remainder is 4 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 0 , e ) 7
Rationale: "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 4 n = 4 ( 4 ) = 16 , which leaves a remainder of 0 when divided by 8 . answer d"
Answer: d
Problem: tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 3 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 60 , b ) 72 , c ) 84 , d ) 96 , e ) 108
Rationale: "d is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 3 t ) = 8 t = = > t = 2 / 5 = = > 24 minutes to travel double distance , 2 ( 2 + 3 t ) = 8 t = = > 2 = = > 120 minutes difference , 96 minutes d"
Answer: d
Problem: 35 - [ 23 - { 15 - x } ] = 12 × 2 ÷ 1 / 2
Options: a ) 34 , b ) 32 , c ) 17 , d ) 27 , e ) 28
Rationale: explanation : 35 - [ 23 - { 19 - ( 15 - x ) } ] = 12 × 2 × 2 = 48 = > 35 - 23 + ( 19 - 15 + x ) = 48 = > 12 + 4 + x = 48 = > x = 48 - ( 4 + 12 ) = 32 answer : option b
Answer: b
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.2 km ?
Options: a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "c 300 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1200 ) = 300 m answer is c"
Answer: c
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 20 . what is the value of f ( 6 ) ?
Options: a ) 9 , b ) 0 , c ) 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 20 then f ( 5 ) = 20 - 5 = 15 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 15 - 6 = 9 . answer : a . questions on funtions to practice :"
Answer: a
Problem: what is the remainder when 14,453 × 15,654 × 16,788 is divided by 5 ?
Options: a ) 2 , b ) 1 , c ) 5 , d ) 4 , e ) 3
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 3 * 4 * 8 = will give units digit as 5 so , whatever be the number , if it ends in 6 , the remainder after dividing with 5 will be 1 . optionb"
Answer: b
Problem: a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?
Options: a ) 22 hours , b ) 21 hours , c ) 23 hours , d ) 20 hours , e ) 28 hours
Rationale: "d 20 hours | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 50 40 d = 20 rs = 50 – 40 = 10 t = 20 / 10 = 2 hours"
Answer: d
Problem: what is the smallest 5 digit number that is divisible by 15 , 32 , 45 , and 54 ?
Options: a ) 11260 , b ) 11860 , c ) 12360 , d ) 12960 , e ) 13560
Rationale: 15 = 3 * 5 32 = 2 ^ 5 45 = 3 ^ 2 * 5 54 = 2 * 3 ^ 3 lcm = 2 ^ 5 * 3 ^ 3 * 5 = 4320 the smallest five - digit number that is a multiple of 4320 is 3 * 4320 = 12,960 the answer is d .
Answer: d
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 45 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 , b ) 88 , c ) 77 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 45 km with stoppages . stoppage time = time take to travel ( 60 - 45 ) km i . e 15 km at 60 km / hr . stoppage time = 15 / 60 hrs = 15 min . answer : a"
Answer: a
Problem: a rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 14 cms
b ) 21 cms
c ) 42 cms
d ) none of these
e ) can not be determined
Rationale: solution largest size of the tile . h . c . f of 378 cm and 525 cm = 21 cms . answer b
Answer: b
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel five times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 5 and w = 5 s then we have 1 / ( 5 * s ) + 1 / s = 1 / 5 < = > 6 / ( 5 * s ) = 1 / 5 < = > s = 6 ans : b"
Answer: b
Problem: the diagonal of a rhombus are 80 m and 120 m . its area is :
Options: a ) 4500 , b ) 4000 , c ) 4800 , d ) 4600 , e ) 4320
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 80 ã — 120 ) cm ( power ) 2 = 80 ã — 60 = 4800 cm ( power ) 2 answer is c ."
Answer: c
Problem: 3 bodies x , y and z start moving around a circular track of length 960 m from the same point simultaneously in the same direction at speeds of 12 m / s , 20 m / s and 36 m / s respectively . when will they meet for the first time after they started moving ?
Options: a ) 240 seconds , b ) 120 seconds , c ) 60 seconds , d ) 180 seconds , e ) 100 seconds
Rationale: if they all meet after t seconds , it means they covered the distances 12 t , 20 t , and 36 t respectively . since they all arrive to the same spot , it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track , which is 960 m . so , 8 t , 16 t , and 24 t must all be multiples of 960 . 8 t multiple of 960 means t multiple of 120 . the smallest t with this property is 120 and is on the list of answers . answer b .
