regisss/math_qa huggingface dataset:
Problem: with both inlets open , a water tank will be filled with water in 36 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 4,500 , c ) 1,750 , d ) 1,000 , e ) 2,000
Rationale: "the work done by inlet a and b together in 1 min = 1 / 36 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 36 ) - ( 1 / 120 ) = 1 / 51 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 51 ) - ( 1 / 120 ) = 50 cubic meter i . e . 4500 cubic meter answer : option b"
Answer: b
Problem: what is the angle between the hands of a clock when time is 16 : 40 ?
Options: a ) 625 deg , b ) 420 deg , c ) 145 deg , d ) 150 deg , e ) 300 deg
Rationale: "angle between two hands = 40 h - 11 / 2 m = 40 * 16 - 40 * 11 / 2 = 640 - 220 = 420 deg answer : b"
Answer: b
Problem: solve the equation for x : 8 ( x + y + 2 ) = 8 y - 8
Options: a ) - 3 , b ) - 2 , c ) - 1 , d ) 1 , e ) 2
Rationale: "a - 3 8 ( x + y + 2 ) = 8 y - 8 8 x + 8 y + 16 = 8 y - 8 8 x + 16 = - 8 8 x = - 24 = > x = - 3"
Answer: a
Problem: during a special promotion , a certain filling station is offering a 8 percent discount on gas purchased after the first 10 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 105 % , c ) 115 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 4 + 0.9 * 16 = 18.4 gallons , so the overall discount she got was 1.6 / 20 = 8 % . isabella purchased 25 gallons of gas . she paid for 4 + 0.9 * 21 = 22.9 gallons , so the overall discount she got was 2.1 / 25 = 8.4 % . 8.4 / 8 * 100 = 105 % . answer : b ."
Answer: b
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 90 only . men â € ™ s wages are ?
Options: a ) rs . 6 , b ) rs . 6.5 , c ) rs . 8 , d ) rs . 5 , e ) rs . 2
Rationale: "answer : option a 5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs ."
Answer: a
Problem: stacy has a 33 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 11 , d ) 8.5 , e ) 6
Rationale: "33 / 3 = 11 answer : c"
Answer: c
Problem: the smallest value of n , for which 2 n + 1 is not a prime number , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) none , e ) 6
Rationale: "solution ( 2 × 1 + 1 ) = 3 . ( 2 × 2 + 1 ) = 5 . ( 2 × 3 + 1 ) = 7 . ( 2 × 4 + 1 ) = 9 . which is not prime , n = 4 . answer b"
Answer: b
Problem: a train running at the speed of 50 km / hr crosses a pole in 18 seconds . find the length of the train .
Options: a ) 150 , b ) 188 , c ) 250 , d ) 288 , e ) 300
Rationale: "speed = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec length of train ( distance ) = speed * time ( 125 / 9 ) * 18 = 250 meter answer : c"
Answer: c
Problem: what sum of money put at c . i amounts in 2 years to rs . 7000 and in 3 years to rs . 9261 ?
Options: a ) 4000 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "7000 - - - - 2261 100 - - - - ? = > 32.3 % x * 1323 / 100 * 1323 / 100 = 7000 x * 1.75 = 7000 x = 7000 / 1.75 = > 3999.25 answer : a"
Answer: a
Problem: two employees m and n are paid a total of $ 583 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 ) $ 245 , b ) $ 255 , c ) $ 265 , d ) $ 275 , e ) $ 285
Rationale: "1.2 n + n = 583 2.2 n = 583 n = 265 the answer is c ."
Answer: c
Problem: if remainder is 1 , quotient is 54 and dividend is 217 then what is divisor ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 14 , e ) 16
Rationale: "we know dividend = divisor * quotient + remainder = = = > 217 = divisor * 54 + 1 = = = = = > 216 / 54 = divisor = = = > divisor = 4 ans - b"
Answer: b
Problem: 4 , 7 , 13 , 25 , 49 , ( . . . )
Options: a ) 22 , b ) 35 , c ) 97 , d ) 32 , e ) 25
Rationale: "explanation : 4 4 × 2 - 1 = 7 7 × 2 - 1 = 13 13 × 2 - 1 = 25 25 × 2 - 1 = 49 49 × 2 - 1 = 97 answer : option c"
Answer: c
Problem: find the least number that must be subtracted from 1387 so that the remaining number is divisible by 15 .
