regisss/math_qa huggingface dataset:
Problem: a company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters . if the price of a box did not change and all boxes are full of juice , by approximately what percent did the price of the juice decrease ?
Options: a ) 12.00 % , b ) 16.67 % , c ) 18.33 % , d ) 20.00 % , e ) 21.50 %
Rationale: suppose when v = 5 x 10 x 20 = 1000 cm , the price is $ 1200 per cm price = $ 1.2 the price is $ 1200 if v = 6 x 10 x 20 = 1000 cm . per cm price = $ 1.0 so the price is decreased by $ 0.2 so the % price decreased by $ 0.2 / 1.20 = 16.67 % answer : b
Answer: b
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 19,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 950 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 19,000 * 5 % = 950 . thus , d is the answer ."
Answer: d
Problem: a man can row 4.2 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.4 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 4.2 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.4 km / hr . answer : c"
Answer: c
Problem: divide rs . 116000 among 3 persons a , b and c such that the ratio of the shares of a and b is 3 : 4 and that of b : c is 5 : 6 . find the share of a ?
Options: a ) 29491 , b ) 28491 , c ) 39491 , d ) 49491 , e ) 59491
Rationale: compound ratio of a : b : c a : b = 3 : 4 b : c = 5 : 6 - - - - - - - - - - a : b : c = 15 : 20 : 24 we can divide rs . 116000 in this ratio . share of a = 15 / 59 * 116000 = 29491 answer : a
Answer: a
Problem: the diagonal of a rhombus are 40 m and 30 m . its area is :
Options: a ) 600
b ) 450
c ) 350
d ) 500
e ) 620
Rationale: area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 40 ã — 30 ) cm ( power ) 2 = 40 ã — 15 = 600 cm ( power ) 2 answer is a .
Answer: a
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 40 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 7 / 10 , e ) 11 / 15
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.4 * 300 / 450 = 120 / 450 = 4 / 15 the sum of the probabilities is 9 / 15 = 3 / 5 the answer is c ."
Answer: c
Problem: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 20 ducks and in the larger pond there are 80 ducks . if 20 % of the ducks in the smaller pond are green and 15 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "number of ducks in small pond = 20 green ducks in small pond = 20 % of 20 = 4 ducks number of ducks in large pond = 80 green ducks in large pond = 15 % of 80 = 12 ducks total number of ducks = 20 + 80 = 100 total number of green ducks = 4 + 12 = 16 ducks percentage of green ducks = 16 / 100 * 100 = 16 % answer : d"
Answer: d
Problem: the current of a stream runs at the rate of 5 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7.63 , b ) b ) 2.6 , c ) c ) 8.83 , d ) d ) 6.69 , e ) e ) 3
Rationale: "s = 5 m = x ds = x + 5 us = x - 5 6 / ( x + 5 ) + 6 / ( x - 5 ) = 2 x = 8.83 answer : c"
Answer: c
Problem: if two projectiles are launched at the same moment from 1386 km apart and travel directly towards each other at 445 km per hour and 545 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "the projectiles travel a total of 990 km per hour . the time to meet is 1386 / 990 = 1.4 hours = 84 minutes the answer is c ."
Answer: c
Problem: find the average of all the numbers between 11 and 21 which are divisible by 2 .
Options: a ) 15 , b ) 18 , c ) 16 , d ) 22 , e ) none
Rationale: "sol . average = ( 12 + 14 + 16 + 18 + 20 / 5 ) = 80 / 5 = 16 . answer c"
Answer: c
Problem: a train speeds past a pole in 15 sec and a platform 140 m long in 25 sec , its length is ?
Options: a ) 238 , b ) 150 , c ) 988 , d ) 210 , e ) 171
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 140 ) / 25 = x / 15 = > x = 210 m . answer : d"
Answer: d
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) rs . 25000 , b ) rs . 20000 , c ) rs . 15000 , d ) rs . 22000 , e ) none of these
Rationale: let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 400 = > x = 20000 answer : b
Answer: b
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 12 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 21 / 26 , b ) 25 / 26 , c ) 11 / 26 , d ) 6 / 26 , e ) 22 / 33
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 12 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 12 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 12 * 2 b * b 3 b - 2 b ^ 2 = 24 b ^ 2 3 b = 26 b ^ 2 b = 3 / 26 = 3 / 26 so , a = 2 b = 6 / 26 the correct answer is d ."
