regisss/math_qa huggingface dataset:
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 8 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 8 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 8 = 7 / 8 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 7 / 8 = 4 / 9 - - - > p ( of burning out in a six mnth period ) = 1 - 4 / 9 = 4 / 7 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 7 / 8 * 4 / 7 = 1 / 2 ans c"
Answer: c
Problem: a train 360 m long is running at a speed of 90 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 26 sec , d ) 20 sec , e ) 34 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 25 = 20 sec answer : d"
Answer: d
Problem: the sale price sarees listed for rs . 200 after successive discount is 20 % and 5 % is ?
Options: a ) 187 , b ) 169 , c ) 152 , d ) 178 , e ) 175
Rationale: "200 * ( 80 / 100 ) * ( 95 / 100 ) = 152 answer : c"
Answer: c
Problem: the radius of the base of cone is 3 cm and height is 4 cm . find the volume of the cone ?
Options: a ) 12
b ) 75
c ) 97
d ) 15
e ) 91
Rationale: 1 / 3 * π * 3 * 3 * 4 = 12 π answer : a
Answer: a
Problem: bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ?
Options: a ) 40 , b ) 80 , c ) 120 , d ) 160 , e ) 180
Rationale: bexy walks 5 miles from point a to point b in one hour , then bicycles back to point a along the same route at 15 miles per hour . ben makes the same round trip , but does so at half of bexy ’ s average speed . how many minutes does ben spend on his round trip ? average speed = total distance / total time we know the total distance is 5 + 5 ( going from a to b then from b to a ) time = distance / speed time = 5 / 15 time = 1 / 3 hour average speed = ( 10 ) / ( 1 hr + 1 / 3 hr ) average speed ( bexi ) = 10 / 1.33 therefore , if ben ' s average speed is 1 / 2 of bexi ' s then his speed = 10 / 2.66 . this means it took him 2.66 hours to cover the same 10 miles bexi did . 2.66 hours = roughly 160 minutes . answer : d ) . 160
Answer: d
Problem: the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 260
Rationale: "x - y = 1365 divide larger number by the smaller , we get 6 as quotient and the 15 as remainder x / y = 6 quotient and 15 reminder convert this as x = 6 y + 15 apply this x in above eqn therefore , 6 y + 15 - y = 1365 5 y + 15 = 1365 y + 3 = 273 y = 270 answer : b"
Answer: b
Problem: running at the same constant rate , 4 identical machines can produce a total of 16 bottles per minute . at this rate , how many bottles could 8 such machines produce in 3 minutes ?
Options: a ) 11 , b ) 92 , c ) 96 , d ) 174 , e ) 115
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 16 / 4 = 4 . 8 machines = 32 per minute . 3 minutes worth = 96 bottles . looking at the answers it is clear . . . we can only choose ( c ) the correct answer is c ."
Answer: c
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 12 , the how old is b ?
Options: a ) 10 years , b ) 4 years , c ) 6 years , d ) 15 years , e ) 16 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 12 5 x = 10 x = 2 . hence , b ' s age = 2 x = 4 years . b )"
Answer: b
Problem: how many digits are required to number a book containing 300 pages ?
Options: a ) 792 , b ) 684 , c ) 492 , d ) 372 , e ) 340
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 300 - ( 90 + 9 ) = 201 pages will require 201 * 3 = 603 digits . the total number of digits is 9 + 180 + 603 = 792 . the answer is a ."
Answer: a
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 4 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.25 , e ) 3.5
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 4 km / hour x / 3 = 4 x = 12 km the average speed while climbing = distance / time = 12 / 4 = 3 km / h the answer is c ."
Answer: c
Problem: there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 36 , then find the smaller number ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 60 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 36 3 x = 36 = > x = 12 = > smaller number = 5 x = 60 . answer : d"
Answer: d
Problem: if x = 1 - q and y = 2 q + 1 , then for what value of q , x is equal to y ?
Options: a ) 0 , b ) 1 , c ) - 1 , d ) - 2 , e ) 3
Rationale: explanation : x = y < = > 1 - q = 2 q + 1 < = > 3 q = 0 < = > q = 0 . answer : a
Answer: a
Problem: if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 2 / 3 : 3 / 4 , then the third part is ?