Options: a ) 1 , b ) 5 , c ) 7 , d ) 9 , e ) 13
Rationale: on dividing 1387 by 15 we get the remainder 7 , so 7 should be subtracted . the answer is c .
Answer: c
Problem: the output of a factory was increased by 5 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "the original output increases by 5 % and then 20 % . total % change = a + b + ab / 100 total % change = 5 + 20 + 5 * 20 / 100 = 26 % now , you want to change it to 0 , so , 0 = 26 + x + 26 x / 100 x = - 26 ( 100 ) / 126 = 20 % approximately answer is a"
Answer: a
Problem: if n is a positive integer and n ^ 2 is divisible by 62 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 12 , is n divisible by 48 ? no . so , n is not always divisible by 48 . b"
Answer: b
Problem: if a and b get profits of rs . 60,000 and rs . 6,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 10 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: ratio = 60000 / 6000 = 10 : 1 answer : b
Answer: b
Problem: what is the 99 th digit after the decimal point in the decimal expansion of 2 / 9 + 3 / 11 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: 2 / 9 = 0.22222 . . . . = = > 99 th digit is 2 3 / 11 = 0.27272727 . . . . = = > every odd digit is 2 . so , 99 th digit will be 2 . 2 + 2 = 4 answer : c
Answer: c
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 10 years from now ?
Options: a ) 17 , b ) 25 , c ) 27 , d ) 35 , e ) 50
Rationale: let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of bren = 8 * 5 = 40 bren ' s age 10 years hence = 40 + 10 = 50 answer = e
Answer: e
Problem: a trainer is standing in one corner of a square ground of side 25 m . his voice can be heard upto 140 m . find the area of the ground in which his voice can be heard ?
Options: a ) 12300
b ) 14500
c ) 15400
d ) 16700
e ) 18200
Rationale: area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because the trainer is standing in a corner of the ground and only in 1 / 4 part , the voice can be heard ) where r = 14 m = length reaching the voice so area = ( 22 / 7 ) * 140 * 140 / 4 = 15400 sq m answer : c
Answer: c
Problem: machine m , n , o working simultaneously machine m can produce x units in 3 / 4 of the time it takes machine n to produce the same amount of units . machine n can produce x units in 2 / 7 the time it takes machine o to produce that amount of units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?
Options: a ) 1 / 2 , b ) 7 / 13 , c ) 4 / 13 , d ) 8 / 29 , e ) 6 / 33
Rationale: now ultimately the speed of every machine is given with respect to mach o . so lets assume the speed of o , say 12 hrs to make x units ( assuming 6 because we can see we will need to divide by 3 and 4 mach o makes x units in 12 hrs so , mach n = 2 / 7 of o = 2 / 7 * 12 = 24 / 7 hrs to make x units and mach m = 3 / 4 of n = 3 / 4 * 24 / 7 = 1 / 6 hrs to make x units no they are running simultaneously . lets see how much each mach makes in 1 hr mach o = x / 12 units mach n = 7 / 24 units mach m = x / 6 units in 1 hr , together they make - x / 12 + 7 / 24 + x / 6 = 13 / 24 so what ratio of this has mach n made ? ( 7 / 24 ) / ( 13 / 24 ) = 7 / 13 ans : b = 7 / 13
Answer: b
Problem: a and b can do a work in 2 days , b and c in 6 days and c and a in 8 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 12 / 28 , b ) 48 / 19 , c ) 16 / 48 , d ) 18 / 48 , e ) 12 / 64
Rationale: "one day work of a and b = 1 / 2 one day work of b and c = 1 / 6 one day work of c and a = 1 / 8 2 ( a + b + c ) = 1 / 2 + 1 / 6 + 1 / 8 2 ( a + b + c ) = 19 / 24 ( a + b + c ) = 19 / 48 number of days required = 48 / 19 days . answer : b"
Answer: b
Problem: a man is 18 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 23 years , d ) 12 years , e ) 16 years
Rationale: "explanation : let ' s son age is x , then father age is x + 18 . = > 2 ( x + 2 ) = ( x + 18 + 2 ) = > 2 x + 4 = x + 20 = > x = 16 years option e"
Answer: e
Problem: ( 0.0088 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.008 ) =
Options: a ) 950 , b ) 940 , c ) 980 , d ) 960 , e ) 990
Rationale: "( 0.0088 ) ( 4.5 ) / ( 0.05 ) ( 0.1 ) ( 0.008 ) = 0.0088 * 450 / 5 * ( 0.1 ) ( 0.008 ) = 0.088 * 90 / 1 * 0.008 = 88 * 90 / 8 = 11 * 90 = 990 answer : e"