Answer: d
Problem: a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 212 , b ) 200 , c ) 220 , d ) 230 , e ) 240
Rationale: "let no of sits in vip enclosure is x then x * 40 + 15 ( 320 - x ) = 7500 or 25 x = 7500 - 4800 , x = 2700 / 25 = 108 vip = 108 general 212 a"
Answer: a
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money r did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ r = 20 answer : b"
Answer: b
Problem: a ’ s speed is 20 / 12 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 6 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 12 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 8 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 8 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 12 meters ) to reach the finish line . so b should get a head start of 8 / 20 th of the race . answer ( d )"
Answer: d
Problem: a train speeds past a pole in 15 seconds and a platform 130 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 175 , b ) 185 , c ) 195 , d ) 205 , e ) 215
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 130 = 25 * ( x / 15 ) 10 x = 1950 x = 195 meters the answer is c ."
Answer: c
Problem: calculate the time it will take for a full tank to become completely empty due to a leak given that the tank could be filled in 7 hours , but due to the leak in its bottom it takes 8 hours to be filled ?
Options: a ) 59 hours , b ) 54 hours , c ) 59 hours , d ) 56 hours , e ) 26 hours
Rationale: part filled without leak in 1 hour = 1 / 7 part filled with leak in 1 hour = 1 / 8 work done by leak in 1 hour = 1 / 7 â ˆ ’ 1 / 8 = 56 hours answer : d
Answer: d
Problem: a is 2 times as fast as b . a alone can do the work in 20 days . if a and b working together in how many days will the work be completed ?
Options: a ) 23 , b ) 13 , c ) 21 , d ) 24 , e ) 25
Rationale: "a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days so answer is b"
Answer: b
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.2 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 3 / 8 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.2 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 24 hours . total hours = 64 . then the fraction would be 24 / 64 = 3 / 8 . therefore answer a ."
Answer: a
Problem: a train leaves mumabai at 9 am at a speed of 30 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 60 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 27 , b ) 279 , c ) 60 , d ) 278 , e ) 379
Rationale: when the second train leaves mumbai the first train covers 30 * 1 = 30 km so , the distance between first train and second train is 30 km at 10.00 am time taken by the trains to meet = distance / relative speed = 30 / ( 60 - 30 ) = 1 hours so , the two trains meet at 11 a . m . the two trains meet 1 * 60 = 60 km away from mumbai . answer : c
Answer: c
Problem: a = 4 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 2 different values and answer is c . . . ."
Answer: c
Problem: a envelop weight 8.5 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: "800 * 8.5 6800.0 gm 6.8 kg answer : b"
Answer: b
Problem: in a city , 35 % of the population is composed of migrants , 20 % of whom are from rural areas . of the local population , 48 % is female while this figure for rural and urban migrants is 30 % and 40 % respectively . if the total population of the city is 728400 , what is its female population ?
Options: a ) 324138 , b ) 248888 , c ) 378908 , d ) 277880 , e ) 379010
Rationale: explanation : total population = 728400 migrants = 35 % of 728400 = 254940 local population = ( 728400 - 254940 ) = 473460 . rural migrants = 20 % of 254940 = 50988 urban migrants = ( 254940 - 50988 ) = 203952 female population = 48 % of 473460 + 30 % of 50988 + 40 % of 203952 = 324138 answer : a
Answer: a
Problem: a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets ?
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 68 % , e ) 70 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b"
Answer: b
Problem: 397 x 397 + 104 x 104 + 2 x 400 x 104 = x ?
Options: a ) 234341 , b ) 235633 , c ) 234677 , d ) 315656 , e ) 251501
Rationale: "given exp . = ( 397 ) 2 + ( 104 ) 2 + 2 x 397 x 104 = ( 397 + 104 ) 2 = ( 501 ) 2 = ( 500 + 1 ) 2 = ( 5002 ) + ( 1 ) 2 + ( 3 x 500 x 1 ) = 250000 + 1 + 1500 = 251501 e"
Answer: e
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 3 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 44 / 7 , b ) 9 / 8 , c ) 25 / 8 , d ) 3 / 4 , e ) 7 / 8
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 3 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 3 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 3 * 2 b * b 3 b - 2 b ^ 2 = 6 b ^ 2 3 b = 8 b ^ 2 b = 3 / 8 = 3 / 8 so , a = 2 b = 3 / 4 the correct answer is d ."
