regisss/math_qa huggingface dataset:
Problem: two pipes a and b can separately fill a tank in 10 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 450 , b ) 540 , c ) 542 , d ) 829 , e ) 279
Rationale: "1 / 10 + 1 / 15 - 1 / x = 1 / 15 x = 10 10 * 45 = 450 answer : a"
Answer: a
Problem: a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6 . if he makes exactly 97 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 35 , e ) 49
Rationale: "7 c + 6 p = 97 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 7 * 1 + 6 * 15 = 7 + 90 = 97 hence a is the answer"
Answer: a
Problem: a cube of edge 17 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 16.37 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 17 * 17 * 17 cm ^ 3 rise in water level = volume / area = 17 * 17 * 17 / 20 * 15 = 16.37 cm answer is d"
Answer: d
Problem: find the simple interest on rs . 520 for 7 months at 8 paisa per month ?
Options: a ) 277 , b ) 270 , c ) 291 , d ) 266 , e ) 121
Rationale: "i = ( 520 * 7 * 8 ) / 100 = 291 answer : c"
Answer: c
Problem: a person incurs 10 % loss by selling a laptop for $ 900 . at what price should the watch be sold to earn 10 % profit ?
Options: a ) 1200 , b ) 1000 , c ) 1100 , d ) 1050 , e ) 1250
Rationale: "let the new s . p . = x then ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 10 ) / 900 = ( 100 + 10 ) / x x = 110 * 900 / 90 = 1100 new price = $ 1100 correct option is c"
Answer: c
Problem: product of two natural numbers is 11 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 122 / 121 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 11 ( 2 ) = 122 / 121 option b"
Answer: b
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 4.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 20 % , c ) 33 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.045 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 45 f - - > s = 2 f - - > f / s = 1 / 2 - - > f / ( s + f ) = 1 / ( 1 + 2 ) = 1 / 3 = 0.33 . answer : c ."
Answer: c
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 45 marks . how many sums did sandy get correct ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 28
Rationale: let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 45 5 x = 105 x = 21 the answer is b .
Answer: b
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many q hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to q = 1 / 3 ( as the work is completed in q = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Problem: if the average ( arithmetic mean ) of a and b is 160 , and c – a = 200 , what is the average of b and c ?
Options: a ) 260 , b ) 250 , c ) 150 , d ) 225 , e ) 325
Rationale: "a + b / 2 = 160 = > a + b = 320 a = c - 200 . . . sub this value c - 200 + b = 320 = > c + b = 520 = > c + b / 2 = 260 answer : a"
Answer: a
Problem: the sum of all the integers k such that – 24 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 45 , d ) - 49 , e ) - 51
Rationale: "- 23 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 23 - 22 sum of which is - 45 . hence option d . c"
Answer: c
Problem: a student is ranked 21 th from right and 11 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 31 , e ) 22
Rationale: "from right 21 , from left 11 total = 21 + 11 - 1 = 31 answer : d"
Answer: d
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 19 . the larger of the two numbers is :
Options: a ) 437 , b ) 299 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 19 ) . larger number = ( 23 x 19 ) = 437 . answer : option a"
Answer: a
Problem: find the sum of the number of combinations possible by using 12 , 34 such that no number is repeated ( ex : - 12234322 are invalid 12344321 are valid ) more than once .
Options: a ) 66660 , b ) 66760 , c ) 66860 , d ) 66960 , e ) 67660
Rationale: total no . formed = 4 ! = 4 * 3 * 2 * 1 = 24 each digit will be used at each positions , 6 times sum of digits at unit place = 6 * 1 + 6 * 2 + 6 * 3 + 6 * 4 = 6 * ( 1 + 2 + 3 + 4 ) = 60 this sum will be same for hundred , tens & unit places sum of all 4 digit numbers formed using digits 12 , 34 = 1000 * 60 + 100 * 60 + 10 * 60 + 60 = 60 * ( 1000 + 100 + 10 + 1 ) = 60 * 1111 = 66660 answer : a
Answer: a
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 240 , what were her original savings ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 960 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 240 . so 1 / 4 of her savings is $ 240 . so her original savings are 4 times $ 240 = $ 960 correct answer c"
Answer: c
Problem: how many seconds will a 800 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 11 , b ) 30 , c ) 99 , d ) 48 , e ) 61
Rationale: speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 800 * 3 / 50 = 48 sec . answer : d
Answer: d
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 13 % below the cost price of the claimed weight .
