regisss/math_qa huggingface dataset:
Problem: a semicircular cubicle has a radius of 14 . what is the approximate perimeter of the cubicle ?
Options: a ) 55
b ) 86
c ) 25
d ) 72
e ) 35
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 14 + 2 * 14 = 71.96 approximately 72 answer d
Answer: d
Problem: a works thrice as much as b . if a takes 60 days less than b to do a work then find the number of days it would take to complete the work if both work together ?
Options: a ) 22.5 days , b ) 21.5 days , c ) 23.5 days , d ) 24.5 days , e ) 25.5 days
Rationale: if a finishes the job in x days b finishes it in 3 x days 3 x = x + 60 thus x = 30 in one hour 1 / t = 1 / 30 + 1 / 90 = 4 / 90 where t is the number of days they finish the job together . t = 90 / 4 = 22.5 days answer : a
Answer: a
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price t of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price t = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 128 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 112 , e ) 210
Rationale: "set up equation : x = total number of workers 128 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 128 = 16 / 30 x x = 240 240 - 128 = 112 answer d"
Answer: d
Problem: calculate the number of urns of water needed to fill a tank of dimensions of 10 x 10 x 5 m to 90 % full , if the volume of the urn is 0.8 m 3 and can only be filled to 80 % .
Options: a ) 520 , b ) 650.2 , c ) 685.5 , d ) 703.1 , e ) 712.2
Rationale: volume of the tank that needed to be filled = 10 x 10 x 5 x 0.9 = 450 volume of the urn that can be filled = 0.8 x 0.8 = 0.64 no . of urns of water needed to fill the tank = 450 / 0.64 = 703.1 answer : d
Answer: d
Problem: a batsman makes a score of 92 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 42 , d ) 44 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 92 = 17 x or x = ( 92 – 48 ) = 44 . answer d"
Answer: d
Problem: a tank can be filled by two pipes a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tank from empty state if b is used for the first half time and then a and b fill it together for the other half .
Options: a ) 15 mins , b ) 20 mins , c ) 25 mins , d ) 30 mins , e ) 35 mins
Rationale: explanation : let the total time be x mins . part filled in first half means in x / 2 = 1 / 40 part filled in second half means in x / 2 = 1 / 60 + 1 / 40 = 1 / 24 total = x / 2 x 1 / 40 + x / 2 x 1 / 24 = 1 x = 30 mins answer is d
Answer: d
Problem: in a division sum , the quotient is 65 , the divisor 24 and the remainder 5 , find the dividend ?
Options: a ) 1595 , b ) 1569 , c ) 1265 , d ) 1555 , e ) 1565
Rationale: "explanation : 65 * 24 + 5 = 1565 answer : e"
Answer: e
Problem: the principal that amounts to rs . 3913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 3913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 3096 . answer : a"
Answer: a
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 240 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 240 , 2 ( 7 / 5 ) w + 2 w = 240 solve the above equation to find : w = 50 m and l = 70 m . correct answer a ) 50"
Answer: a
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 10 years hence ?
Options: a ) 58 , b ) 59 , c ) 62 , d ) 70 , e ) 80
Rationale: "explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 10 years , their ages will be 50 and 30 . sum of their ages = 50 + 30 = 80 . e )"
Answer: e
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 8 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 8 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a"
Answer: a
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 14 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 14 ) ( 3 / 2 ) = 21 minutes at the gym , and 21 + 14 = 35 minutes exercise , so ( 2 / 3 ) ( 35 ) = 23 minutes yoga . answer : d"
Answer: d
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.4 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.85
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 4 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 4 = 2.25 + 9 * . 4 = 5.85 $ answer e"
Answer: e
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many w cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer w = 44 . d"
Answer: d
Problem: a train requires 5 seconds to pass a pole while it requires 25 seconds to cross a stationary train which is 360 mtrs long . find the speed of the train .