Options: a ) a ) 426 , b ) b ) 306 , c ) c ) 207 , d ) d ) 204 , e ) e ) 297
Rationale: given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 8 : 9 1 st part = 782 * 9 / 23 = rs . 306 . answer : b
Answer: b
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.65 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 250 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,628
Rationale: "to maximize number of hot dogs with 250 $ total number of hot dogs bought in 250 - pack = 22.95 * 10 = 229.5 $ amount remaining = 250 - 229.5 = 20.5 $ total number of hot dogs bought in 20 - pack = 3.05 * 6 = 18.3 $ amount remaining = 20.5 - 18.3 = 2.2 $ total number of hot dogs bought in 8 - pack = 1.55 * 1 = 1.55 $ amount remaining = 2.2 - 1.65 = 0.55 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 250 $ = 250 * 10 + 20 * 6 + 8 * 1 = 2628 answer e"
Answer: e
Problem: a start walking from a place at a uniform speed of 5 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 5.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 5 + 5 / 9 = 5.55 answer b"
Answer: b
Problem: the length of the bridge , which a train 110 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 377 , b ) 367 , c ) 237 , d ) 245 , e ) 265
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 x = 265 m . answer : e"
Answer: e
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 7 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 5 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 5 ) , which indeed is 5 / 22 . e"
Answer: e
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 49 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 7
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 49 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 50 incorrect c . 2 / 2 = 2 / 3 + 2 / 51 incorrect d . 2 / 3 = 2 / 4 + 2 / 54 incorrect e . 2 / 4 = 2 / 5 + 2 / 56 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 35,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 35000 × 21 / 50 = 700 × 21 = 14700 answer is a ."
Answer: a
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 75 , then what is the value of k ?
Options: a ) 158 , b ) 161 , c ) 164 , d ) 167 , e ) 170
Rationale: k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 75 ) / 5 + 32 = 167 the answer is d .
Answer: d
Problem: ( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) =
Options: a ) 99 , b ) 9.9 , c ) 990 , d ) 0.99 , e ) 0.099
Rationale: "( 0.0077 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 450 / 5 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : c"
Answer: c
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 2904 cm is ?
Options: a ) 22 , b ) 33 , c ) 17 , d ) 12 , e ) 88
Rationale: "2 * 22 / 7 * 14 * x = 2904 = > x = 33 answer : b"
Answer: b
Problem: jerry went to a shop and bought things worth rs . 25 , out of which 30 $ went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 21.7
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 $ is given as tax = > total tax incurred = 30 $ = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 b )"
Answer: b
Problem: the average age of a class of 25 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 47 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 19 , average would not have changed . since average increased by 2 , age of the teacher = 25 + 22 × 1 = 47 answer : c"
Answer: c
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 30
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 6 = ( r - 10 ) / r 4 r = 6 r - 60 r = 30 the answer is e ."
Answer: e
Problem: of 70 players on a football team , 40 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 60 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 40 rest = 70 - 40 = 30 left handed = 30 / 3 = 10 right handed = 20 if all throwe 0 r are right handed then total right handed is 40 + 20 = 60 so c . 60 is the right answer"
Answer: c
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38000 , 2 have an annual salary of 45700 each , 2 have an annual salary of 42500 each , 3 have an annual salary of 40000 each and 5 have an annual salary of 48500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,700 , e ) 48,500
Rationale: median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.7 so , answer is d .
Answer: d
Problem: average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c"
Answer: c
Problem: a car travels a certain distance taking 7 hrs in forward journey , during the return journey increased speed 12 km / hr takes the times 5 hrs . what is the distance traveled
Options: a ) 210 kms , b ) 30 kms , c ) 20 kms , d ) 40 kms , e ) none of these
Rationale: if x is the distance , then difference in speeds = x / 5 - x / 7 = 12 2 x / 35 = 12 x = 12 * 35 / 2 = 210 kms . answer : a
Answer: a
Problem: a searchlight on top of the watch - tower makes 1 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 20 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "1 revolutions per minute = 1 revolution every 60 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 60 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 20 seconds ) = 1 - p ( man in dark for max of 20 seconds ) = 1 - 20 / 60 = 1 - 1 / 3 = 2 / 3 or the other way would be : p ( man in dark for at least 20 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 60 seconds because that is the max . in this approach it would be 20 / 60 seconds = 1 / 3 . answer is b"
Answer: b
Problem: what is the area of a square with perimeter 12 p ?