Options: a ) 19.63 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 13 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 87 / 100 = ( 1 + p % ) profit % = 19.63 % a"
Answer: a
Problem: if log 64 = 1.8061 , then the value of log 16 will be ( approx ) ?
Options: a ) 1.204 , b ) 1.9874 , c ) 1.3564 , d ) 1.2547 , e ) 1.6547
Rationale: "log 64 = 1.8061 log 4 ^ 3 = 1.8061 log 4 = 0.6020 2 log 4 = 1.2040 log 4 ^ 2 = 1.2040 log 16 = 1.2040 ( approx ) answer a"
Answer: a
Problem: the student manager of the university theater estimated that for every 6 movie tickets sold on valentine ' s weekend , the theater will sell 3 packs of grain crackers at $ 2.25 each , 4 bottles of a beverage at $ 1.50 each , and 4 chocolate bars at $ 1.00 each . find the approximate average ( arithmetic mean ) amount of estimated snack sales per movie ticket sold .
Options: a ) $ 1.40 , b ) $ 1.58 , c ) $ 2.00 , d ) $ 2.64 , e ) $ 2.79
Rationale: 3 * 2.25 + 4 * 1.50 + 4 * 1 = 6.75 + 6 + 4 = 16.75 . this is the sale for 6 tickets avg sale per ticket : 16.75 / 6 = $ 2 . 79 answer : e
Answer: e
Problem: the sum of the ages of 5 children born at the intervals of 4 years each is 50 years . what is the age of the eldest child ?
Options: a ) 15 , b ) 8 , c ) 18 , d ) none of these , e ) can not be determined
Rationale: "explanation : let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 , x + 16 . we know that the sum of their ages is 50 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) + ( x + 16 ) = 50 x = 2 the youngest child is 2 years old . age of eldest child is = 2 + 16 = 18 answer : c"
Answer: c
Problem: a 28 cm long wire is to be cut into two pieces so that one piece will be 2.00001 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 8 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 28 = 8 answer : b"
Answer: b
Problem: eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old as his son . then the sum of the present ages of the son and the father is :
Options: a ) 120 , b ) 76 , c ) 108 , d ) 105 , e ) 86
Rationale: let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) x = 36 . required sum = ( 2 x + x ) = 3 x = 108 years . answer is c
Answer: c
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 828 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1978 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 828 × 100 ) / ( 6 × 12 ) = rs . 1150 bg = bd – td = > 828 = bd - 1150 = > bd = 1978 answer : option d"
Answer: d
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 12 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 12 t 1 = 12 and so t 2 = 24 . the answer is c ."
Answer: c
Problem: the racing magic takes 40 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 40 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 40 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d"
Answer: d
Problem: every day daniel drives 96 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 96 miles at 4 miles / hour . d = ( r ) ( t ) 96 = ( 4 ) ( t ) 96 / 4 = 24 = t it takes 24 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 64 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 64 = ( 2 ) ( t ) 64 / 2 = 32 = t it takes 32 hours for the second part total time to drive home on monday = 4 + 32 = 36 hours we ' re asked by what percent 36 hours is greater than 32 hours . 36 / 32 = 1.5 , so it is 50 % greater . e"
Answer: e
Problem: a train running at the speed of 108 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 140 meter , d ) 135 meter , e ) 210 meter
Rationale: "explanation : speed = 108 * ( 5 / 18 ) m / sec = 30 m / sec length of train ( distance ) = speed * time = 30 * 7 = 210 meter option e"
Answer: e
Problem: a train crosses a bridge of length 2500 m in 120 seconds and a lamp post on the bridge in 30 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 / 3 m , c ) 2500 / 3 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 2500 + l ( while crossing the bridge ) time = 120 seconds i . e . speed = distance / time = ( 2500 + l ) / 120 case - 2 : distance = l ( while passing the lamp post ) time = 30 seconds i . e . speed = distance / time = ( l ) / 30 but since speed has to be same in both cases so ( 2500 + l ) / 120 = ( l ) / 30 i . e . 4 l = 2500 + l i . e . 3 l = 2500 i . e . l = 2500 / 3 answer : option c"
Answer: c
Problem: find the sum of all odd number upto 250 .