Options: a ) 66.8 kmph , b ) 65.8 kmph , c ) 54.8 kmph , d ) 64.8 kmph , e ) 44.8 kmph
Rationale: "in 5 s the train crosses the pole and in 25 sec the train crosses one more stationary train in 20 sec the train travels a distance of 360 mtrs speed = 360 / 20 = 18 m / s = 18 ( 3600 / 1000 ) = 18 * 18 / 5 = 64.8 kmph answer : d"
Answer: d
Problem: a two digit number is 18 less than the square of the sum of its digits . how many such numbers are there ?
Options: a ) 2233 , b ) 2222 , c ) 2211 , d ) 6382 , e ) 23,17
Rationale: option 2 take n = 10 a + b . given that , ( 10 a + b ) + 18 = k 2 = ( a + b ) 2 given number = k 2 - 18 = ( 10 a + b ) that means , when we add 18 to the given number it should be a perfect square . so k 2 takes the following values . 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , . . . . 1 to 16 are ruled out as if we subtract 18 from them , the resulting number is a single digit number . now 25 - 18 = 7 36 - 18 = 18 49 - 18 = 31 64 - 18 = 46 81 - 18 = 63 100 - 18 = 82 121 - 18 = 103 now 63 , 82 satisfies . answer : d
Answer: d
Problem: what is the average ( arithmetic mean ) of 10 , 20,30 , 40,50 , 60,70 , 80,90 ?
Options: a ) 90 , b ) 95 , c ) 70 , d ) 85 , e ) 50
Rationale: "so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e ."
Answer: e
Problem: if the average of 6 x and 8 y is greater than 100 , and x is twice y , what is the least integer value of x ?
Options: a ) 22 , b ) 20 , c ) 21 , d ) 23 , e ) 24
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 6 x and 4 x is greater than 100 . average of 6 x and 4 x is 5 x . so , 5 x > 100 x > 20 answer : b"
Answer: b
Problem: two cubes of their volumes in the ratio 343 : 729 . the ratio of their surface area is :
Options: a ) 7 : 9 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5
Rationale: "the ratio of their surface area is 343 : 729 7 : 9 answer is a ."
Answer: a
Problem: two pipes p and q can fill a cistern in 12 and 14 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 11 1 / 2 min , b ) 11 1 / 4 min , c ) 11 2 / 4 min , d ) 11 1 / 5 min , e ) 10 1 / 2 min
Rationale: "3 / 12 + x / 14 = 1 x = 10 1 / 2 answer : e"
Answer: e
Problem: a can complete a project in 20 days and b can complete the same project in 20 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 16 days , e ) 15 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 20 ) * ( x ) = 1 ( x / 20 ) + ( x / 20 ) - ( 10 / 20 ) = 1 x / 10 = 3 / 2 x = 15 therefore , the answer is e : 15 ."
Answer: e
Problem: a work crew of 4 men takes 5 days to complete one - half of a job . if 11 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 1 1 / 3 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 4 men will do in . . 4 / x = 1 / 5 * 1 / 2 as half job is done x = 40 now 11 more are added then 15 / 40 = 1 / 2 * 1 / d for remaining half job d = 1 1 / 3 number of days c"
Answer: c
Problem: a train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 67 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 120 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2160 < = > x = 67 speed of the train is 67 kmph . answer : option a"
Answer: a
Problem: a small company reduced its faculty by approximately 13 percent to 195 employees . what was the original number of employees ?
Options: a ) 182 , b ) 208 , c ) 220 , d ) 224 , e ) 302
Rationale: "if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of employees is 224 correct answer - d"
Answer: d
Problem: population is 22000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 29282 , c ) 36620 , d ) 26620 , e ) 26820
Rationale: "population after 1 st year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24000 population after 2 nd year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26620 population after 3 rd year = 26620 * 10 / 100 = 2662 = = = > 26620 + 2662 = 29282 answer : b"
Answer: b
Problem: a 180 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 54 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 180 / 12 * 18 / 5 = 54 kmph answer : a"
Answer: a
Problem: ( 26.3 * 12 * 20 ) / 3 + 125 = ?