Options: a ) 16 p ^ 2
b ) 4 p
c ) 9 p ^ 2
d ) p / 16
e ) p ^ 2 / 16
Rationale: each side is 3 p a = ( 3 p ) ^ 2 = 9 p ^ 2 answer c
Answer: c
Problem: exactly 10 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 85 % , e ) 84 %
Rationale: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 10 % of all reporters reporters covering politics / all reporters = 10 / 70 = 1 / 7 reporters not covering politics / all reporters = 6 / 7 = 85 % = d"
Answer: d
Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 5 : 12 , find the age of sachin
Options: a ) 9 , b ) 24.8 , c ) 2 , d ) 3 , e ) 5
Rationale: explanation : if rahul age is x , then sachin age is x - 7 , so , 12 x - 84 = 5 x 7 x = 84 x = 12 so sachin age is 12 - 7 = 5 answer : e ) 5
Answer: e
Problem: in a 6 - sided polygon xqrstv ∠ x measures 48 ° less than the average ( arithmetic mean ) of the remaining 5 angles . what does ∠ x equal to , in degrees ?
Options: a ) 72 , b ) 80 , c ) 88 , d ) 96 , e ) 104
Rationale: the sum of interior angle in a polygon is ( n - 2 ) * 180 so for a six sided figure , ( 6 - 2 ) * 180 = 720 let the a . m of the other 5 angles be ' m ' - - > m * 5 + ∠ x = 720 , we know ∠ x = m - 48 - - > m * 5 + m - 48 = 720 , solving we get m = 128 hence ∠ x = 128 - 48 = 80 ans b .
Answer: b
Problem: a train crosses a platform of 150 m in 15 sec , same train crosses another platform of length 220 m in 18 sec . then find the length of the train ?
Options: a ) 200 m , b ) 180 m , c ) 272 m , d ) 210 m , e ) 267 m
Rationale: "length of the train be ‘ x ’ ( x + 150 ) / 15 = ( x + 220 ) / 18 5 x + 1100 = 6 x + 900 x = 200 m answer : a"
Answer: a
Problem: if ( - 4 ) ^ ( 6 x ) = 4 ^ ( 30 + x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 6
Rationale: "since x is an integer , ( - 4 ) ^ ( 6 x ) is always positive . so , 4 ^ 6 x = 4 ^ ( 30 + x ) 6 x = 30 + x 5 x = 30 x = 6 answer : e"
Answer: e
Problem: working alone , a can complete a certain kind of job in 10 hours . a and d , working together at their respective rates , can complete one of these jobs in 5 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let total time taken by d to complete the job = d total time taken by a to complete the job = 10 work done by a in an hour 1 / a = 1 / 10 working together a and d can complete the job in 5 hours 1 / a + 1 / d = 1 / 5 = > 1 / d = 1 / 5 - 1 / a = 1 / 5 - 1 / 10 = 1 / 10 = > d = 10 hours answer b"
Answer: b
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 160 m long ?
Options: a ) 41.6 sec , b ) 11 sec , c ) 88 sec , d ) 19 sec , e ) 10 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 160 = 520 m required time = 520 * 2 / 25 = 41.6 sec answer : a"
Answer: a
Problem: man can row upstream at 10 kmph and downstream at 20 kmph , and then find the speed of the man in still water ?
Options: a ) 5 , b ) 20 , c ) 30 , d ) 25 , e ) 15
Rationale: us = 10 ds = 20 m = ( 10 + 20 ) / 2 = 15 answer : e
Answer: e
Problem: at what rate percent of simple interest will a sum of money double itself in 44 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 2.27 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 44 ) = 100 / 44 = 2.27 % answer : e"
Answer: e
Problem: which is greatest in 16 ( 2 / 3 ) % , 2 / 5 and 0.17 ?