Options: a ) 15345 , b ) 15645 , c ) 15625 , d ) 15342 , e ) 15683
Rationale: "explanation : number of odd numbers upto 250 = n / 2 = 250 / 2 = 125 sum of first 125 odd numbers = ( 125 ) 2 = 15625 answer : option c"
Answer: c
Problem: a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 2 cm x 7 cm x 3 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 8000000 , b ) 1000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 2 * 7 * 3 = 8000000 answer : a
Answer: a
Problem: x can finish a work in 18 days . y can finish the same work in 15 days . yworked for 5 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 12 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: work done by x in 1 day = 1 / 18 work done by y in 1 day = 1 / 15 work done by y in 5 days = 5 / 15 = 1 / 3 remaining work = 1 – 1 / 3 = 2 / 3 number of days in which x can finish the remaining work = ( 2 / 3 ) / ( 1 / 18 ) = 12 a
Answer: a
Problem: the diameter of the wheel of a car is 120 m . how many revolution / min mustthe wheel makeing order to keep a speed of 60 km / hour approximately ?
Options: a ) 140 , b ) 160 , c ) 220 , d ) 250 , e ) 265
Rationale: "distance to be covered in 1 min . = ( 60 x 1000 ) / ( 60 ) m = 1000 m . circumference of the wheel = ( 2 x ( 22 / 7 ) x 0.60 ) m = 3.77 m . number of revolutions per min . = ( 1000 / 3.77 ) = 265 e"
Answer: e
Problem: a and b together can do a work in 5 days . if a alone can do it in 15 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 7.5 , d ) 55 , e ) 21
Rationale: "1 / 5 – 1 / 15 = 2 / 15 = > 7.5 answer : c"
Answer: c
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666
Rationale: "p = ncm * p ^ m * q ^ ( n - m ) n - the total number of trials . m - the number of trials with heads . n - m - the number of trials with tails . p - probability of heads . q - probability of tails . p = 3 c 2 * ( 1 / 2 ) ^ 2 * ( 1 / 2 ) ^ 1 = 3 / 8 = 0.375 answer : c"
Answer: c
Problem: the length of the bridge , which a train 110 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 240 , c ) 245 , d ) 250 , e ) 265
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 110 + x ) / 30 = 25 / 2 = > 2 ( 110 + x ) = 750 = > x = 265 m . answer : option e"
Answer: e
Problem: one hour after yolanda started walking from x to y , a distance of 40 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 2 miles per hour and bob â s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23.5 , c ) 22 , d ) 21.2 , e ) 25.32
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 2 ( t + 1 ) miles . these distances must sum to 40 miles , so 4 t + 2 ( t + 1 ) = 40 , which may be solved for t as follows 4 t + 2 ( t + 1 ) = 40 4 t + 2 t + 2 = 40 6 t = 38 t = 6.33 ( hours ) therefore , bob had walked 4 t = 4 ( 7.6 ) = 25.32 miles when they met . the best answer is e ."
Answer: e
Problem: 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 59 answer : d"
Answer: d
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 4 years ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 180 * 4 * r ) / 100 r = 5 % answer : a"
Answer: a
Problem: a and b can do a piece of work in 4 2 / 3 days and 5 days respectively . they work together for 1 days and then a leaves . in how many days after that b will complete the work alone .