Options: a ) 2339 , b ) 2229 , c ) 4429 , d ) 5529 , e ) 2669
Rationale: b 2229 ? = [ ( 26.3 * 12 * 20 ) / 3 ] + 125 ? = 2104 + 125 = 2229
Answer: b
Problem: rectangular tile each of size 45 cm by 50 cm must be laid horizontally on a rectangular floor of size 250 cm by 180 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 35 , b ) 40 , c ) 25 , d ) 18 , e ) 20
Rationale: "area of tile = 45 * 50 = 2250 area of floor = 250 * 180 = 45000 no of tiles = 45000 / 2250 = 20 so , the no of tile = 20 answer : e"
Answer: e
Problem: if 15 people contributed a total of $ 30.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 16 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "b for me 14 people with 1 $ each - > maximum = 16"
Answer: b
Problem: a water tank , having the shape of a rectangular prism of base 100 square centimeters , is being filled at the rate of 1 liter per minute . find the rate at which the height of the water in the water tank increases . express your answer in centimeters per minute .
Options: a ) 30 cm
b ) 10 cm
c ) 50 cm
d ) 90 cm
e ) 70 cm
Rationale: the volume of a rectangular prism is given by area of base ? height the rate at which the tank is being filled is 1 liter per minute which we need to convert 1 liter = 1 dm 3 but 1 dm = 10 cm . hence 1 liter = ( 10 cm ) 3 = 1000 cm 3 the height h of the water is related to the volume by volume = area of base * h in one minute the volume increases by 1 liter or 1000 cm 3 and the height increases by h = volume / area of base = 1000 cm 3 / 100 cm 2 = 10 cm correct answer b
Answer: b
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 72 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 72 ⇔ 9 ( x - y ) = 72 ⇔ x - y = 8 answer d"
Answer: d
Problem: machine a can put caps on a set of bottles in 8 hours at a constant rate . if machine a does the job for 6 hours and machine b does the rest of the job , which works at 1 / 4 constant rate of machine a . how long will it take for machine b alone to do the rest of the job ?
Options: a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 10 hrs , e ) 16 hrs
Rationale: machine a will do 6 / 8 in 6 hrs , so a does 3 / 4 of the work . . therefore , b will do the remaining 1 / 4 th work alone . . as the speed of b is 1 / 4 rate of a , b will do the 1 / 4 th work in same time that a takes to complete full job . . . ans 8 c
Answer: c
Problem: a ’ s speed is 16 / 15 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 15 , d ) 1 / 32 , e ) 1 / 31
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 16 v / 15 ) = xd / v ( 15 / 16 ) * d / v = x * d / v x = 15 / 16 b should have a head start of 1 / 16 of the full distance . the answer is b ."
Answer: b
Problem: 6 women can do 75 unit of work in 8 days by working 5 hr / day in how many days 4 women do 30 units of work by working 8 hr / day
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: ( 6 x 8 x 5 ) / 75 = ( ax 4 x 8 ) / 30 a = 3 answer : a
Answer: a
Problem: 50 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 640 , b ) 278 , c ) 800 , d ) 267 , e ) 121
Rationale: "( 50 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 2 x = 320 x = 640 answer : a"
Answer: a
Problem: what is the units digit of the expression 14 ^ 7 − 16 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 8 , d ) 6 , e ) 4
Rationale: i think answer on this one should be c too . since we know that 14 ^ 7 > 16 ^ 4 , as will said one should always check if the number is positive .
Answer: c
Problem: when xyz co discontinued an agency arrangement with john , management held his commission of rs . 25000 / - for one month . earlier john had availed an advance agency fees of 8280 / - from company . but robert forgot that . after one month john asked his fees and accountant gives rs . 18500 / - to him . what is the incentive amount given to john ?