Answer: d
Problem: john goes to his office by car at a speed of 40 kmph and reaches 8 minutes earlier . if he goes at a speed of 30 kmph , he reaches 4 mins late . what is the distance from his house to office ?
Options: a ) 18 km , b ) 20 km , c ) 22 km , d ) 24 km , e ) 30 km
Rationale: let his office time be 10 a . m . he reaches office at 8 minutes earlier when he travels at 40 kmph = > he reaches at 9 : 52 a . m he reaches his office 4 minutes late when travels at 30 kmph speed = > he reaches at 10.04 a . m the time difference is ( 10.04 – 9.52 ) = 12 minutes let the distance be d and time = distance speed t 1 – t 2 = 12 minutes = 12 / 60 hours = 1 / 5 hours d / 30 – d / 40 = 1 / 5 ( 4 d - 3 d ) / 120 = 1 / 5 d = 24 km
Answer: d
Problem: a certain list consists of 11 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 10 numbers in the list , then n is what fraction of the sum of the 11 numbers in the list ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 3 / 5 , e ) 1 / 6
Rationale: "series : a 1 , a 2 . . . . a 10 , n sum of a 1 + a 2 + . . . + a 10 = 10 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 10 + n = 15 x so , the fraction asked = 5 x / 15 x = 1 / 3 answer is a"
Answer: a
Problem: compound interest of rs . 4000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 630 , e ) none of the above
Rationale: 10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 4000 [ 1 + ( 5 / 100 ) ] ^ 3 - 4000 = 4000 [ ( 21 / 20 ) ^ 3 - 1 ] = 4000 ( 9261 - 8000 ) / 8000 = 4 * 1261 / 8 = 630 answer : d
Answer: d
Problem: find the length of the longest pole that can be placed in an indoor stadium 24 m long , 18 m wide and 16 m high
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "sqrt ( 1156 ) = 34 becoz max length is cuboid diagonal d = sqrt ( l ^ 2 + b ^ 2 + h ^ 2 ) where l lenght b breadth & h height answer : d"
Answer: d
Problem: one hour before john started walking from p to q , a distance of 13 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 ) 9 miles , d ) 9,6 miles , e ) 12 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 13 - 3 = 10 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 10 miles so it will take them 10 / 5 = 2 hours to meet . in 2 hrs , ann would have covered 2 hrs * 3 miles per hour = 6 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 6 = 9 miles . answer ( c )"
Answer: c
Problem: sheela deposits rs . 3800 in bank savings account . if this is 22 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 25123 , d ) 17272 , e ) none of these
Rationale: "explanation : 22 % of income = rs . 3800 100 % of income = 3800 x 100 / 22 = rs . 17272 answer : d"
Answer: d
Problem: one pipe can fill a pool 1.5 times faster than a second pipe . when both pipes are opened , they fill the pool in four hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 9 , e ) 10
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.5 r = 3 r / 2 . since when both pipes are opened , they fill the pool in four hours , then their combined rate is 1 / 4 pool / hour . thus we have that r + 3 r / 2 = 1 / 4 - - > r = 1 / 10 pool / hour - - > time is reciprocal of rate thus it ' s 10 / 1 = 10 hours . answer : e ."
Answer: e
Problem: 3 photographers , lisa , mike and norm , take photos of a wedding . the total of lisa and mikes photos is 60 less than the sum of mike ' s and norms . if norms photos number 10 more than twice the number of lisa ' s photos , then how many photos did norm take ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 110 , e ) 80
Rationale: l + m = m + n - 60 / n = 2 l + 10 60 = m + n - l - m 60 = n - l 60 = 2 l + 10 - l 50 = l 2 ( 50 ) + 10 = 110 d
Answer: d
Problem: the area of a rectangle is 360 sq . m . if its length is increased by 10 m and its width is decreased by 6 m , then its area does not change . find the perimeter of the original rectangle .