Answer: e
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 210 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1007 , d ) s . 1006 , e ) s . 1500
Rationale: explanation : 90 % 104 % - - - - - - - - 14 % - - - - 210 100 % - - - - ? = > rs . 1500 answer : e
Answer: e
Problem: ( 4300631 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1765013 , d ) 1675123 , e ) none of them
Rationale: "let 4300631 - x = 2535618 then x = 4300631 - 2535618 = 1765013 answer is c"
Answer: c
Problem: two trains 250 m and 500 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 10.9 , c ) 10.4 , d ) 27 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 250 + 500 = 750 m . required time = 750 * 9 / 250 = 27 sec answer : d"
Answer: d
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 3 , 1 ) , ( 1 , 1 ) , ( 1 , - 2 ) and ( - 3 , - 2 ) ?
Options: a ) 12 , b ) 24 , c ) 20 , d ) 30 , e ) 36
Rationale: "length of side 1 = 3 + 1 = 4 length of side 2 = 2 + 1 = 3 area of rectangle = 4 * 3 = 12 a is the answer"
Answer: a
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 22,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 158 % , e ) 225 %
Rationale: "the percent increase is ( 22947 - 8902 ) / 8902 = 14045 / 8902 = 1.58 so the approximate answer is d"
Answer: d
Problem: a can finish a piece of work in 4 days . b can do it in 8 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 2 , e ) 8
Rationale: "2 / 4 + ( 2 + x ) / 8 = 1 = > x = 2 days 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 90 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 80 / 6 , b ) 80 / 7 , c ) 80 / 9 , d ) 80 / 2 , e ) 80 / 1
Rationale: "relative speed = ( 90 + 72 ) * 5 / 18 = 45 mps . the time required = d / s = ( 100 + 100 + 200 ) / 45 = 400 / 45 = 80 / 9 sec . answer : c"
Answer: c
Problem: a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 32 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 3 ) + 65 ∴ x = 32 answer a"
Answer: a
Problem: of 30 applicants for a job , 13 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 6 , e ) 5
Rationale: "d . 6 30 - 3 = 27 27 - 13 - 18 = - 6 then 6 are in the intersection between 4 years experience and degree . answer d"
Answer: d
Problem: a train is 360 meter long is running at a speed of 72 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 65 seconds , b ) 46 seconds , c ) 25 seconds , d ) 97 seconds , e ) 26 seconds
Rationale: "speed = 72 km / hr = 72 * ( 5 / 18 ) m / sec = 20 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 20 ) = 25 seconds answer : c"
Answer: c
Problem: a certain university will select 2 of 3 candidates eligible to fill a position in the mathematics department and 4 of 5 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 10 , c ) 40 , d ) 65 , e ) 15
Rationale: "3 c 2 * 5 c 4 = 3 * 5 = 15 the answer is ( e )"
Answer: e
Problem: if 9 spiders make 9 webs in 9 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 5 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) 6 days
Rationale: "let , 1 spider make 1 web in a days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 9 : 1 } : : a : 9 ( webs ) 1 : 9 ⇒ 7 × 1 × 7 = 1 × 7 × a ⇒ a = 7 answer : b"
Answer: b
Problem: a bullet train 220 m long is running with a speed of 59 kmph . in what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 15 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec
Rationale: "c 12 sec speed of the bullet train relative to man = ( 59 + 7 ) kmph = 66 * 5 / 18 m / sec = 55 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 * 3 / 55 ) sec = 12 sec"
Answer: c
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , 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 $ 208 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,160 , e ) 2,256
Rationale: "i think it should be d . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 8 20 - pack for 3.05 * 8 = $ 24.40 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2160"
Answer: d
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 26 seconds . the ratio of their speeds is ?