Options: a ) a ) 1780 , b ) b ) 1250 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600
Rationale: total fees = rs . 25000 / - advance fees = 8280 / - balance fees = 25000 - 8280 = 16720 paid amount = 18500 / - incentive amount = 18500 - 16720 = 1780 / - answer is a
Answer: a
Problem: if | 5 x - 5 | = 150 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 6 , d ) - 3 , e ) 5
Rationale: "there will be two cases 5 x - 5 = 150 or 5 x - 5 = - 150 = > x = 31 or x = - 29 sum of both the values will be - 29 + 31 = 2 answer is a"
Answer: a
Problem: x is the product of each integer from 1 to 100 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 100 = 100 ! no . of trailing zeros in 100 ! = 100 / 5 + 100 / 5 ^ 2 = 20 + 4 = 24 100 ^ k = 10 ^ 2 k → k = 24 / 2 = 12 e"
Answer: e
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 9 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 9 / 49 = ( 3 / 7 ) * ( 3 / 7 ) therefore probability that the next one she draws is pink = 4 / 7 option ( b )
Answer: b
Problem: a sum was put a simple interest at a certain rate for 2 years . had it been put at 4 % higher rate , it would have fetched rs . 60 more . the sum is :
Options: a ) rs . 750 , b ) rs . 700 , c ) rs . 820 , d ) rs . 940 , e ) rs . 900
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x × ( r + 4 ) × 2 / 100 − x × r × 2 / 100 = 60 ⇒ x × 4 × 2 / 100 = 60 ⇒ x × 2 / 100 = 15 ⇒ 2 x = 1500 ⇒ x = 750 answer : option a"
Answer: a
Problem: three coins are tossed . find the probability of at least 2 tails ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 3 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 let e is the event of getting at least 2 tails n ( e ) = ttt , tth , htt , tht = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 ans - a"
Answer: a
Problem: a train can travel 50 % faster than a car . both start from point a at the same time and reach point b at 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is ?
Options: a ) 2387 , b ) 267 , c ) 120 , d ) 277 , e ) 271
Rationale: "let speed of the car be x km / hr . then , speed of the train = 150 / 100 x = 3 / 2 x km / hr . 75 / x - 75 / ( 3 / 2 x ) = 125 / ( 10 * 60 ) 75 / x - 50 / x = 5 / 24 = 120 km / hr . answer : c"
Answer: c
Problem: tom traveled the entire 60 miles trip . if he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 40 mph , e ) 42 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 12 + 48 ) / ( ( 12 / 24 ) + ( 48 / 48 ) ) = 60 * 2 / 3 = 40 mph d"
Answer: d
Problem: a grocer has a sale of rs . 2435 , rs . 2920 , rs . 2855 , rs . 3230 and rs . 2560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 2500 ?
Options: a ) 5000 , b ) 4000 , c ) 1000 , d ) 6000 , e ) 8000
Rationale: "total sale for 5 months = rs . ( 2435 + 2920 + 2855 + 3230 + 2560 ) = rs . 14000 . required sale = rs . [ ( 2500 x 6 ) - 14000 ] = rs . ( 15000 - 14000 ) = rs . 1000 answer : option c"
Answer: c
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 5 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 10 litres , b ) 20 litres , c ) 30 litres , d ) 5 litres , e ) 14 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 5 ) = 4 / 5  20 x = 4 ( 3 x + 5 )  8 x = 20  x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer a 10 litres"
Answer: a
Problem: evaluate 28 % of 550 + 45 % of 280
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 280
Rationale: "explanation : = ( 28 / 100 ) * 550 + ( 45 / 100 ) * 280 = 154 + 126 = 280 answer : option e"
Answer: e
Problem: what sum of money put at c . i amounts in 2 years to rs . 8840 and in 3 years to rs . 9261 ?