Options: a ) 74 m
b ) 75 m
c ) 76 m
d ) 77 m
e ) 78 m
Rationale: let l and b are the length and width of the original rectangle . since , l * b = 360 sq . m - ( 1 ) now , a / c to the problem ( l + 10 ) * ( b - 6 ) = 360 sq . m therefore , b = 6 ( 1 + l / 10 ) - ( 2 ) l * l + 10 l - 600 = 0 { by using equations 1 and 2 } thereafter , ( l - 20 ) ( l + 30 ) = 0 hence , l = 20 m b = 18 m { by using equation 2 } now , perimeter of the original rectangle = 2 ( l + b ) = 2 ( 20 + 18 ) = 76 m answer : c
Answer: c
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 39 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 39 / 3 = 13 kmph answer : b"
Answer: b
Problem: in measuring the sides of a rectangle , one side is taken 7 % in excess , and the other 6 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.58 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 61 / 57 ) x ( 47 / 50 ) y = ( 867 / 862 ) ( xy ) error in measurement = ( 867 / 862 ) xy - xy = ( 5 / 862 ) xy error percentage = [ ( 5 / 862 ) xy ( 1 / xy ) 100 ] % = ( 29 / 50 ) % = 0.58 % . answer is e ."
Answer: e
Problem: how many squares are there between 2011 to 2300 ? ? ? ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: nos . are 2025 , 2116 , 2209 answers is 3 answer : a
Answer: a
Problem: the average age of a group of 10 students is 14 years . if 5 more students join the group , the average age rises by 1 year . the average age of the new students is :
Options: a ) 22 , b ) 38 , c ) 11 , d ) 17 , e ) 91
Rationale: explanation : total age of the 10 students = 10 × 14 = 140 total age of 15 students including the newly joined 5 students = 15 × 15 = 225 total age of the new students = 225 − 140 = 85 average age = 85 / 5 = 17 years answer : d
Answer: d
Problem: average expenditure of a person for the first 3 days of a week is rs . 310 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 310 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 310 + rs . 40 = rs . 350 correct option : a"
Answer: a
Problem: if the perimeter of a rectangular garden is 800 m , its length when its breadth is 100 m is ?
Options: a ) 286 m , b ) 899 m , c ) 300 m , d ) 166 m , e ) 187 m
Rationale: "2 ( l + 100 ) = 800 = > l = 300 m answer : c"
Answer: c
Problem: two equal sums of money were invested , one at 4 % and the other at 4.5 % . at the end of 7 years , the simple interest received from the latter exceeded to that received from the former by 31.50 . each sum was :
Options: a ) 1200 , b ) 600 , c ) 750 , d ) 900 , e ) none of these
Rationale: difference of s . i . = √ 31.50 let each sum be x . then x × 4 1 / 2 × 7 / 100 − x × 4 × 7 / 100 = 31.50 or 7 ⁄ 100 x × 1 ⁄ 2 = 63 ⁄ 2 or x = 900 answer d
Answer: d
Problem: shekar scored 76 , 65 , 82 , 67 and 75 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 73
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 hence average = 73 answer : e"
Answer: e
Problem: tickets for all but 100 seats in a 10000 - seat stadium were sold . of the tickets sold , 30 % were sold at half price and the remaining tickets were sold at the full price of $ 2 . what was the total revenue from ticket sales ?