Options: a ) 2 / 3 , b ) 0.17 , c ) 3 / 2 , d ) 0.71 , e ) none of them
Rationale: 16 ( 2 / 3 ) % = [ ( 50 / 3 ) * ) 1 / 100 ) ] = 1 / 6 = 0.166 , 2 / 15 = 0.133 . clearly , 0.17 is the greatest . answer is b .
Answer: b
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 11 and 41 inclusive .
Options: a ) 351 , b ) 364 , c ) 416 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 11 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 11 + 41 = 52 2 ) now look at the ' next smallest ' and the ' next biggest ' : 13 + 39 = 52 now we have proof that there is no middle term . we have 8 bunches of 52 . 8 ( 52 ) = 416 c"
Answer: c
Problem: if 25 / 999 = 0.002 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "0 . [ u ] 25 [ / u = 0.002002002002 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 2 . since 81 is multiple of 3 , the 81 st digit is 2 . answer e"
Answer: e
Problem: if x is an integer and 6.1 × 10 ^ x is less than 620 what is the greatest possible value for x ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: if x = 2 6.1 × 10 ^ 2 = 610 < 620 so , x = 2 answer : a
Answer: a
Problem: in the game of dubblefud , red balls , blue balls and green balls are each worth 2 , 4 and 5 points respectively . in a certain selection of balls , the product of the point values of the balls is 16000 . if the number of blue balls in this selection equals the number of green balls , how many red balls are in the selection ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of red balls = 4 hence d
Answer: d
Problem: if the area of a circle is 49 pi square feet , find its circumference .
Options: a ) 14 pi feet , b ) 28 pi feet , c ) 38 pi feet , d ) 48 pi feet , e ) 58 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 49 pi r * r = 49 ; hence r = 49 feet the circumference is given by 2 * pi * r = 2 * pi * 7 = 14 pi feet correct answer a"
Answer: a
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability q that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days q = 15 / 64 ans a it is ."
Answer: a
Problem: a man can row 4.5 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 4.5 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.5 km / hr . answer : d"
Answer: d
Problem: sides of a rectangular park are in the ratio 4 : 3 and its area is 3750 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) s . 132.3 , b ) s . 129 , c ) s . 125 , d ) s . 120 , e ) s . 121
Rationale: "4 x * 3 x = 3750 = > x = 17.7 2 ( 82.3 + 50 ) = 264.6 m 264.6 * 1 / 2 = rs . 132.3 answer : a"
Answer: a
Problem: what is the smallest no . which must be added to 8261955 so as to obtain a sum which is divisible by 11 ?
Options: a ) 8 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 8261955 , difference = ( 8 + 6 + 9 + 5 ) - ( 2 + 1 + 5 ) = 28 - 8 = 20 . the units digit is at odd place . so we add 2 to the number = > 8261955 + 2 = 8261957 now , ( 8 + 6 + 9 + 7 ) - ( 2 + 1 + 5 ) = 30 - 8 = 22 = > 22 is a multiple of 11 and hence 8261957 is also divisible by 11 b
Answer: b
Problem: if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 2 y ^ 2 = ?
Options: a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 32
Rationale: "3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 2 y ^ 2 = 2 * 16 = 32 answer is e"
Answer: e
Problem: a ’ s speed is 20 / 14 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 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 14 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 6 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 6 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 14 meters ) to reach the finish line . so b should get a head start of 6 / 20 th of the race . answer ( d )"
Answer: d
Problem: what is the product of all the possible values of x if x ^ 2 ( x + 2 ) + 7 x ( x + 2 ) + 6 ( x + 2 ) = 0 ?