Options: a ) 8054 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8840 - - - - 421 100 - - - - ? = > 4.76 % x * 104.76 / 100 * 104.76 / 100 = 8840 x * 1.0975 = 8840 x = 8840 / 1.0975 = > 8054.54 answer : a"
Answer: a
Problem: if square - root of 15 is 3.87 . then find the value of square - root of ( 5 / 3 )
Options: a ) 1.29 , b ) 1.39 , c ) 1.49 , d ) 1.59 , e ) 1.69
Rationale: = > root 5 / root 3 = ( root 5 / root 3 ) * ( root 3 / root 3 ) = root 15 / root 9 = 3.87 / 3 = 1.29 answer : a
Answer: a
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 480 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "3 x = 480 x = 160 therefore , the salesman sold 160 kg in the morning and 2 ⋅ 160 = 320 kg in the afternoon . so answer is e ."
Answer: e
Problem: 0.004 × 0.5 = ?
Options: a ) none of these , b ) 0.02 , c ) 0.002 , d ) 0.0002 , e ) 2
Rationale: "explanation : 0.004 × 0.5 = 0.002 . answer : option c"
Answer: c
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 20 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: t = the number of cups of tea c = the number of cups of hot chocolate t + c = 20 t - c = 10 - > t = 15 . c = 5 . mo drinks 3 cups of tea a day then number of days that are not rainy = 15 / 3 = 5 so number of rainy days = 7 - 5 = 2 a is the answer .
Answer: a
Problem: how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 10 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 72 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / sec distance = 50 * 4 = 200 m time taken = 200 * 9 / 25 = 72 sec answer is c"
Answer: c
Problem: the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 675 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 30 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 3 x = 675 x ^ 2 = 225 x = 15 length = 3 * 15 = 45 difference = 45 - 15 = 30 b is the answer"
Answer: b
Problem: a grocery shop has a sale of rs . 6235 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 5191 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6235 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6235 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 33809 + x = 39000 = > x = 39000 − 33809 = 5191 answer : d"
Answer: d
Problem: a train 225 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 86 , b ) 50 , c ) 12 , d ) 13 , e ) 67
Rationale: "speed of the train relative to man = ( 225 / 10 ) m / sec = ( 45 / 2 ) m / sec . [ ( 45 / 2 ) * ( 18 / 5 ) ] km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 81 = = > x = 86 km / hr . answer : option a"
Answer: a
Problem: 0.0006688 / 0.0000120 x 17.05 = ?
Options: a ) 450.1 , b ) 910.1 , c ) 930.1 , d ) 920.1 , e ) 950.1
Rationale: "explanation : ? = 0.0006688 / 0.0000120 x 17.05 = 950.1 answer : option e"
Answer: e
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 45 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 15 , e ) 14
Rationale: initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 45 + q = > q = 15 answer : d
Answer: d
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 75 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 30 , b ) 35 , c ) 25 , d ) 40 , e ) 45
Rationale: "assume total distance = 100 miles time taken for 75 miles = 75 / 75 = 1 hour time taken for the rest of the 25 miles = 25 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 25 / v hence v = 25 mph answer : c"
Answer: c
Problem: if 20 men can build a wall 66 metres long in 15 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 151.36 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 15 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 15 * 20 ) = 151.36 mtrs answer : a"
Answer: a
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "we are given that orangeade is made on day 1 with an equal amount of water and orange juice . we can set this information up into a ratio using a variable multiplier : w : oj = x : x thus , orangeade quantity = amount of water + amount of oj = x + x = 2 x we are next given that orangeade on day 2 was made by mixing the same amount of orange juice with twice the amount of water . we can set this information up into a ratio using a variable multiplier : w : oj = 2 x : x thus , orangeade quantity = amount of water + amount of oj = 2 x + x = 3 x we also know that all orangeade made was sold and that the revenue on both days was the same . we can therefore set up the following equation : day 1 revenue = day 2 revenue that is , ( quantity sold day 1 ) ( price per glass day 1 ) = ( quantity sold day 2 ) ( price per glass day 2 ) let a be the amount of orangeade a glass can hold , then quantity sold day 1 = the number of glasses of orangeade sold on day 1 = 2 x / a similarly , quantity sold day 2 = the number of glasses of orangeade sold on day 2 = 3 x / a we also know that the price per glass on day 1 = $ 0.6 but we don ’ t know the price per glass on day 2 , so let ’ s label it as variable p . we now have : ( 2 x / a ) ( 0.6 ) = ( 3 x / a ) ( p ) multiplying both sides by a , we have : ( 2 x ) ( 0.6 ) = ( 3 x ) ( p ) 1.2 x = 3 xp 1.2 = 3 p p = 0.4 thus , each glass of orangeade was sold for $ 0.40 on day 2 . answer d ."