Options: a ) 3 / 1 , b ) 9 / 1 , c ) 3 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 26 = = > 27 x + 17 y = 26 x + 26 y = = > 1 x = 9 y = = > x / y = 9 / 1 . answer : b"
Answer: b
Problem: the spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls . the diameters of two of these are 1 ½ cm and 2 cm respectively . the diameter of third ball is ?
Options: a ) 2.66 cm , b ) 2.5 cm , c ) 3 cm , d ) 3.5 cm , e ) 4 cm
Rationale: 4 / 3 π * 3 * 3 * 3 = 4 / 3 π [ ( 3 / 2 ) 3 + 23 + r 3 ] r = 1.25 d = 2.5 answer : b
Answer: b
Problem: find the number which when multiplied by 15 is increased by 196
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "explanation : let the number be x . then , 15 x = x + 196 = › 14 x = 196 = › x = 14 . answer : option c"
Answer: c
Problem: a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 175 , d ) 165 , e ) 315
Rationale: "5 c 1 * 7 c 4 = 5 * 35 = 175 the answer is ( c )"
Answer: c
Problem: if the speed of a man is 51 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 375 m , d ) 425 m , e ) 440 m
Rationale: "the distance traveled in 30 sec = 51 * ( 5 / 18 ) * 30 = 425 m answer : d"
Answer: d
Problem: the ratio between the sale price and the cost price of an article is 6 : 4 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 4 x and s . p . = rs . 6 x . then , gain = rs . 2 x required ratio = 2 x : 4 x = 1 : 2 b"
Answer: b
Problem: a person want to give his money of $ 5400 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 1800 , c ) $ 2500 , d ) $ 1500 , e ) $ 1600
Rationale: "b ' s share = 5400 * 3 / 9 = $ 1800 answer is b"
Answer: b
Problem: what is the product of first three whole no .
Options: a ) 0 , b ) 1 , c ) 6 , d ) 2 , e ) 3
Rationale: "first three whole no . are 0 , 1,2 . remember whole no . start from 0 and natural no . from 1 so product will 0 only . answer a"
Answer: a
Problem: the perimeter of one face of a cube is 32 cm . its volume will be :
Options: a ) 125 cm 3 , b ) 400 cm 3 , c ) 512 cm 3 , d ) 625 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 32 / 4 = 8 cm volume = a * a * a = 8 * 8 * 8 = 512 cm cube option c"
Answer: c
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 4 - 1 / 6 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 1 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 4 - 1 / 6 = ( 6 - 4 ) / 24 = 2 / 24 = 1 / 12 so 17 / 12 / 1 / 12 = 17 / 12 * 12 = 17 / 1 answer - d"
Answer: d
Problem: income and expenditure of a person are in the ratio 10 : 7 . if the income of the person is rs . 10000 , then find his savings ?
Options: a ) 3005 , b ) 3098 , c ) 3300 , d ) 3010 , e ) 3000
Rationale: "let the income and the expenditure of the person be rs . 10 x and rs . 7 x respectively . income , 10 x = 10000 = > x = 1000 savings = income - expenditure = 10 x - 7 x = 3 x = 3 ( 1000 ) so , savings = rs . 3000 . answer : e"
Answer: e
Problem: if the price of an article went up by 15 % , then by what percent should it be brought down to bring it back to its original price ?