Options: a ) – 29 , b ) – 12 , c ) 12 , d ) 29 , e ) 168
Rationale: x ^ 2 ( x + 2 ) + 7 x ( x + 2 ) + 6 ( x + 2 ) = 0 = > ( x + 2 ) ( x ^ 2 + 7 x + 6 ) = 0 = > ( x + 2 ) ( x + 1 ) ( x + 6 ) = 0 = > x = - 1 or - 2 or - 6 product = - 12 answer option - 12 answer : b
Answer: b
Problem: jar x is 1 / 5 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 7 / 10 , d ) 7 / 20 , e ) 9 / 20
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 5 + p / 4 = 9 / 20 the answer is e ."
Answer: e
Problem: a babysitter is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 30 hours per week . for any overtime hours worked in excess of 30 hours per week , the babysitter is paid a rate that is 75 % higher than his regular rate . if last week the babysitter earned $ 760 , how many total hours did she work that week ?
Options: a ) 40 , b ) 30 , c ) 35 , d ) 25 , e ) 45
Rationale: for 30 hrs = 30 * 16 = 480 excess = 760 - 480 = 280 for extra hours = . 75 ( 16 ) = 12 in addition to $ 16 . thus , 12 + 16 = 28 number of extra hrs = 280 / 28 = 10 total hrs = 30 + 10 = 40 answer a 40
Answer: a
Problem: by travelling at 80 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 25 kmph , b ) 40 kmph , c ) 35 kmph , d ) 46 kmph , e ) 50 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 80 * 3 x = 240 x km he covered 2 / 3 * 240 x = 160 x km in 1 / 3 * 3 x = x hours so , the remaining 80 x km , he has to cover in 2 x hours . required speed = 80 x / 2 x = 40 kmph . answer : b"
Answer: b
Problem: two employees m and n are paid a total of $ 594 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 240 , b ) $ 250 , c ) $ 260 , d ) $ 270 , e ) $ 280
Rationale: 1.2 n + n = 594 2.2 n = 594 n = 270 the answer is d .
Answer: d
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 42 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 7 min , c ) 8.2 min , d ) 9.6 min , e ) 40 min
Rationale: "d 9.6 min due to stoppages , it covers 8 km less . time taken to cover 9 km = ( 8 / 50 x 60 ) min = 9.6 min"
Answer: d
Problem: tough and tricky questions : functions . let a be a positive integer . let n # a equal n ^ ( 2 a ) if a is odd and n ^ ( 3 a ) if a is even . then ( 2 # 3 ) + ( 2 # 3 ) – ( 3 # 3 ) is equal to
Options: a ) 64 , b ) 82 , c ) 128 , d ) 729 , e ) 1522
Rationale: "answer : 3 ^ 6 + 3 ^ 6 - 3 ^ 6 = 3 ^ 6 = 729 ans d"
Answer: d
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 900 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units , b ) 120 sq . units , c ) 187 sq . units , d ) 607 sq . units , e ) 815 sq . units
Rationale: "given that the area of the square = 900 sq . units = > side of square = √ 900 = 30 units the radius of the circle = side of the square = 30 units length of the rectangle = 2 / 5 * 30 = 12 units given that breadth = 10 units area of the rectangle = lb = 12 * 10 = 120 sq . units answer : b"
Answer: b
Problem: a rectangular grass field is 60 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1200 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 60 + 55 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : b"
Answer: b
Problem: a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 5 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 40 min , e ) 55 min
Rationale: "there are 8 hours in between 9 a . m . to 5 p . m . 8 * 5 = 40 minutes . answer : d"
Answer: d
Problem: a plant manager must assign 6 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 24 , b ) 27 , c ) 33 , d ) 45 , e ) 54
Rationale: "whatever : my take selecting team of 2 out of 10 to assign to the shifts = 6 c 2 = 15 ways . now 2 out of 10 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 2 out of 6 ) * arranging those teams in shifts = 15 * 3 = 45 ans : d"
Answer: d
Problem: the average of first four multiples of 4 is :
Options: a ) 3 , b ) 9 , c ) 10 , d ) 15 , e ) 17
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 ) / 4 = 40 / 4 = 10 answer c"
Answer: c
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 15 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 28 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 60.00
Rationale: without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 43 % , thus he must pay slightly more than $ 57 . only answer choice e fits . answer : e .