Answer: d
Problem: two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many r hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many r hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Problem: the number 1254 is divisible by which number ?
Options: a ) 8 , b ) 7 , c ) 4 , d ) 5 , e ) 6
Rationale: last 3 digit can not divisible by 8 so , reject option a 1254 is not divisible by 7 last number is not 0 or 5 , so neglect 4 is not divide 1254 divisibility rule of 6 is a number divisible both by 3 and 2 . 1254 attains both divisible . so the number is divisible by 6 option e
Answer: e
Problem: what is the cost of leveling the field in the form of parallelogram at the rate of rs . 40 / 10 sq . metre , whose base & perpendicular distance from the other side being 24 m & 34 m respectively ?
Options: a ) s . 600 , b ) s . 630 , c ) s . 640 , d ) s . 648 , e ) s . 816
Rationale: "area of the parallelogram = length of the base * perpendicular height = 24 * 34 = 816 m . total cost of levelling = rs . 816 e"
Answer: e
Problem: a certain no . when divided by 35 leaves aremainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) c
Answer: c
Problem: on a certain road , 40 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 50 %
Rationale: "suppose there are x motorists . 40 % of them exceeded the speed limit and received the ticket , i . e . 2 x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = 2 x / 5 or y / x = 1 / 2 or y / x * 100 = 1 / 2 * 100 = 50 % e"
Answer: e
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 56 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 280 , b ) $ 800 , c ) $ 892 , d ) $ 1,108 , e ) $ 1,200
Rationale: "( a ) $ 280 ( b ) $ 800 ( c ) $ 892 ( d ) $ 1,108 ( e ) $ 1,200 y = 2000 - x . 1 x - . 08 ( 2000 - x ) = 56 . - 160 + . 18 x = 56 x = 1200 and y = 800 answer : b"
Answer: b
Problem: if a mixture is 1 ⁄ 2 alcohol by volume and 3 ⁄ 2 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 3 ⁄ 7 , b ) 4 ⁄ 7 , c ) 3 ⁄ 4 , d ) 4 ⁄ 3 , e ) 7 ⁄ 4
Rationale: "should be a sub - 600 level q . . volume = { 1 / 2 } / { 3 / 2 } = 1 / 3 c"
Answer: c
Problem: a number when divided by 342 gives a remainder 38 , what remainder will be obtained by dividing the same number 21 ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 342 + 38 = 380 / 21 = 2 ( remainder ) answer : d"
Answer: d
Problem: at the beginning of 1992 , maria ' s stock portfolio was worth $ 600000 . during 1992 , the portfolio ' s value increased by 95 % . during the next year , the portfolio increased its worth by only 5 % . what was maria ' s portfolio worth , in dollars , by the end of 1993 ?