Options: a ) 17.39 % , b ) 2 / 8 % , c ) 2 / 1 % , d ) 1 / 3 % , e ) 2 / 7 %
Rationale: "let the price of the article be rs . 100 . 15 % of 100 = 15 new price = 100 + 15 = rs . 115 required percentage = ( 115 - 100 ) / 115 * 100 = 20 / 115 * 100 = 17.39 % . answer : a"
Answer: a
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 100 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 300 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 100 then y = 300 answer : c"
Answer: c
Problem: one millisecond is 0.001 of a second . the costs for a single run of a computer program are $ 1.07 for operating - system overhead , $ 0.023 per millisecond of computer time , and $ 5.35 for the mounting of a data tape . what is the total of these 3 costs for 1 run of a program that requires 1.5 seconds of computer time ?
Options: a ) $ 7.15 , b ) $ 8.87 , c ) $ 28.96 , d ) $ 35.57 , e ) $ 40.92
Rationale: operating system overhead for 1 run = 1.07 $ mounting of data tape = 5.35 $ cost per 1 millisecond of computer time = . 023 $ total cost of 1 run of a program that requires 1.5 seconds of computer time = 1.07 + ( . 023 * 1500 ) + 5.35 = 1.07 + 34.5 + 5.35 = 40.92 $ answer e
Answer: e
Problem: if 20 typists can type 46 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 216 , e ) 207
Rationale: "20 typists can type 46 letters , so 30 typists can type = 46 * 30 / 20 46 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 46 * 30 * 60 / 20 * 20 = 207 e is the answer"
Answer: e
Problem: the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit h on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft
Rationale: "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer h is 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b"
Answer: b
Problem: if 4 x + y = 34 , 2 x - y = 20 , for integers of x and y , y ^ 2 = ?
Options: a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 3
Rationale: 4 x + y = 34 2 x - y = 20 6 x = 54 x = 9 y = - 2 y ^ 2 = 4 answer is b
Answer: b
Problem: what is the sum of mean and median of 17 , 45 , 59 , 113 , 76 , 95 , 59 , 35 , 1236 ?
Options: a ) 50.2 , b ) 45.8 , c ) 54.7 , d ) 61.8 , e ) 10.5
Rationale: mean = ( 17 + 45 + 59 + 113 + 76 + 95 + 59 + 35 + 12 + 36 ) / 10 = 547 / 10 = 54.7 answer is c
Answer: c
Problem: if 0 is the remainder when m is divided by 4 , what is the remainder when 6 m is divided by 4 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "for any m that is divisible by 4 , any multiple of m ( such as 6 m ) will also be divisible by 4 . m = 4 * a 6 m = 6 * 4 * a the answer is , therefore , ( a ) ."
Answer: a
Problem: if a / b = 5 / 2 , b / c = 1 / 2 , c / d = 1 , d / e = 3 / 2 and e / f = 4 / 3 , then what is the value of abc / def ?
Options: a ) 15 / 8 , b ) 14 / 3 , c ) 41 / 7 , d ) 3 / 18 , e ) 18 / 4
Rationale: say a = 2 . then : a / b = 5 / 2 - - > b = 2 / 5 ; b / c = 1 / 2 - - > c = 4 / 5 ; c / d = 1 - - > d = 4 / 5 ; d / e = 3 / 2 - - > e = 8 / 15 ; e / f = 4 / 3 - - > f = 2 / 5 . abc / def = ( 1 * 2 / 5 * 4 / 5 ) / ( 4 / 5 * 8 / 15 * 2 / 5 ) = 15 / 8 . answer : a .
Answer: a
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 75 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 187 , c ) $ 110 , d ) $ 138 , e ) $ 192
Rationale: "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 75 + 150 * 2 . = 16500 + 11250 + 300 p = $ 187 b"
Answer: b
Problem: if paint costs $ 3.20 per quart , and a quart covers 10 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60 , b ) $ 16.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 192.00
Rationale: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 10 = 60 cost will be 60 * 3.2 = $ 192 ans : e"
Answer: e
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 3 min early . find his usual time to reach the school ?
Options: a ) 21 , b ) 28 , c ) 99 , d ) 77 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 3 - - - - - - - - - ? = 21 m answer : a"
Answer: a
Problem: in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ?