Answer: b
Problem: a part of certain sum of money is invested at 10 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 2 , b ) 4 : 8 , c ) 4 : 3 , d ) 4 : 0 , e ) 6 : 5
Rationale: "12 : 10 = 6 : 5 answer : e"
Answer: e
Problem: kelly and chris are moving into a new city . both of them love books and thus packed several boxes with books . if chris packed 60 % of the total number of boxes , what was the ratio of the number of boxes kelly packed to the number of boxes chris packed ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 4 , e ) 1 / 4
Rationale: the ratio of the number of boxes kelly packed to the number of boxes chris packed = 40 / 60 = 2 / 3 answer : b
Answer: b
Problem: there are 6 more women than there are men on a local co - ed softball team . if there are a total of 24 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 9 / 15 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 6 w + m = 24 m + 6 + m = 24 2 m = 18 m = 9 w = 15 ratio : 9 : 15 ans : b"
Answer: b
Problem: two cars start at the same time from opposite ends of a highway that is 60 miles long . one car is riding at 13 mph and the second car is riding at 17 mph . how long after they begin will they meet ?
Options: a ) 0.75 , b ) 1 , c ) 1.25 , d ) 1.5 , e ) 2.0
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 17 + 13 = 30 mph total distance to be covered = 60 miles . time taken would be : 60 miles / 30 mph = 2.0 hours e is the answer ."
Answer: e
Problem: ( x + 6 ) is a factor in x ^ 2 - mx - 42 . what is the value of m ?
Options: a ) 2 , b ) 2.2 , c ) 1 , d ) 4 , e ) 5
Rationale: i solved the second degree equation and found it like this : x ^ 2 - mx - 42 = 0 ( x - 7 ) ( x + 6 ) = 0 x = 7 or x = - 6 substituting both values for x in the equation we find : x ^ 2 - mx - 42 = > ( - 6 ) ^ 2 - m ( - 6 ) = 42 = > 36 + 6 m = 42 = > 6 m = 42 - 36 = 6 = > m = 1 and with 7 , using a similar process we end up with : ( 7 ) ^ 2 - m ( 7 ) = 42 - 7 m = 42 - 49 = - 7 m = - 1 ao , ans c
Answer: c
Problem: local kennel has cats and dogs in the ratio of 6 : 8 . if there are 10 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 30 , b ) 35 , c ) 45 , d ) 50 , e ) 40
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 6 : 8 or cats 6 dogs 8 we can write number of cats as 6 x and number of dogs as 8 x and we know that 8 x - 6 x = 10 ( therefore 2 x = 10 = > x = 5 ) then # of dogs = 8 x 5 = 40 answer is e"
Answer: e
Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 144 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 ( too high ) 18 * 8 = 144 the length is 18 meters . the answer is b ."
Answer: b
Problem: add 15 % of 25 and 12 % of 45 .
Options: a ) 9.2 , b ) 10.5 , c ) 11.5 , d ) 12.3 , e ) 15
Rationale: 15 % of 25 + 12 % of 45 25 * 15 / 100 + 45 * 12 / 100 3.8 + 5.4 = 9.2 answer a
Answer: a
Problem: there are cats got together and decided to kill the mice of 999919 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009
Rationale: "999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 9 ) * ( 1000 - 9 ) = ( 1009 ) * ( 991 ) given that number of cats is less than number if mice . so number of cats is 991 and number of mice were 1009 answer c"
Answer: c
Problem: a crate measures 4 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "to fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet now since the limiting number in the base is 8 feet ; therefore a cylinder { we can visualise that a cylinder ' s width is its diameter } can only fit inside the crate if it is 8 feet or less . therefore the radius of the cylinder will become diameter 2 = = = > 8 / 2 = 4 diameter answer : d"
Answer: d
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 45 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm
Rationale: "we have 45 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 22.5 and continues . so we have 45 , 22.5 , 11.25 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 45 / 1 - ( 1 / 2 ) = 90 equilateral triangle perimeter is 3 a = 3 * 90 = 270 . so option d ."
Answer: d
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 120 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,080
Rationale: "10 / 100 p = 120 > > p = 120 * 100 / 10 = 1200 1200 - 120 = 1080 answer : e"
Answer: e
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 6 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 27 , b ) 22 , c ) 24 , d ) 26 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : a"
Answer: a
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 3 years ?
Options: a ) 14300 , b ) 17280 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 3 = 17280 b )"
Answer: b
Problem: a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 18 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : b"
Answer: b
Problem: how many even multiples of 15 are there between 149 and 301 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "150 = 10 * 15 300 = 20 * 15 the even multiples are 15 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Problem: what least number should be added to 1101 , so that the sum is completely divisible by 24
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1056 / 24 ) gives remainder 21 21 + 3 = 24 , so we need to add 3 . answer : option d"
Answer: d
Problem: a and b can do a work in 6 days , b and c in 2 days and c and a in 8 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 12 / 24 , b ) 48 / 63 , c ) 45 / 56 , d ) 48 / 19 , e ) 28 / 12
Rationale: "one day work of a and b = 1 / 6 one day work of b and c = 1 / 2 one day work of c and a = 1 / 8 2 ( a + b + c ) = 1 / 6 + 1 / 2 + 1 / 8 2 ( a + b + c ) = 19 / 24 ( a + b + c ) = 19 / 48 number of days required = 48 / 19 days . answer : d"
Answer: d
Problem: working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 10 % , but hillary becomes distracted and her rate decreases by 10 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 5 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 5 + ( 1 / 10 * 1 / 5 ) = 2 / 9 per hour hillary = 1 / 3 - ( 1 / 10 * 1 / 3 ) = 3 / 10 per hour together they work 2 / 9 + 3 / 10 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Problem: how many 3 digit no ' s are between 100 - 500 , where sum of two digit is 3 rd ?