Options: a ) 1 , 180000 , b ) 1 , 200000 , c ) 1 , 200300 , d ) 1 , 228500 , e ) 1 , 330,000
Rationale: by the end of 1992 , the port folio worth is 1.95 * ( $ 600 k ) by 1993 , the portfolio is 1.05 * ( 1.95 * $ 600 k ) = $ 1 , 228,500 answer : d
Answer: d
Problem: amit and ananthu can do a work in 15 days and 45 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 30 days , c ) 33 days , d ) 35 days , e ) 39 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 45 ananthu can do work in = 4 / 5 * 45 = 36 days so total days = 36 + 3 = 39 days answer : e"
Answer: e
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 5 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 20 : 25 , c ) 1 : 5 , d ) 2 : 5 , e ) 4 : 6
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 5 - - > x ( a - b ) = 5 . since 5 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 5 . the above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 5 * 4 = 20 and dogs = 5 * 5 = 25 . answer : b ."
Answer: b
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of w is less than the square root of w . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "w 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Problem: 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is
Options: a ) 24 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "solution let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = 12 x = 240 ‹ = › x = 20 . therefore bigger part = ( 54 - x ) = 34 . answer d"
Answer: d
Problem: a work which could be finished in 9 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "explanation : x - - - - - - - 9 ( x + 10 ) - - - - 6 x * 9 = ( x + 10 ) 6 x = 20 answer : b"
Answer: b
Problem: if the compound interest on a certain sum of money for 6 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 1800 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 6 yrs = ( 3000 x 10 x 6 ) / 100 = 1800 / - answer : c ."
Answer: c
Problem: a bicycle wheel has a diameter of 0.66 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 1408 , d ) 482 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.66 m ) = 482.5 . hence 482 complete revolutions . answer d"
Answer: d
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12015 after 8 years at the same rate of simple interest . the rate of interest per annum is ?
Options: a ) 12.05 % , b ) 5 % , c ) 13.05 % , d ) 22.05 % , e ) 18.05 %
Rationale: s . i . for 3 years = ( 12015 - 9800 ) = rs . 2215 s . i . for 5 years = rs . 2215 / 3 * 5 = rs . 3691 . principal = ( 9800 - 3675 ) = rs . 6108 hence , rate = ( 100 * 3691 ) / ( 6125 * 5 ) = 12.05 % answer : a
Answer: a
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 51 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: a + b / ab = 2 / 3 3 = 1 * 3 or 3 * 1 a + b in both case = 4 correct 0 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 8 , 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 ) 20 , b ) 22 , c ) 24 , d ) 27 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : d ."
Answer: d
Problem: the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff
Options: a ) 50 , b ) 52 , c ) 49 , d ) 32 , e ) 35
Rationale: total age of students = > 32 × 16 = 512 yrs total age inclusive staff = 33 × ( 16 + 1 ) = 561 = > staff ' s age 561 - 512 = 49 yrs answer c
Answer: c
Problem: the area of a rectangular plot is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the plot ?
Options: a ) 14 m , b ) 20 m , c ) 18 m , d ) 12 m , e ) 15 m
Rationale: "lb = 460 m 2 let breath = b l = b * ( 100 + 15 ) / 100 = 115 b / 100 from these 115 b / 100 * b = 460 b 2 = 46000 / 115 = 400 b = root of 400 = 20 m answer b"
Answer: b
Problem: a man purchased 5 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 250 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: "explanation : 10 * 150 = 1500 5 * 100 + 5 * 150 = 1250 1500 – 1250 = 250 a"
Answer: a
Problem: working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 8 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 4 days ?
Options: a ) 30 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: 5 machines do x units in 8 days we have x / 8 = > rate of the 5 machines we know that we need to have 3 x units in 4 days therefore , we need to get to 3 x / 4 rate of the machines . rate of one machine is x / 8 * 1 / 5 = x / 40 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 4 days . 3 x / 4 work needs to be done by machines that work at x / 40 rate . let ' s assign a constant y for the number of machines : ( x / 40 ) * y = 3 x / 4 y = 3 x / 4 * 40 / x cancel 4 with 40 , and x with x and get - > 30 . answer choice a
Answer: a
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 2,2 ) , ( 8,2 ) , ( 3,5 ) , ( 9,5 ) ?