Options: a ) 29
b ) 30
c ) 31
d ) 32
e ) 33
Rationale: the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 8 and a height of 4 . the area of this part is ( 1 / 2 ) ( 8 ) ( 4 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 8 ) ( 4 ) = 32 . the answer is d .
Answer: d
Problem: in a school of 850 boys , 40 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 187 , d ) d ) 721 , e ) e ) 159
Rationale: "40 + 28 + 10 = 78 % 100 – 78 = 22 % 850 * 22 / 100 = 187 answer : c"
Answer: c
Problem: if a rectangular room measures 9 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 18 , 000,000 , d ) 24 , 000,000 , e ) 240 , 000,000
Rationale: "c . 180 , 000,000 9 * 100 * 5 * 100 * 4 * 100 = 180 , 000,000"
Answer: c
Problem: the price of a certain painting increased by 20 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 140 %
Rationale: "assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.15 = 120 * 0.85 = 102 hence required answer = ( 102 / 100 ) * 100 % = 102 % answer is a ."
Answer: a
Problem: there are 7 books on a shelf , of which 2 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 30 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Rationale: "approach 1 at - least 1 paper back = total - no paper back 7 c 4 - 5 c 4 = 30 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 5 c 3 + 2 c 2 * 5 c 2 = 30 answer is a"
Answer: a
Problem: a man sold 18 toys for rs . 25200 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1200
Rationale: let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 25200 . gain = sp â € “ cp 3 x = 25200 â € “ 18 x 21 x = 25200 x = rs . 1200 . answer : option e
Answer: e
Problem: a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 180 , b ) 270 , c ) 360 , d ) 500 , e ) 550
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 870 = 270 answer b"
Answer: b
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 3 % more . she would get how much ?
Options: a ) 9920 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 3 ) / 100 = 720 9200 - - - - - - - - 9920 answer : a"
Answer: a
Problem: the average of first five prime numbers greater than 17 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 32.3 , d ) 32.8 , e ) 27.8
Rationale: "19 + 23 + 29 + 31 + 37 = 139 / 5 = 27.8 answer : e"
Answer: e
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number i and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number i of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d .
Answer: d
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 10 : 11 , e ) 7 : 9
Rationale: "mixture a has a total of 7 + 5 = 12 parts . if in the final mixture this represents 6 parts , then the total number of parts in mixture b should be ( 12 / 6 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 6 parts , respectively . this will give us in the final mixture ( 7 + 3 ) : ( 5 + 6 ) , which means 10 : 11 answer d ."
Answer: d
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 60 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 1
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 60 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 60 = 55 * ( n + 1 ) - - > n = 1 . answer : e ."
Answer: e
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 55 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 8.5 % , b ) 11.7 % , c ) 14.2 % , d ) 17.6 % , e ) 20.5 %
Rationale: "55 % is 25 % - points above 30 % and 5 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 1 : 5 . 1 / 6 * 70 % = 11.7 % the answer is b ."
Answer: b
Problem: think of a number , divide it by 4 and add 9 to it . the result is 15 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 29
Rationale: answer : a
Answer: a
Problem: what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 81 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 81 is 7 because powers of 7 end in 7 , 9 , 3 or 1 cyclically . since 81 is in the form 4 n + 1 , the units digit is 7 . then 6 + 7 = 13 . the answer is d ."
Answer: d
Problem: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 10 feet between each tree . how many trees can be planted if the road is 166 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16
Rationale: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 10 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 10 feet spaces will be t - 1 . then , the length of sidewalk required for 10 feet spaces will be 10 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 10 ( t - 1 ) + t = 166 or 10 t - 10 + t = 166 or t = 16 answer : - e"
Answer: e
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many l cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . l = 4 + 4 + 4 = 12 . answer a"
Answer: a
Problem: let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the game remainder in each case . then sum of the digits in n is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: solution n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 . answer a
Answer: a
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 3 , - 1 ) , ( 3 , 8 ) , ( 12 , 2 ) , ( 12 , - 7 ) ?