Options: a ) 24 , b ) 54 , c ) 60 , d ) 84 , e ) 94
Rationale: total permutations possible = 18 + 16 + 14 + 12 = 60 answer : c
Answer: c
Problem: find the perimeter and area of a square of side 19 cm .
Options: a ) 324 , b ) 361 , c ) 400 , d ) 441 , e ) 484
Rationale: "we know that the perimeter of square = 4 ã — side side = 19 cm therefore , perimeter = 4 ã — 19 cm = 76 cm now , area of the square = ( side ã — side ) sq . units = 19 ã — 19 cm â ² = 361 cm â ² answer : b"
Answer: b
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 21 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 6 / 5 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 21 ) = 36 / 30 = 6 / 5 . answer : c ."
Answer: c
Problem: the cross - section of a stream is a trapezium in shape . if the stream is 10 m wide at the top and the area of cross - section is 640 sq m , the depth of stream is 80 m and width at the bottom is ?
Options: a ) 2 m , b ) 6 m , c ) 4 m , d ) 8 m , e ) 9 m
Rationale: 1 / 2 * 80 ( 10 + b ) = 640 b = 6 m answer : b
Answer: b
Problem: the cost of 2 books and 2 magazines is $ 26 . the cost of 1 book and 3 magazines is $ 27 . how much does 1 magazine cost ?
Options: a ) 8 , b ) 5 , c ) 7 , d ) 4 , e ) 6
Rationale: let the cost of 1 book = x , let the cost of 1 magazine = y 2 x + 2 y = 26 x = ( 26 - 2 y ) / 2 x = 13 - y again , ( 13 - y ) + 3 y = 27 13 + 2 y = 27 2 y = 14 y = 7 answer : c
Answer: c
Problem: 6,11 , 21 , 41 , 81 , ( . . . )
Options: a ) 22 , b ) 35 , c ) 27 , d ) 32 , e ) 161
Rationale: "explanation : 6 6 × 2 - 1 = 11 11 × 2 - 1 = 21 21 × 2 - 1 = 41 41 × 2 - 1 = 81 81 × 2 - 1 = 161 answer : option e"
Answer: e
Problem: the organizers of a fair projected a 25 percent increase in attendance this year over that of last year , but attendance this year actually decreased by 20 percent . what percent of the projected attendance was the actual attendance ?
Options: a ) 45 % , b ) 56 % , c ) 64 % , d ) 75 % , e ) 80 %
Rationale: last year attendance = 100 ( assume ) ; projected attendance = 125 ; actual attendance = 80 . the actual attendance therefore was ( actual ) / ( project ) = 80 / 125 * 100 = 64 $ of the projected attendance . answer : c .
Answer: c
Problem: the length of the longest tape in cm which can be used to measure exactly , the length 10 m ; 3 m 85 cm ; and 11 m 50 cm is :
Options: a ) 5 , b ) 35 , c ) 34 , d ) 36 , e ) 38
Rationale: "the three lengths in cm are 1000 , 385 & 1150 . hcf of 700 , 385 & 1295 is 5 . hence , the answer is 5 cm . answer : a"
Answer: a
Problem: if x + y = 270 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 235 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 270 x - y = 200 2 x = 70 x = 35 y = 235 answer is b"
Answer: b
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 11 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 66 / 5 days , d ) 21 days , e ) 22 / 5 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 11 work in 1 day b alone can do ( 1 / 6 - 1 / 11 ) = 5 / 66 work in 1 day = > complete work can be done in 66 / 5 days by b answer : option c"
Answer: c
Problem: the average weight of 22 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.89 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25
Rationale: explanation : average weight of 22 boys = 50.25 total weight of 22 boys = 50.25 × 22 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 16 ) + ( 45.15 × 8 ) total boys = 22 + 8 = 30 average weight of all the boys = ( ( 50.25 × 22 ) + ( 45.15 × 8 ) ) / 30 = 48.89 answer : option a
Answer: a
Problem: profits in the partnership of bess , bill and bob are shared in the ratio 1 : 2 : 3 . if bill ' s share of the profits is $ 300 , what is bob ' s share ?