Options: a ) $ 16,830 , b ) $ 17,820 , c ) $ 18,000 , d ) $ 19,800 , e ) $ 21,780
Rationale: 10000 seats - - > full price : half price = 7000 : 3000 price when all seats are filled = 14000 + 3000 = 17000 100 seats are unsold - - > loss due to unfilled seats = 30 + 2 * 70 = 170 revenue = 17000 - 170 = 16830 answer : a
Answer: a
Problem: a and b started a business investing rs . 10,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 2 , e ) 18 : 4
Rationale: "a : b = 10000 : 20000 = 1 : 2 answer : d"
Answer: d
Problem: rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 9 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 9 : 3 , b ) 9 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 9 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 9 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 9 / 100 ( 6000 - x ) = 540 - 2 x / 100 = > 540 - 1 / 50 x = 450 = > x = 4500 amount lent at 10 % = 1500 required ratio = 4500 : 1500 = 9 : 3 answer : a"
Answer: a
Problem: a man sitting in a train which is travelling at 15 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 97 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 15 ) kmph = 97 kmph . answer c"
Answer: c
Problem: there are 35 student in a school . 20 if them speek hindi 19 of them speak eng 9 of them speak both , then how many student neithe speak eng nor speak hindi
Options: a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) none of these
Rationale: total number of students = 35 no of hindi speaking students ( h ) = 20 no of english speaking students ( e ) = 19 h intersection e = 9 thus h union e = 20 + 19 - 9 = 30 thus number of student neithe speak eng nor speak hindi = 35 - 30 = 5 answer : e
Answer: e
Problem: a student chose a number , multiplied it by 2 , then subtracted 152 from the result and got 102 . what was the number he chose ?
Options: a ) 127 , b ) 100 , c ) 129 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 152 = 102 2 x = 254 x = 127 correct answer a"
Answer: a
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 50 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 min , b ) 1200 min , c ) 1300 min , d ) 1400 min , e ) 1600 min
Rationale: volume of pool = 50 * 150 * 10 cu . ft , 80 % full = 50 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 50 * 150 * 10 * 0.8 / 60 min = 1000 min a
Answer: a
Problem: if a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31 , what is the range of a / b ?
Options: a ) 1 , b ) 1 / 2 , c ) 5 / 6 , d ) 2 / 3 , e ) 4 / 3
Rationale: "range of a / b = max ( a / b ) - min ( a / b ) to get max ( a / b ) = > max ( a ) / min ( b ) = 25 / 15 to get min ( a / b ) = > min ( a ) / max ( b ) = 10 / 30 range = 25 / 15 - 10 / 30 = 4 / 3"
Answer: e
Problem: if the cost price is 40 % of selling price . then what is the profit percent .
Options: a ) 150 % , b ) 120 % , c ) 130 % , d ) 200 % , e ) none of these
Rationale: "explanation : let the s . p = 100 then c . p . = 40 profit = 60 profit % = ( 60 / 40 ) * 100 = 150 % . answer : a"
Answer: a
Problem: when positive integer x is divided by positive integer y , the remainder is 12 . if x / y = 75.12 , what is the value of y ?
Options: a ) 84 , b ) 98 , c ) 51 , d ) 65 , e ) 100
Rationale: "when positive integer x is divided by positive integer y , the remainder is 12 - - > x = qy + 12 ; x / y = 75.12 - - > x = 75 y + 0.12 y ( so q above equals to 75 ) ; 0.12 y = 12 - - > y = 100 . answer : e ."
Answer: e
Problem: the cost to park a car in a certain parking garage is $ 20.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 3.58 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 20 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 20 + 7 * 1.75 = 32.25 thus the average parking price = 32.25 / 9 = 3.58 $ a is the correct answer ."
Answer: a
Problem: the unit digit in the product ( 611 * 704 * 912 * 261 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 1 * 4 * 2 * 1 ) = 2 answer : a"
Answer: a
Problem: two trains are moving in opposite directions with speed of 150 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 48 , c ) 47 , d ) 30 , e ) 25
Rationale: "explanation : relative speed = 150 + 90 = 240 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 240 hr = 1 / 120 hr = 3600 / 120 seconds = 30 seconds answer : option d"
Answer: d
Problem: a train 60 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 2 , e ) 3
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 60 * 3 / 55 = 3 sec . answer e"
Answer: e
Problem: if the sum and difference of two numbers are 20 and 10 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 200 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 10 = 200 . answer : d"
Answer: d
Problem: a 340 - liter solution of kola is made from 75 % water , 5 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 12 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 19.6 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 340 + 12 + 3.2 + 6.8 = 362 numerator : 340 ( 1 - . 75 - . 05 ) + 3.2 340 ( 0.2 ) + 3.2 68 + 3.2 71.2 ratio : 71.2 / 362 = 0.196 answer : c"
Answer: c
Problem: the average mark of the students of a class in a particular exam is 90 . if 2 students whose average mark in that exam is 45 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?