Options: a ) 3.92 days , b ) 1.92 days , c ) 2.12 days , d ) 2.02 days , e ) 2.92 days
Rationale: 3 / 14 * 1 + ( 1 + x ) / 5 = 1 x = 2.92 days answer : e
Answer: e
Problem: a semicircle is drawn with ab as its diameter . from c , a point on ab , a line perpendicular to ab is drawn , meeting the circumference of the semicircle at d . given that ac = 2 cm and cd = 6 cm , the area of the semicircle in square cm will be ?
Options: a ) 30 pi
b ) 40 pi
c ) 50 pi
d ) 60 pi
e ) 70 pi
Rationale: let o be center of circle and radius be x . c can be anywhere on ab . let us suppose that c is somewhere between a and o . ac = 2 cm . . . . so co = ( x - 2 ) do = x , cd = 6 cm cdo form a right angled triangle with right angle at c . using pythagoras theorem , x ^ 2 = 6 ^ 2 + ( x - 2 ) ^ 2 4 x = 40 x = 10 cm area = [ pi ( x ) ^ 2 ] / 2 area = 50 pi answer : c
Answer: c
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 24 hours and 8 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 1 : 3 , d ) 4 : 8 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 8 : 24 = 1 : 3 . answer : c
Answer: c
Problem: length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m , b ) 60 m , c ) 65 m , d ) 75 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b"
Answer: b
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 17.1 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 17.1 s distance covered , d = vt = ( 400 / 36 ) ã — 17.1 = 190 m distance covered is equal to the length of the train = 190 m correct answer is 190 metres a"
Answer: a
Problem: of the 160 people at a party , 70 were women , and 50 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "total people at party = 160 women = 70 so men 160 - 70 = 90 no . of pple who tried appetizer = 160 - 50 ( given info ) = 110 no of women who tried appetizer = 50 so remaining ppl ( men ) who tried the appetizer = 110 - 50 = 60 correct option c"
Answer: c
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 20 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 285 m , d ) 299 m , e ) 219 m
Rationale: "speed = 300 / 20 = 15 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 15 = > x = 285 m . answer : c"
Answer: c
Problem: a box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 78 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 42 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 42 / 7 * 14 / 7 = 84 ans c ."
Answer: c
Problem: the height of cylinder is 14 cm and its diameter is 10 cm . the volume of the cylinder is :
Options: a ) 4400
b ) 2200
c ) 5500
d ) 1100
e ) 3300
Rationale: h = 14 cm and r = 5 cm cylinder volume = π r ( power 2 ) h = ( 22 / 7 × 5 × 5 × 14 ) cm ( power 3 ) = 1100 cm ( power 3 ) answer is d .
Answer: d
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 20 % chemical x and 80 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 30 % , b ) 33 % , c ) 36 % , d ) 39 % , e ) 42 %
Rationale: "the amount of chemical x in the solution is 20 + 0.2 ( 80 ) = 36 liters . 36 liters / 100 liters = 36 % the answer is c ."
Answer: c
Problem: working together , jose and jane can complete an assigned task in 20 days . however , if jose worked alone and completed half the work and then jane takes over and completes the second half , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose .
Options: a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "explanatory answer step 1 : assign variables and frame equations let jose take ' x ' days to complete the task if he worked alone . let jane take ' y ' days to complete the task if she worked alone . statement 1 of the question : they will complete the task in 20 days , if they worked together . in 1 day , jose will complete 1 / x of the task . in 1 day , jane will complete 1 / yof the task . together , in 1 day they will complete 1 / 20 of the task . therefore , 1 / x + 1 / y = 1 / 20 . . . . ( 1 ) statement 2 of the question : if jose worked alone and completed half the work and then jane takes over and completes the second half , the task will be completed in 45 days . jose will complete half the task in x / 2 days . jane will complete half the task in y / 2 days . ∴ x / 2 + y / 2 = 45 or , x + y = 90 or x = 90 - y . . . . ( 2 ) step 2 : solve the two equations and find x and y substitute the value of x as ( 90 - y ) in the first equation 1 / 90 − y + 1 / y = 1 / 20 or y 2 - 90 + 1800 = 0 . the quadratic equation factorizes as ( y - 60 ) ( y - 30 ) = 0 so , y = 60 or y = 30 . if y = 60 , then x = 90 - y = 90 - 60 = 30 and if y = 30 , then x = 90 - y = 90 - 30 = 60 . the question clearly states that jane is more efficient than jose . therefore , jane will take lesser time than jose . hence , jose will take 60 days to complete the task if he worked alone and jane will take 30 days to complete the same task . choice c"
Answer: c
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 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 4 candidates are there to fill the 4 positions ?
Options: a ) 420 , b ) 770 , c ) 840 , d ) 165 , e ) 315
Rationale: "1 of 7 will be chosen for the math 3 of 10 will be chosen for the computer none of the 4 chosen people can be in more than one departments . we can choose any of the 7 candidates for the math dep . , which gives as 7 selections . we can choose 3 of the 10 candidates for the computer dep . , which gives us 3 selections and 7 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 3 ! * 7 ! = 120 we are multiplying our individual selections : 7 * 120 = 840 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans c"
Answer: c
Problem: the volume of a cube is 343 cc . find its surface .
Options: a ) 864 , b ) 556 , c ) 294 , d ) 287 , e ) 267
Rationale: "a 3 = 343 = > a = 7 6 a 2 = 6 * 7 * 7 = 294 answer : c"
Answer: c
Problem: a boeing 757 flies a direct route from dallas , tx , to phoenix , az and then returns to dallas , tx . the flight is 900 miles one way . it took 2 hrs and 15 minutes for the flight to phoenix and 2 hrs for the flight back to dallas . what was the speed of the wind in mph ?
Options: a ) 20 mph , b ) 25 mph , c ) 30 mph , d ) 35 mph , e ) 40 mph
Rationale: explanation : change the times in the problem to minutes first . speed of airplane from dallas to phoenix : ( 900 / 135 ) x 60 = 400 mph speed of airplane from phoenix to dallas : ( 900 / 120 ) x 60 = 450 mph wind speed : 1 / 2 ( 450 - 400 ) = 50 / 2 = 25 mph answer : option b
Answer: b
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 5 meters and a circumference of 4 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 10 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: for a , r = 4 / 2 pi . its capacity = ( 2 pi ) ^ 2 * 5 = 20 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 20 pi / 200 pi = 0.1 a
Answer: a
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 180 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 90
Rationale: let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 180 + p c + m = 180 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 180 / 2 = 90 . answer : e
Answer: e
Problem: rahim bought 27 books for rs . 581 from one shop and 20 books for rs . 594 from another . what is the average price he paid per book ?
Options: a ) 28 , b ) 18 , c ) 27 , d ) 25 , e ) 21
Rationale: "average price per book = ( 581 + 594 ) / ( 27 + 20 ) = 1175 / 47 = rs . 25 answer : d"
Answer: d
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 24000 . a ' s share is ?
Options: a ) 2999 , b ) 8000 , c ) 6000 , d ) 2889 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 24000 = 8000 answer : b"
Answer: b
Problem: the ratio of flour to water to sugar in a recipe is 10 : 6 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the ratio of flour to water is 10 : 3 . the ratio of flour to sugar is 5 : 3 = 10 : 6 . the new ratio of flour to water to sugar is 10 : 3 : 6 if we need 2 cups of water , then we need 4 cups of sugar . the answer is b ."