Answer: e
Problem: what is the sum of the greatest common factor and the lowest common multiple of 45 and 125 ?
Options: a ) 1920 , b ) 2201 , c ) 3240 , d ) 1130 , e ) 3840
Rationale: "prime factorization of the given numbers 45 = 3 ^ 2 125 = 5 ^ 3 greatest common factor = 5 lowest common multiple = 3 ^ 2 * 5 ^ 2 * 5 = 1125 sum = 5 + 1125 = 1130 answer d"
Answer: d
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability e that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days e = 15 / 64 ans a it is ."
Answer: a
Problem: you collect pens . suppose you start out with 10 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 59
Rationale: "solution start with 10 pens . mike gives you 22 pens : 10 + 22 = 39 pens . cindy doubles the number of pens you have : 39 ã — 2 = 78 pens . sharon takes 19 pens from you : 78 - 19 = 59 pens . so you have 59 at the end . correct answer : e"
Answer: e
Problem: how many integer values are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: the inequality given is 1 < 3 x + 5 < 17 it can further reduced to - 4 < 3 x < 12 finally - 4 / 3 < x < 4 so can only take 5 integer values i . e . - 1 , 0,1 , 2,3 correct answer - d
Answer: d
Problem: a portion of the 85 % solution of chemicals was replaced with an equal amount of 30 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 11 , b ) 6 / 11 , c ) 7 / 11 , d ) 9 / 11 , e ) 13 / 6
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.85 ( 1 - x ) + 0.3 * x = 0.4 - - > x = 9 / 11 . answer : d ."
Answer: d
Problem: if the price of a book is first decreased by 20 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 4 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 20 % = 80 then increased 20 % on rs 80 = 80 + 16 = 96 net change in price = 100 - 96 = 4 answer : c"
Answer: c
Problem: a basketball is dropped from a height of 30 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 3 full bounces .
Options: a ) 50 , b ) 82.5 , c ) 60 , d ) 75 , e ) 80
Rationale: "initial distance = 30 feet first bounce = 15 feet up + 15 feet down = 30 feet second bouche = 7.5 feet up + 7.5 feet down = 15 feet third bounce = 375 feet up and 3.75 feet down = 7.5 feet total distance covered = 30 + 30 + 15 + 7.5 = 82.5 answer is b"
Answer: b
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 600 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 50 sec , e ) 40 min
Rationale: "they meet every 600 / 7 + 8 = 40 sec answer is e"
Answer: e
Problem: praveen age after 10 years will be 3 times his age 3 years back . what is the present age of chris ?
Options: a ) 20 , b ) 25 , c ) 10 , d ) 30 , e ) 15
Rationale: chris present age = x after 10 years = x + 10 3 years back = x - 3 x + 10 = 3 ( x - 3 ) x = 20 answer is a
Answer: a
Problem: how many multiples of 2 are there between 10 and 52 , 10 and 52 inclusive ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 21 , e ) 22
Rationale: "2 multiples are . . . 10,12 , 14,16 , 18,20 , 22,24 , 26,28 , 30,32 , 34,36 , 38,40 , 42,44 , 46,48 , 50,52 , . . . , the answer is = 22 answer is e"
Answer: e
Problem: what is the next number 12 13 15 17 111 113 117 119 123 129 ?
Options: a ) 154 , b ) 220 , c ) 129 , d ) 131 , e ) 224
Rationale: 131 . these are the first 10 prime numbers ( 2 , 3 , 5 . . . ) prefixed with a 1 answer : d
Answer: d
Problem: david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 6 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 4 , e ) 1 / 3
Rationale: "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 2 x total tips for all months = 6 * x + 2 x = 8 x tips for august / total tips for all months = 2 x / 8 x = 1 / 4 answer : d"
Answer: d
Problem: if the average of 10 x and 8 y is greater than 70 , and x is twice y , what is the least integer value of x ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 10 , e ) 20
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 10 x and 4 x is greater than 70 . average of 10 x and 4 x is 7 x . so , 7 x > 70 x > 10 answer : d"
Answer: d
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 35 % water ?