Options: a ) 10 , b ) 40 , c ) 20 , d ) 30 , e ) 25
Rationale: "let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 2 ) students = 95 ( x - 2 ) 90 x - ( 2 * 45 ) = 95 ( x - 2 ) 100 = 5 x = > x = 20 answer : c"
Answer: c
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 250 more than a :
Options: a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 250 total earning = \ inline \ frac { 58 xy } { 100 } = 7250 answer : b ) rs . 7250"
Answer: b
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 11 , the remainder is 9 . what is the smallest positive integer k such that k + n is a multiple of 33 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 11 q + 9 n + 2 = 3 p + 3 = 11 q + 11 n + 2 is a multiple of 3 and 11 , so it is a multiple of 33 . the answer is a ."
Answer: a
Problem: a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 75 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 3,300 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 35 + 75 = 110 copies per minute . so , in half an hour they will make 110 * 30 = 3,300 copies . answer : c ."
Answer: c
Problem: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 750 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 750 ã — 22 ) = rs . 16500 . answer : option c"
Answer: c
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 5.26 % , e ) 12 %
Rationale: 950 - - - 50 100 - - - ? = > 5.26 % answer : d
Answer: d
Problem: find the compound interest on rs . 25000 in 2 years at 4 % per annum . the interest being compounded half yearly .
Options: a ) rs 2060.808 , b ) rs 2060.801 , c ) rs 2060.804 , d ) rs 2060.802 , e ) rs 2060.805
Rationale: "explanation : given : principal = rs . 25000 , rate = 4 % per half year , time = 2 years = 4 half years therefore , amount = p ( 1 + ( r / 2 ) / 100 ) 2 n amount = rs . [ 25000 * ( 1 + 2 / 100 ) 4 ] = rs . ( 25000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 27060.804 therefore , c . i . = rs . ( 27060.804 – 25000 ) = rs 2060.804 answer : c"
Answer: c
Problem: ravi covers a distance of 900 mtrs in 180 secs . find his speed in kmph ?
Options: a ) 10 kmph , b ) 18 kmph , c ) 20 kmph , d ) 26 kmph , e ) 28 kmph
Rationale: given distance d = 900 meters and time = 180 seconds speed = distance / time = 900 / 180 = 5 m / s . but speed is asked in kmph , to convert 5 mps to kmph , multiply it by 18 / 5 . speed in kmph = 5 x 18 / 5 = 18 kmph b
Answer: b
Problem: find the value of x from the below equation ? : 3 x ^ 2 - 5 x + 2 = 0
Options: a ) 2 / 3 , b ) - 1 , c ) 0 , d ) - 2 / 3 , e ) 2
Rationale: "a = 3 , b = - 5 , c = 2 x 1,2 = ( 5 â ± â ˆ š ( ( - 5 ) ^ 2 - 4 ã — 3 ã — 2 ) ) / ( 2 ã — 3 ) = ( 5 â ± â ˆ š ( 25 - 24 ) ) / 6 = ( 5 â ± 1 ) / 6 x 1 = ( 5 + 1 ) / 6 = 6 / 6 = 1 x 2 = ( 5 - 1 ) / 6 = 4 / 6 = 2 / 3 a"
Answer: a
Problem: n ^ ( n / 2 ) = 4 is true when n = 4 in the same way what is the value of n if n ^ ( n / 2 ) = 8 ?
Options: a ) 4 , b ) 8 , c ) 2 , d ) 6 , e ) 10
Rationale: n ^ ( n / 2 ) = 8 apply log n / 2 logn = log 8 nlogn = 2 log 8 = log 8 ^ 2 = log 64 logn = log 64 now apply antilog n = 64 / n now n = 8 . answer : b
Answer: b
Problem: if n = 2 ^ 0.25 and n ^ b = 8 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 12 , d ) 5 / 3 , e ) 80 / 3
Rationale: "25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 3 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 3 b = 12 answer : c"
Answer: c
Problem: [ ( 3.242 x 15 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.04863
Rationale: "answer multiplying 3.242 x 15 = 4.863 now divide 4.863 by 100 so , 4.863 ÷ 100 = 0.04863 ∴ shift the decimal two places to the left as 100 correct option : e"
Answer: e
Problem: there are 41 students in a class , number of girls is one more than number of guys . we need to form a team of 4 students . all 4 in the team can not be from same gender . number of girls and guys in the team should not be equal . how many ways can such a team be made ?