Options: a ) 69 , b ) 75 , c ) 81 , d ) 87 , e ) 93
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 9 + 9 ) × 9 = 81 . the answer is c ."
Answer: c
Problem: a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 380 - meter long platform ?
Options: a ) 47 , b ) 49 , c ) 51 , d ) 53 , e ) 55
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 380 ) / 10 = 53 seconds the answer is d ."
Answer: d
Problem: a train running at the speed of 60 km / hr crosses a pole in 21 sec . what is the length of the train ?
Options: a ) 350 m , b ) 490 m , c ) 115 m , d ) 210 m , e ) 150 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 21 = 350 m answer : a"
Answer: a
Problem: the sum of the first 70 positive even integers is 4,970 . what is the sum of the first 70 odd integers ?
Options: a ) 4500 , b ) 4600 , c ) 4300 , d ) 4900 , e ) 5000
Rationale: sum of first n even numbers = n ( n + 1 ) = 4970 sum of first n odd numbers = n ^ 2 = 70 * 70 = 4900 ( here n = 70 ) answer : d
Answer: d
Problem: a family consists of two grandparents , two parents , and 3 grandchildren . the average age of the grandparents is 64 years , the average age of the parents is 39 years , and the average age of the grandchildren is 6 years . what is the average age ( in years ) of the family ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: total age of the grandparents = 64 ã — 2 = 128 total age of the parents = 39 ã — 2 = 78 total age of the grandchildren = 6 ã — 3 = 18 average age of the family = ( 128 + 78 + 18 ) / 7 = 224 / 7 = 32 years the answer is b .
Answer: b
Problem: if 0.5 % of a = 70 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 140 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 70 / 100 ∴ a = rs . ( 70 / 0.5 ) = rs . 140 correct option : b"
Answer: b
Problem: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 10.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
Rationale: the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 15 x = 10.5 minutes answer : a
Answer: a
Problem: what is the least common multiple of 5,40 , 36,50
Options: a ) 3698 , b ) 874 , c ) 3692 , d ) 1800 , e ) 3214
Rationale: "the given numbers are 5,40 , 36,50 thus the l . c . m is 5 * 2 * 2 * 1 * 2 * 9 * 5 = 1800 the answer is d"
Answer: d
Problem: the sale price of a trolley bag including the sale tax is rs . 280 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 200 , b ) rs 220 , c ) rs 260 , d ) rs 280 , e ) none of these
Rationale: "explanation : 112 % of s . p . = 280 s . p . = rs . ( 280 x 100 / 112 ) = rs . 250 . c . p . = rs ( 100 / 125 x 250 ) = rs 200 answer : a"
Answer: a
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 150 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 10 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 150 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 150 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 150 r 2 = ( 159 * 2 ) / 3 = 100 = > r = 10 rate = 10 % answer : option c"
Answer: c
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 50 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 50 ) / 100 × 16 = 24 answer e"
Answer: e
Problem: in a school 10 % of the boys are same in number as 1 / 3 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 10 : 3 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 3 g 10 b / 100 = g / 3 b = 10 g / 3 b / g = 10 / 3 b : g = 10 : 3 answer is c"
Answer: c
Problem: in what time will a train 120 meters long completely pass an electric pole , if it travels at a speed of 60 kmph .
Options: a ) 6.18 , b ) 5.18 , c ) 4.18 , d ) 4.18 , e ) 7.18
Rationale: "sol . speed = [ 60 x 5 / 18 ] m / sec = 16.7 m / sec . time taken = ( 120 / 16.7 ) sec = 7.18 sec . answer e"
Answer: e
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 e 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 e = $ 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: how many numbers from 49 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 3 , e ) 12
Rationale: "49 / 11 = 4 and 79 / 11 = 7 = = > 7 - 4 = 3 numbers answer : d"
Answer: d
Problem: in a class of 40 students , 5 students did not borrow any books from the library , 15 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 18
Rationale: "the average number of books per student was 2 means that total of 2 * 40 = 80 books were borrowed ; 5 + 15 + 10 = 30 students borrowed total of 5 * 0 + 15 * 1 + 10 * 2 = 35 books ; so 80 - 35 = 45 books are left to distribute among 40 - 30 = 10 students , these 10 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 10 could have borrowed we shouldminimizethe number of books other 9 students from 10 could have borrowed . minimum these 9 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 9 * 3 = 27 books . so the 10 th student could have borrowed is 45 - 27 = 18 books . answer : e ."