Options: a ) 1.3 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 65 % ( 100 - 35 ) . therefore 0.5 x amount of flower - nectar = 0.65 x amount of honey = 0.65 x 1 kg therefore amount of flower - nectar needed = ( 0.65 / 0.51 ) kg = 1.3 kgs answer : a
Answer: a
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 1205 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 31897 , c ) 48799 , d ) 50000 , e ) 52782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 1205 p = 50000 answer : d"
Answer: d
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 61.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 4.50 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 61.2 - - > { original price } = $ 72 . { final price } = $ 61.2 * 1.25 = $ 76.5 . the difference = $ 76.5 - $ 72 = $ 4.5 answer : b ."
Answer: b
Problem: the smallest number which when diminished by 12 , is divisible 12 , 24 , 36 , 48 and 56 is :
Options: a ) 1008 , b ) 1015 , c ) 1020 , d ) 1032 , e ) 1048
Rationale: "required number = ( l . c . m . of 12 , 24 , 36 , 48,56 ) + 12 = 1008 + 12 = 1020 answer : option c"
Answer: c
Problem: there are 100 students in 3 sections a , b and c of a class . the average marks of all the 3 sections was 84 . the average of b and c was 87.5 and the average marks of students in a section was ?
Options: a ) 20 , b ) 99 , c ) 28 , d ) 27 , e ) 12
Rationale: numbers of students in section a = x numbers of students in section b and c = ( 100 – x ) x 70 + ( 100 – x ) 87.5 = 84 100 70 x + 87.5 100 – 87.5 x = 8400 8750 – 17.5 x = 8400 17.5 x = 8750 – 8400 = > x = 20 . answer : a
Answer: a
Problem: a trader bought a car at 5 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 52 % , d ) 19 % , e ) 22 %
Rationale: original price = 100 cp = 95 s = 95 * ( 160 / 100 ) = 152 100 - 152 = 52 % answer : c
Answer: c
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 275 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 275 + x ) / 2 on solving , x = 425 . answer : d"
Answer: d
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 18 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 8 , b ) 16 , c ) 11 , d ) 12 , e ) 21
Rationale: "relative speed = ( 18 + 72 ) * 5 / 18 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec . answer : b"
Answer: b
Problem: if x : y = 1 : 3 , find the value of ( 2 x + 3 y ) : ( 5 x – y )
Options: a ) 11 : 3 , b ) 11 : 2 , c ) 3 : 2 , d ) 7 : 2 , e ) 9 : 5
Rationale: "explanation : given : x / y = 1 / 3 ( 2 x + 3 y ) / ( 3 x – y ) = ( 2 * 1 + 3 * 3 ) : ( 5 * 1 – 3 ) = 11 : 2 answer : b"
Answer: b
Problem: if x # y is defined to equal x ^ 3 / y for all x and y , then ( - 1 # 2 ) # 3 =
Options: a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 12 , d ) - 1 / 12 , e ) 1 / 24
Rationale: "( - 1 ) ^ 3 / 2 = 1 / 2 ( 1 / 2 ) ^ 3 / 3 = 1 / 24 so e is my answer"
Answer: e
Problem: in a restaurant , the profit is 150 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 55 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 150 , s . p . = rs . 250 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 250 . profit = rs . ( 250 - 112 ) = rs . 138 . required percentage = ( 138 / 250 * 100 ) % = 55 % appox answer : b"
Answer: b
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter e of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) e = 7 * 3 = 21 . c"
Answer: c
Problem: a can do a piece of work in 14 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 14
Rationale: "8 / 14 + 6 / x = 1 x = 14 days answer : e"
Answer: e
Problem: 8 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 66 , b ) 52 , c ) 58 , d ) 55 , e ) 56
Rationale: "though 2 * ( 8 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 7 , so he ' ll play 14 matches . similarly , second guy has to play with the rest of 6 as his 2 games with the first guy are already played . so he plays 12 matches . this continues like this and the total matches are 14 + 12 + 10 . . . + 2 14 + 12 + . . . + 2 = 2 ( 7 + 6 + . . . + 1 ) = 2 ( ( 7 * 8 ) / 2 ) = 7 * 8 = 56 . answer : e"