Options: a ) 50540 ways , b ) 60540 ways , c ) 50840 ways , d ) 40540 ways , e ) 51540 ways
Rationale: boys = 20 and girls = 21 now the combinations are { girl , girl , girl , boy } or { boy , boy , boy , girl } so 21 c 3 * 20 c 1 + 20 c 3 * 21 c 1 = 50540 ways answer : a
Answer: a
Problem: find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is e ."
Answer: e
Problem: pipe p can drain the liquid from a tank in 3 / 4 the time that it takes pipe q to drain it and in 3 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 3 / 8 , d ) 3 / 11 , e ) 3 / 4
Rationale: suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 3 / 4 ) rq ] = 4 / 3 also , rp = rr / ( 3 / 3 ) = > 4 / 3 = rr / ( 3 / 3 ) = > rr = 4 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 4 / 3 + 4 / 3 = 11 / 3 = 1 / ( 3 / 11 ) thus running simultaneously , pipe q will drain 3 / 11 of the liquid . thus answer = d .
Answer: d
Problem: xavier starts from p towards q at a speed of 40 kmph and after every 12 mins increases his speed by 20 kmph . if the distance between p and q is 56 km , then how much time does he take to cover the distance ?
Options: a ) 40 , b ) 48 , c ) 44 , d ) 36 , e ) 30
Rationale: "first 12 min = 40 * 12 / 60 = 8 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 80 * 12 / 60 = 16 km 4 th 12 min = 100 * 12 / 60 = 20 km total time 12.4 = 48 min b"
Answer: b
Problem: in the next cricket world cup t - 20 , team w has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team w score these 200 runs ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: team w can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d
Answer: d
Problem: in a class of 50 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "total = english + german - both + neither - - > 50 = english + 22 - 12 + 0 - - > english = 40 - - > only english = english - both = 40 - 12 = 28 . answer : d ."
Answer: d
Problem: the perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm . what is the area of the triangle ?
Options: a ) 22 , b ) 30 , c ) 77 , d ) 54 , e ) 23
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3 * 20 / 2 = 30 cm 2 answer : b"
Answer: b
Problem: a train 130 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: "speed of train relative to man : 130 / 6 * 18 / 5 km / hr = 78 km / hr let speed of train = x therefore x + 6 = 78 x = 78 - 6 x = 72 km / hr answer : d"
Answer: d
Problem: two pipes can fill a tank in 30 minutes and 20 minutes . an outlet pipe can empty the tank in 15 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 30 + v / 20 - v / 15 = v / 60 per minute the tank will be filled in 60 minutes . the answer is c ."
Answer: c
Problem: a barrel full of beer has 2 taps one midway , , which draw a litre in 6 minutes and the other at the bottom , which draws a litre in 4 minutes . the lower tap is lower normally used after the level of beer in the barrel is lower than midway . the capacity of the barrel is 36 litres . a new assistant opens the lower tap when the barrel is full and draws out some beer . as a result the lower tap has been used 24 minutes before the usual time . for how long was the beer drawn out by the new assistant ?
Options: a ) 15 minutes , b ) 16 minutes , c ) 17 minutes , d ) 18 minutes , e ) none of these
Rationale: sol . the top tab is operational till 18 litres is drawn out . ∴ time after which the lower tap is usually open = 18 × 6 = 108 minutes ∴ time after which it is open now = 108 – 24 = 84 minutes ∴ litres drawn = 84 / 6 = 14 litres ∴ 18 – 14 = 4 litres were drawn by the new assistant . ∴ time = 4 × 4 = 16 minutes answer b
Answer: b
Problem: if a cube has a volume of 125 , what is the surface area of one side ?