Answer: b
Problem: an artist wishes to paint a circular region on a square poster that is 4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 8 / pi ) , c ) 1 , d ) 2 / sqrt ( pi ) , e ) pi / 2
Rationale: "area of the poster is 4 x 4 = 16 1 / 2 the area = 8 pi * r ^ 2 = 8 r ^ 2 = 8 / pi r = sqrt ( 8 / pi ) answer : c"
Answer: c
Problem: the smallest number which when diminished by 4 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1012 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 4 = 1008 + 4 = 1012 answer : b"
Answer: b
Problem: two numbers are in the ratio 3 : 5 . if 9 is subtracted from each , the new numbers are in the ratio 12 : 23 . the smaller number is :
Options: a ) 15 , b ) 33 , c ) 58 , d ) 56 , e ) 91
Rationale: "let the numbers be 3 x and 5 x . then , ( 3 x - 9 ) / ( 5 x - 9 ) = 12 / 23 9 x = 99 = > x = 11 the smallest number = 3 * 11 = 33 . answerb"
Answer: b
Problem: two cars , car 1 and car 2 move towards each other from q and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach q starting from y ?
Options: a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec
Rationale: q - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance qy = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d
Answer: d
Problem: in a division sum , the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :
Options: a ) 200 , b ) 251 , c ) 250 , d ) 262 , e ) 254
Rationale: "diver = ( 8 * 3 ) + 3 = 27 3 * quotient = 27 quotient = 9 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 9 ) + 8 = 251 b"
Answer: b
Problem: the area of a sector of a circle of radius 5 cm formed by an arc of length 4.5 cm is ?
Options: a ) 8.78 , b ) 11.25 , c ) 8.75 , d ) 8.98 , e ) 8.28
Rationale: "( 5 * 4.5 ) / 2 = 11.25 answer : b"
Answer: b
Problem: if x = - 5 and y = 8 , what is the value of 2 ( x - y ) ^ 2 - xy ?
Options: a ) 358 , b ) 348 , c ) 368 , d ) 388 , e ) 378
Rationale: x = - 5 and y = 8 x - y = - 5 - 8 = - 13 x * y = - 5 * 8 = - 40 now we apply it in the equation 2 ( x - y ) ^ 2 - xy = 2 ( - 13 ) ^ 2 - ( - 40 ) = = > 2 * 169 + 40 = 338 + 40 = 378 answer : e
Answer: e
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 6 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 6 , b ) - 1 , c ) 0 , d ) 1 , e ) 6
Rationale: when x = 1 and when x = - 6 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 6 ) f ( 0 ) = - 6 the answer is a .
Answer: a
Problem: kim has 7 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 14 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 11 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "can be tackled in this way as well : probability of selecting any 1 out of 14 shoes = 14 / 14 = 1 probability of selecting the next shoe ( out of 14 available ) having the same color = 1 / 14 ( as after selecting the 1 st one , there is only 1 another shoe left with the same color ) . thus the total probability = 1 * 1 / 13 = 1 / 13 . a is the correct answer ."
Answer: a
Problem: find the distance covered by a man walking for 36 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 6 km , d ) 5 km , e ) 6 km
Rationale: distance = 10 * 36 / 60 = 6 km answer is c
Answer: c
Problem: a can finish a piece of work in 5 days . b can do it in 10 days . they work together for 1 day and then a goes away . in how many days will b finish the work ?
Options: a ) 8 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 9 days
Rationale: "1 / 5 + ( 1 + x ) / 10 = 1 = > x = 7 days answer : d"
Answer: d
Problem: in an xy - coordinate plane , a line is defined by y = kx + 1 . if ( 4 , b ) , ( a , 5 ) , and ( a , b + 1 ) are 3 points on the line , where a and b are unknown , then k = ?
Options: a ) 1 / 2 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 5 / 2
Rationale: b = 4 k + 1 . . . ( 1 ) b + 1 = ak + 1 . . . ( 2 ) 5 = ak + 1 . . . ( 3 ) taking ( 2 ) and ( 3 ) 5 = b + 1 b = 4 taking ( 1 ) 4 = 4 k + 1 k = 3 / 4 answer : c
Answer: c
Problem: david has $ 1,500 at the beginning of his trip , after spending money , he still has exactly $ 500 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 500 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 500 x + x - 500 = 1500 x = 1000 money not spend = 1000 - 500 = 500 answer : c"
Answer: c
Problem: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 18 more than the correct answer . find the number .