Answer: e
Problem: a small college reduced its faculty by approximately 14 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 227 , d ) 254 , e ) 302
Rationale: if x is the original number of faculty members , then after 14 % reduction in faculty members number is . 86 x but we are given . 86 x = 195 x = 227 so the original number of faculty members is 227 correct answer - c
Answer: c
Problem: one fourth of one third of two fifth of a number is 16 . what will be 40 % of that number
Options: a ) 140 , b ) 150 , c ) 180 , d ) 192 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 16 then x = 16 * 30 = 480 40 % of 480 = 192 answer : option d"
Answer: d
Problem: hree number are in the ratio of 3 : 4 : 5 and their l . c . m . is 2400 . their h . c . f . is :
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: let the numbers be 3 x , 4 x and 5 x . then , their l . c . m . = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 x 40 ) , ( 4 x 40 ) and ( 5 x 40 ) . hence , required h . c . f . = 40 . answer : a
Answer: a
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 625 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 99 , c ) 100 , d ) 72 , e ) 12
Rationale: "given that the area of the square = 625 sq . units = > side of square = √ 625 = 25 units the radius of the circle = side of the square = 25 units length of the rectangle = 2 / 5 * 25 = 10 units given that breadth = 10 units area of the rectangle = lb = 10 * 10 = 100 sq . units answer : c"
Answer: c
Problem: if x + y = 250 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 225 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 250 x - y = 200 2 x = 50 x = 25 y = 225 answer is b"
Answer: b
Problem: if the area of a circle is 36 pi square feet , find its circumference .
Options: a ) 65 pi feet , b ) 43 pi feet , c ) 12 pi feet , d ) 18 pi feet , e ) 64 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 81 pi r * r = 36 ; hence r = 36 feet the circumference is given by 2 * pi * r = 2 * pi * 6 = 128 pi feet correct answer c"
Answer: c
Problem: to fill a tank , 42 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifths of its present ?
Options: a ) 102 , b ) 103 , c ) 104 , d ) 105 , e ) 106
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 42 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 42 x ) / ( 2 x / 5 ) = ( 42 x ) x 5 / 2 x = 210 / 2 = 105 answer is d ."
Answer: d
Problem: a factory produces 1 defective bulb out of 10 bulbs a yr . if it produces 870 bulbs a yr , how many defective bulbs are produced ?
Options: a ) 84 , b ) 85 , c ) 86 , d ) 87 , e ) 88
Rationale: 10 out of 1 is defective 20 out of 2 is defective 100 out of 10 is defective and so on 800 out of 80 is defective 70 out of 7 is defective 80 + 7 = 87 answer : d
Answer: d
Problem: the area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is ?
Options: a ) 48 , b ) 40 , c ) 52 , d ) 54 , e ) 58
Rationale: "isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 16 will be divided into 3 parts = 10 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 26 * 4 = 52 c is the answer"
Answer: c
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 25 in two years , at the same percent rate per annum ?
Options: a ) s . 40 , b ) s . 48 , c ) s . 49 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 25 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 25 – 20 ) / 20 ] * 100 = 25 % p . a . let the principal be rs . x time = t = 2 years % rate = 25 % p . a . si = ( prt / 100 ) 20 = ( x * 25 * 2 ) / 100 x = rs . 40 answer : a"
Answer: a
Problem: a shopkeeper sells 400 metres of cloth for $ 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) $ 20 , b ) $ 43 , c ) $ 50 , d ) $ 70 , e ) $ 40
Rationale: "c $ 50 sp per metre = 18000 / 400 = $ 45 loss per metre = $ 5 cp per metre = 45 + 5 = $ 50"
Answer: c
Problem: 36 * 36 * 36 = 6 ^ ?
Options: a ) 3 , b ) 2 , c ) 6 , d ) 1 , e ) 5
Rationale: "6 ^ 2 * 6 ^ 2 * 6 ^ 2 = 6 ^ ( 2 + 2 + 2 ) = 6 ^ 6 answer : 6 answer : c"
Answer: c