Options: a ) 5
b ) 25
c ) 50
d ) 150
e ) 625
Rationale: volume of a cube = side ^ 3 125 = side ^ 3 so side = 5 area of one side of the cube = side ^ 2 = 5 ^ 2 = 25 correct answer - b
Answer: b
Problem: xy = 1 then what is ( 6 ^ ( x + y ) ^ 2 ) / ( 6 ^ ( x - y ) ^ 2 )
Options: a ) 1296 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 6 ^ 4 = 1296 answer a"
Answer: a
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 192 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 4 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 192 12 r 2 = 192 r 2 = 16 r = 4 . answer : c"
Answer: c
Problem: √ ( 25 ) ^ 2
Options: a ) 5 , b ) 14 , c ) 25 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 25 ) ^ 2 = ? or , ? = 25 answer c"
Answer: c
Problem: x can finish a work in 15 days . y can finish the same work in 20 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 5 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 15 work done by y in 1 day = 1 / 20 work done by y in 12 days = 12 / 20 = 3 / 5 remaining work = 1 – 3 / 5 = 2 / 5 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 15 ) = 5 a"
Answer: a
Problem: the average of first 18 natural numbers is ?
Options: a ) 5.6 , b ) 9.5 , c ) 9.1 , d ) 9.8 , e ) 5.2
Rationale: "sum of 18 natural no . = 342 / 2 = 171 average = 171 / 18 = 9.5 answer : b"
Answer: b
Problem: what is the sum of 20 consecutive integers from - 9 inclusive , in a increasing order ?
Options: a ) - 9 , b ) 9 , c ) - 10 , d ) 10 , e ) 20
Rationale: "from - 9 to - 1 - - > 9 nos . zero - - > 1 number from + 1 to + 9 - - > 9 nos . when we add up nos . from - 9 to + 9 sum will be zero . total 19 nos will be added . 20 th number will be 10 . sum of these 20 nos . = 10 . d is the answer ."
Answer: d
Problem: if log 1087.5 = 2.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 26 , e ) 40
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 2087.5 + 1 ) = 10 ( 2.9421 + 1 ) = 10 ( 3.9421 ) = 39.421 x = antilog ( 39.421 ) therefore , number of digits in x = 40 . answer : e"
Answer: e
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 20 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 20 minutes , sam rides 4 km so sam will be 2 km ahead . it will take annie 40 minutes to catch sam . the answer is b ."
Answer: b
Problem: last year the range of the annual yield on equal amount of investments in 100 mutual funds was $ 10000 . if the annual yield this year for each of the 100 mutual funds has improved by 15 percent this year than it was last year , what is the range of the annual yield on mutual funds this year ?
Options: a ) $ 12700 , b ) $ 13000 , c ) $ 23000 , d ) $ 11500 , e ) $ 33000
Rationale: let the lowest yield be x . therefore , highest yield is x + 10000 . now yield of each mutual fund investment is improved by 10 % . therefore the yields will remain arranged in the same order as before . or lowest yield = 1.15 x and highest = 1.15 * ( x + 10000 ) or range = highest - lowest = 1.15 * ( x + 10000 ) - 1.15 x = 11500 , hence , d
Answer: d
Problem: a customer purchased a package of ground beef at a cost of $ 1.80 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 25 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 2.00 , b ) $ 2.15 , c ) $ 2.30 , d ) $ 2.40 , e ) $ 2.65
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.80 . let x be the price per pound for the steak . then 0.75 x = 180 x = 180 / 0.75 = $ 2.40 the answer is d ."
Answer: d
Problem: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 100 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 150 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 100 kmph , speed of b must be 100 * ( 3 / 2 ) = 150 kmph answer c"
Answer: c
Problem: a soft drink company had 6000 small and 15000 big bottles in storage . if 12 % of small 14 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 16010 , c ) 18180 , d ) 14930 , e ) 16075
Rationale: "6000 + 15000 - ( 0.12 * 6000 + 0.14 * 15000 ) = 18180 . answer : c ."
Answer: c
Problem: in a box of 10 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 12 , b ) 7 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: "first , there are 8 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 10 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 8 c 3 / 10 c 3 = 56 / 120 = 7 / 15 answer is b"
Answer: b
Problem: company workers decided to raise rs . 3 lakhs by equal contribution from each . had they contributed rs . 50 each extra , the contribution would have been rs . 3.25 lakhs . how many workers were they ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: explanation : n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 option c
Answer: c
Problem: the average of 7 numbers is 20 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 100 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145
Rationale: "explanation : average of new numbers = 20 * 5 = 100 answer : option a"
Answer: a