Answer: e
Problem: working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 7 pages a minute more than printer a ?
Options: a ) 600 , b ) 840 , c ) 1000 , d ) 1200 , e ) 1500
Rationale: answer : b .
Answer: b
Problem: the jogging track in a sports complex is 640 m in circumference . lata and geeta start from the same point and walk in opposite directions at 4.2 km / hr and 3.8 km / hr respectively . they will meet for the first time in ?
Options: a ) 2.9 min , b ) 3.9 min , c ) 4.2 min , d ) 4.8 min , e ) 5.6 min
Rationale: clearly , the two will meet when they are 640 m apart . to be ( 4.2 + 3.8 ) = 8.0 km apart , they take 1 hour . that is 60 min . to be 640 m apart , they take ( 640 / 8000 * 60 ) min = 4.8 min . answer : d
Answer: d
Problem: village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: let the population of two villages be equal after p years then , 68000 - 1200 p = 42000 + 800 p 2000 p = 26000 p = 13 answer is e .
Answer: e
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 2145 , and if 1 < p < q < r < s , how many students in the class are marketing majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "pqrs = 2145 = 3 * 5 * 11 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 11 . the answer is d ."
Answer: d
Problem: if a man lost 4 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28 % ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 10
Rationale: "96 % - - - - 16 128 % - - - - ? 96 / 128 * 16 = 12 answer : a"
Answer: a
Problem: the population of a town increased from 1 , 25,000 to 1 , 50,000 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 2 % , c ) 6 % , d ) 8.75 % , e ) none of these
Rationale: "solution increase in 10 year = ( 150000 - 125000 ) = 25000 . increase % = ( 25000 / 125000 x 100 ) % = 20 % â ˆ ´ required average = ( 20 / 10 ) % = 2 % answer b"
Answer: b
Problem: 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 6 like all . how many people like apple ?
Options: a ) 47 , b ) 49 , c ) 54 , d ) 58 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 6 40 + 10 + 6 - 7 = 49 like apple answer : b"
Answer: b
Problem: a man purchased 15 pens , 12 books , 10 pencils and 5 erasers . the cost of each pen is rs . 36 , each book is rs . 45 , each pencil is rs . 8 , and the cost of each eraser is rs . 40 less than the combined costs of pen and pencil . find the total amount spent ?
Options: a ) 2388 , b ) 2337 , c ) 1192 , d ) 2827 , e ) 1180
Rationale: explanation : cost of each eraser = ( 36 + 8 - 40 ) = rs . 4 required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4 540 + 540 + 80 + 20 = rs . 1180 answer : e
Answer: e
Problem: john was 22 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 9 of john ' s . how old is betty ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 21 , e ) 32
Rationale: assume betty ' s age on marriage = x years . john ' s age on marriage = 22 john ' s age after 5 years = 27 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 9 ( 27 ) = 21 therefore betty ' s current age = 21 option d
Answer: d
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 60 % profit ?
Options: a ) 1024 , b ) 960 , c ) 277 , d ) 266 , e ) 121
Rationale: let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 160 % of rs . 640 = 160 / 100 * 640 = rs . 1024 . answer : a
Answer: a
Problem: workers at a campaign office have 1000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 800 , c ) 1100 , d ) 600 , e ) 1900
Rationale: "( 1 / 5 ) * 1000 = 200 remaining = 1000 - 200 = 800 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 800 = 200 remaining now = 800 - 200 = 600 answer : option d"
Answer: d
Problem: a cycle is bought for rs . 1000 and sold for rs . 1080 , find the gain percent ?
Options: a ) 11 , b ) 20 , c ) 12 , d ) 40 , e ) 8
Rationale: "1000 - - - - 80 100 - - - - ? = > 8 % answer : e"
Answer: e