Options: a ) 18 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 8 - 2 = 6 unit delta y will give us the dimension of the other side of parallelogram = 5 - 2 = 3 unit area of parallelogram = 6 * 3 = 18 answer is a"
Answer: a
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 10 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,000
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 10 % . 10 x = 200 = > x = 2000 answer e"
Answer: e
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 50 %
Options: a ) 40.8 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 50 / 100 = 50.40 so x = 40.8 answer : a"
Answer: a
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much q does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) q = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Problem: machine p and machine q are each used to manufacture 440 sprockets . it takes machine p 10 hours longer to produce 440 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 440 / x = 440 / 1.1 x + 10 1.1 ( 440 ) = 440 + 11 x 11 x = 44 x = 4 the answer is b ."
Answer: b
Problem: a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 110 , b ) 175 , c ) 212 , d ) 218 , e ) 220
Rationale: "let the market price of each pen be $ 1 then , cost price of 100 pens = $ 36 selling price of 100 pens = 99 % of $ 100 = $ 99 profit % = ( ( 63 * 100 ) / 36 ) % = 175 % answer b"
Answer: b
Problem: 3 litre of water is added to 11 litre of a solution containing 42 % of alcohol in the water . the percentage of alcohol in the new mixture is ?
Options: a ) 30 % , b ) 33 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 × 42 100 = 11 × 42100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 × 42 100 14 × 100 = 11 × 4210014 × 100 = 11 × 3 100 = 33 % b )
Answer: b
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 26 , d ) 1 / 13 , e ) 5 / 13
Rationale: "the total number of cards is 52 . the number of red cards is 26 . p ( red card ) = 26 / 52 = 1 / 2 the answer is a ."
Answer: a
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 26 , b ) 95 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 10 = rs . 95 answer : b"
Answer: b
Problem: a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 375
Rationale: max no . of crates = 5 . max weight = 120 kg max . weight carried = 5 * 120 = 600 kg = c
Answer: c
Problem: a student completes a 3 part exam as follows . the student completes sections a in 24 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 7 : 8 , b ) 6 : 7 , c ) 5 : 6 , d ) 4 : 5 , e ) 3 : 4
Rationale: the time spent on section b and section c is 18 minutes each . the ratio of c to a is 18 : 24 = 3 : 4 the answer is e .
Answer: e
Problem: the average of first 3 prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50
Rationale: 23 + 29 + 31 = 83 / 3 = 27.7 answer : d
Answer: d
Problem: a reduction of 44 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.3 , b ) 8.3 , c ) 7.3 , d ) 3.3 , e ) 1.3
Rationale: "explanation : 40 * ( 44 / 100 ) = 17.6 - - - 64 ? - - - 12 = > rs . 3.30 answer : d"
Answer: d
Problem: if x and y are integers , what is the least positive number of 24 x + 16 y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "24 x + 16 y = 8 ( 3 x + 2 y ) which will be a minimum positive number when 3 x + 2 y = 1 . 3 ( 1 ) + 2 ( - 1 ) = 1 then 8 ( 3 x + 2 y ) can have a minimum positive value of 8 . the answer is e ."
Answer: e
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1987 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1987 + 19 = 2006 . answer : d ."
Answer: d
Problem: a cistern is filled by a tap in 3 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how long will it take the leak to empty it ?
Options: a ) 11 , b ) 12 , c ) 29 , d ) 28 , e ) 29
Rationale: 2 / 7 - 1 / x = 1 / 4 x = 28 answer : d
Answer: d
Problem: in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 3 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 19 / 3 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 3 means that its equation is y = 1 / 3 * x . thus : ( x , 1 ) = ( 3 , 1 ) and ( 10 , y ) = ( 10,10 / 3 ) - - > x + y = 3 + 10 / 3 = 19 / 3 . answer : d ."
Answer: d
Problem: a 40 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 810 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 4.0 assume x gallons of water are added . 4.0 / 40 + x = 8 / 100 400 = 8 x + 320 8 x = 80 x = 10 correct option : a"
Answer: a