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 18 25 x = 16 x + 360 9 x = 360 x = 40 the answer is c ."
Answer: c
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 3 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 5 / 3 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 25 : 15 : 2 i . e . u : b = 25 : 2 answer : option e"
Answer: e
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 5 percent , but profits were 10 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 95 %
Rationale: "the profit 0 f 2009 interms of 2008 = 0.95 * 10 / 10 * 100 = 95 % e"
Answer: e
Problem: a house wife saved $ 3.50 in buying an item on sale . if she spent $ 32.50 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 32.50 + 3.50 = $ 36 saving = 3.50 / 36 * 100 = 10 % approximately answer is c"
Answer: c
Problem: a garrison of 1000 men has provisions for 60 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1000 , b ) 2250 , c ) 60 , d ) 45 , e ) 1250
Rationale: "1000 - - - - 60 1000 - - - - 45 x - - - - - 20 x * 20 = 1000 * 45 x = 2250 1000 - - - - - - - 1250 answer : e"
Answer: e
Problem: on an order of 99 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 0.1 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %
Rationale: "clearly , the retailer gets 1 dozen out of 100 dozens free . equivalent discount = 1 / 100 * 100 = 1 % . answer c ) 1 %"
Answer: c
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 35 , find the value of ab .
Options: a ) 12 , b ) 13 , c ) 10 , d ) 18 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 35 - 9 = 26 ab = 13 . answer is b ."
Answer: b
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 320 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 640 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 320 ) = 2 + 2 ( extra ) = > 2 x - 640 = x = > x = 640 . answer : b"
Answer: b
Problem: 45 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 17 , b ) 97 , c ) 18 , d ) 55 , e ) 72
Rationale: "( 45 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 100 100 – 45 = 55 answer : d"
Answer: d
Problem: one hour before john started walking from p to q , a distance of 38 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 19 miles , d ) 19,6 miles , e ) 24 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 38 - 3 = 35 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 35 miles so it will take them 35 / 5 = 7 hours to meet . in 7 hrs , ann would have covered 7 hrs * 3 miles per hour = 21 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 21 = 24 miles . answer ( e )"
Answer: e
Problem: simplify 586645 * 9999
Options: a ) 5865863355 , b ) 5665863355 , c ) 4865863355 , d ) 4665863355 , e ) none of these
Rationale: explanation : although it is a simple question , but the trick is to save time in solving this . rather than multiplying it we can do as follows : 586645 * ( 10000 - 1 ) = 5866450000 - 586645 = 5865863355 option a
Answer: a
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is :
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 = 189 or x = 1575 . ∴ p . w . = rs . 1575 . ∴ sum due = p . w . + t . d . = rs . ( 1575 + 189 ) = rs . 1764 . answer b"
Answer: b
Problem: if the price of petrol increases by 30 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 23 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 30 ) i . e 130 . now , his consumption should be reduced to : - = ( 130 − 100 ) / 130 ∗ 100 . hence , the consumption should be reduced to 23 % . answer : b"
Answer: b
Problem: pipe a that can fill a tank in two hour and pipe b that can fill the tank in an hour are opened simultaneously when the tank is empty . pipe b is shut 30 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 36 mins , b ) 35 mins , c ) 40 mins , d ) 32 mins , e ) 30 mins
Rationale: the last 30 minutes only pipe a was open . since it needs 2 hour to fill the tank , then in 30 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : e
Answer: e
Problem: two family reunions are happening at the taj hotel , the oates reunion and the hall reunion . all 150 guests at the hotel attend at least one of the reunions . if 70 people attend the oates reunion and 52 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 28
Rationale: no of people in oates reunion = 70 no of people in hall reunion = 52 attending both = x all guests attend at least one . therefore , 150 = 70 + 52 - ( both ) both = 28 answer e
Answer: e
Problem: you buy a piece of land with an area of â ˆ š 1024 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 1024 . answer e"
Answer: e
Problem: divide rs . 720 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 180 , e ) s . 900
Rationale: "a + b + c = 720 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 720 = > 180 answer : d"
Answer: d
Problem: the least common multiple of positive integer e and 3 - digit integer n is 690 . if n is not divisible by 3 and e is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and e is 690 = 2 * 3 * 5 * 23 . e is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to e . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Problem: half a number plus 5 is 15 . what is the number ?