Options: a ) $ 150 , b ) $ 900 , c ) $ 600 , d ) $ 450 , e ) none
Rationale: ans is d given profit ratio , bess : bill : bob = 1 : 2 : 3 to make bill ' s portion $ 300 , multiply by $ 150 = > bess : bill : bob = $ 150 : $ 300 : $ 450 = > bob ' s share = $ 450
Answer: b
Problem: a sporting goods store sold 60 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 204 , what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 8 , d ) 4 , e ) 2
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 60 3 x + 4 y = 204 x = 60 - y 3 ( 60 - y ) + 4 y = 204 180 - 3 y + 4 y = 204 y = 24 answer : a"
Answer: a
Problem: patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils . the cost of 90 pencils is how many times the selling price of 90 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.44
Rationale: "say the cost price of 90 pencils was $ 90 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 90 - 90 p = 40 p - - > p = 9 / 13 . ( cost price ) / ( selling price ) = 1 / ( 9 / 13 ) = 13 / 9 = 1.44 . answer : e ."
Answer: e
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1235
Rationale: cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 75 × 9 = 675 . total cost he has to pay = 560 + 675 = 1235 . e )
Answer: e
Problem: it takes joey the postman 1 hours to run a 6 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 8 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 6 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 6 * x / 6 + x = 8 12 x = 8 x + 48 = > x = 12 b"
Answer: b
Problem: if ( a - b - c + d = 18 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 36 .
Rationale: "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 12 ( 2 ) simplify - b + d = 6 b - d = - 6 ( b - d ) ^ 2 = ( - 6 ) ^ 2 = 36 my answer : e"
Answer: e
Problem: a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 60 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 55
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 60 hours = 3,600 / 60 seconds = 60 seconds ; time to cover 1 kilometer at regular speed is 60 + 5 = 65 seconds = 65 / 3,600 hours = 1 / 55 hours ; so , we get that to cover 1 kilometer 1 / 55 hours is needed - - > regular speed 55 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"
Answer: e
Problem: what is the probability of getting 53 mondays in a leap year ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: "in a leap year contains 52 monday ' s since 52 weeks are present and 2 days extra it may be sunday and monday 2 . monday and tuesday 3 . tuesday and thursday 4 . thursday and friday similary 7 alternatives are possible . among this only 2 are possible cases so 2 / 7 answer : b"
Answer: b
Problem: if a and b are positive integers and ( 5 ^ a ) ^ b = 5 ^ 2 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 3125 , b ) 625 , c ) 5 , d ) 25 , e ) 125
Rationale: "5 ^ ab = 5 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 5 ^ a * 5 ^ b = 5 ^ ( a + b ) = 5 ^ 3 = 125 e"
Answer: e
Problem: if w is the set of all the integers between 10 and 332 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 111 , b ) 28 , c ) 160 , d ) 213 , e ) 107
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 3 : 318 / 3 = 106 step 3 . add 1 : 106 + 1 = 107 . so there are 107 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 2 : 318 / 2 = 159 step 3 . add 1 : 159 + 1 = 160 . so there are 160 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 107 multiples of 3 and the 160 multiples of 2 : 107 + 160 = 267 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 107 + 160 = 267 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 25 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 330 - 12 = 318 step 2 . divide by 6 : 318 / 6 = 53 step 3 . add 1 : 53 + 1 = 54 . so there are 54 multiples of 6 within the range : we counted 54 numbers twice . subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3 : = 107 + 160 - 54 = 267 - 54 = 213 therefore , the final number of multiples of 2 , 3 or 6 is 213 . hence , this is the correct answer . ( d )"
Answer: d
Problem: a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 12 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 2345
b ) 3456
c ) 4567
d ) 5678
e ) 6789
Rationale: the tank is emptied at this rate : 12 + 6 - 3 = 15 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 15 = 3456 minutes . the answer is b .
Answer: b
Problem: an investment yields an interest payment of $ 231 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,800 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 230 = > p = ( 231 * 4 * 10 ^ 2 ) / 3 = 77 * 4 * 10 ^ 2 = 308 * 10 ^ 2 = 30800 answer b"
Answer: b
Problem: if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x × 7.50 = x = 80 kg . ∴ reduction in consumption = 20 % . answer b"
Answer: b
Problem: there are cats got together and decided to kill the mice of 999975 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 995,1005 , d ) 791,1009 , e ) 931,1009
Rationale: 999975 can be written as 1000000 â € “ 25 = 10002 â € “ 52 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 5 ) * ( 1000 - 5 ) = ( 1005 ) * ( 995 ) given that number of cats is less than number if mice . so number of cats is 995 and number of mice were 1005 answer c
Answer: c
Problem: how many positive integers less than 50 have a reminder 01 when divided by 5 ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 5 . so , there are total of 10 numbers . answer : a ."
Answer: a