Options: a ) 8 , b ) 20 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 15 ( 1 / 2 ) x = 15 - 5 ( 1 / 2 ) x = 10 x = 20 correct answer is b"
Answer: b
Problem: a car takes 6 hours to cover a distance of 630 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 70 kmph
Rationale: "time = 6 distence = 630 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 630 / 9 = 70 kmph e"
Answer: e
Problem: population of a city in 20004 was 1100000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2384525 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2384525 / 2 e"
Answer: e
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 750 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 15 minutes = 15 / 18 * 15 * 60 = 750 m answer is d"
Answer: d
Problem: a room 4 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 38636 , b ) 38640 , c ) 38647 , d ) 38591 , e ) 38675
Rationale: "explanation : area of the room = ( 447 x 777 ) cm 2 . size of largest square tile = h . c . f . of 447 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 447 × 777 ) / ( 3 × 3 ) = 38591 answer : option d"
Answer: d
Problem: the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 13 % ?
Options: a ) 31.5 % , b ) 35.9 % , c ) 37.5 % , d ) 39.5 % , e ) 30.5 %
Rationale: "let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 87 gain % = 23 / 64 * 100 = 35.9 % . b"
Answer: b
Problem: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length r of a cube whose surface area is equal to 6 z ?
Options: a ) r = 16 , b ) r = 8 √ 2 , c ) r = 8 , d ) r = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Problem: a candidate got 25 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 8000
Rationale: "25 % - - - - - - - - - - - l 75 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 50 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 8000 answer : e"
Answer: e
Problem: 8 , 24 , 12 , 36 , 18 , 54 , ( . . . . )
Options: a ) 27 , b ) 68 , c ) 107 , d ) 108 , e ) 28
Rationale: "8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 answer is a"
Answer: a
Problem: 39 ! is divided by 41 . then what is the remainder for this ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a
Answer: a
Problem: the ratio 5 : 20 expressed as percent equals to
Options: a ) 50 % , b ) 125 % , c ) 25 % , d ) none of above , e ) 30 %
Rationale: "explanation : actually it means 5 is what percent of 20 , which can be calculated as , ( 5 / 20 ) * 100 = 5 * 5 = 25 option c"
Answer: c
Problem: a sum of money becomes 7 / 6 of itself in 2 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 9 , b ) 50 / 7 , c ) 50 / 6 , d ) 50 / 8 , e ) 50 / 3
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 2 years . rate = ( 100 * x ) / ( x * 6 * 2 ) = 50 / 6 % . answer : c"
Answer: c
Problem: a train travels 325 km in 3.5 hours and 470 km in 4 hours . find the average speed of train ?
Options: a ) 116 kmph , b ) 106 kmph , c ) 186 kmph , d ) 126 kmph , e ) 176 kmph
Rationale: explanation : as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 325 + 470 = 795 km thus , total speed = 7.5 hrs average speed = 795 / 7.5 = > 106 kmph . answer : b
Answer: b
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a sixth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "in one hour , the crow eats 1 / 48 of the nuts . ( 1 / 4 ) / ( 1 / 48 ) = 12 hours the answer is b ."
Answer: b
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7560 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 960 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7560 / 18 + 7560 / 14 = 420 + 540 = 960 hours answer : option e"
Answer: e