regisss/math_qa huggingface dataset:
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability y that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . y = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Problem: if a boat is rowed downstream for 200 km in 10 hours and upstream for 96 km in 12 hours , what is the speed of the boat and the river ?
Options: a ) 14 , 18 , b ) 14 , 6 , c ) 14 , 14 , d ) 6 , 6 , e ) 14 , 10
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 20 ; us = 8 x = ( 20 + 8 ) / 2 = 28 / 2 = 14 km / hr y = ( 20 - 8 ) / 2 = 12 / 2 = 6 km / hr answer : b"
Answer: b
Problem: in what time will a car 10 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 1 sec , c ) 9 sec , d ) 6 sec , e ) 2 sec
Rationale: t = 10 / 36 * 18 / 5 = 1 sec answer : b
Answer: b
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 130 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 61 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 130 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 34.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 61 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d"
Answer: d
Problem: if the sum of a number and its square is 306 , what is the number ?
Options: a ) 16 , b ) 77 , c ) 25 , d ) 17 , e ) 171
Rationale: "explanation : let the integer be x . then , x + x 2 = 306 x 2 + x - 306 = 0 ( x + 18 ) ( x – 17 ) = 0 x = 17 answer : d"
Answer: d
Problem: the price of a t . v . set worth rs . 15000 is to be paid in 20 installments of rs . 2000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 28088 , c ) 27098 , d ) 13000 , e ) 2799
Rationale: "money paid in cash = rs . 2000 balance payment = ( 15000 - 2000 ) = rs . 13000 . answer : d"
Answer: d
Problem: a train 180 m long running at 70 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 208 , b ) 277 , c ) 350 , d ) 881 , e ) 271
Rationale: "d = 70 * 5 / 18 = 20 = 388 – 180 = 208 answer : a"
Answer: a
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 2700 , then his salary per month in rupees is :
Options: a ) 4000 , b ) 6000 , c ) 18000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 2700 , salary = 18000 rs . answer : c ."
Answer: c
Problem: two trucks each 250 m long are running in opposite directions on parallel paths . their speeds are 30 km / hr and 20 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 77 sec , b ) 66 sec , c ) 48 sec , d ) 55 sec , e ) 36 sec
Rationale: relative speed = 20 + 30 = 50 km / hr . 50 * 5 / 18 = 125 / 9 m / sec . distance covered = 250 + 250 = 500 m . required time = 500 * 9 / 125 = 36 sec . answer : e
Answer: e
Problem: if a * b * c = 130 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 150 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 1 / 3 , e ) none of these
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 130 / 65 = > a / d = 2 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 150 / 1000 = > f / c = 1 / 4 a / d * f / c = 2 * 15 / 10 = 1 / 3 answer : d"
Answer: d
Problem: two numbers are less than third number by 25 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 6 % , b ) 8 % , c ) 9 % , d ) 11 % , e ) 12 %
Rationale: let the third number is x . then first number = ( 100 - 25 ) % of x = 75 % of x = 75 x / 100 second number is ( 63 x / 100 ) difference = 75 x / 100 - 63 x / 100 = 3 x / 25 so required percentage is , difference is what percent of first number ( 3 x / 25 * 100 / 75 x * 100 ) % = 6 % answer : a
Answer: a
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 6 * / 4 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 1 / 4 d"
Answer: d
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 10 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the product of n and 5 = 5 n . . the difference between an integer n and the product of n and 5 = 5 n - n = 4 n . . the outcome of the binary operation of n is less than 10 ? so 4 n < 10 . . . max value that n can take as an integer is 2 answer : b"
Answer: b
Problem: how many seconds will a 400 meter 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 ) 287 , b ) 288 , c ) 900 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 400 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 400 + x = ( 65 / 3 ) * 60 400 + x = 20 * 65 = 1300 x = 1300 - 400 = 900 meters answer : c"
Answer: c
Problem: if a and b are the roots of the equation x 2 - 8 x + 8 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 48 , c ) 17 , d ) 6 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 8 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 64 - 16 = 48 answer b"
Answer: b
Problem: evaluate : 45678 * 8 * 4 * 8 = ?
Options: a ) 730848 , b ) 705265 , c ) 730846 , d ) 730596 , e ) 731848
Rationale: "according to order of operations , 8 ? 4 ? 8 ( division and multiplication ) is done first from left to right 8 / 4 = 2 * 8 = 16 hence 45678 * 8 * 4 * 8 = 45678 * 16 = 730848 correct answer a"
Answer: a
Problem: what is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1 ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "since 200 = 2 ^ 3 * 5 ^ 2 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 100 odd numbers from 1 to 200 . we then need to eliminate the 20 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 195 . there are a total of 100 - 20 = 80 such numbers between 1 and 200 . the answer is c ."
Answer: c
Problem: it costs $ 6 for the first 1 / 4 hour to use the copier at kinkos . after the first ¼ hour it costs $ 8 per hour . if a certain customer uses the copier for 4 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 23.45 , b ) $ 65.33 , c ) $ 40 , d ) $ 38.27 , e ) $ 39.33
Rationale: 4 hrs 25 min = 265 min first 15 min - - - - - - > $ 6 time left is 250 min . . . now , 60 min costs $ 8 1 min costs $ 8 / 60 250 min costs $ 8 / 60 * 250 = > $ 33.33 so , total cost will be $ 33.33 + $ 6 = > $ 39.33 the answer will be ( e ) $ 39.33
Answer: e
Problem: population of a city in 20004 was 1300000 . 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 at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2818075 / 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 ) = 2818075 / 2 e"
Answer: e
Problem: a man invested rs . 50000 at the rate of 5 % p . a . for the first 3 years , 8 % p . a . for the next 5 years and 10 % p . a . for the period beyond 8 years . at the end of 11 years , he want to distribute total money among his 4 sons , how much money will each son get ?
Options: a ) 30000 , b ) 25375 , c ) 28680 , d ) 32000 , e ) 23125
Rationale: let the interest be i . then , ( 50000 × 3 × 5 / 100 ) + ( 50000 × 5 × 8 / 100 ) + ( 50000 × 3 × 10 / 100 ) = i ⇒ 7500 + 20000 + 15000 = i ⇒ i = 42500 total money = 42500 + 50000 = 92500 each son will get = 92500 / 4 = 23125 answer : e
Answer: e
Problem: a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should a pay ?
Options: a ) 270 , b ) 279 , c ) 226 , d ) 231 , e ) 232
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 8 / 29 * 841 = 232 answer : e"
Answer: e
Problem: what is the probability that the sum of two dice will yield a 7 , and then when both are thrown again , their sum will again yield a 7 ? assume that each die has 6 sides with faces numbered 1 to 6 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Rationale: "in order to get the sum of the two dices to be 7 , there are six combinations that satisfy this requirement . 1 + 6 = 7 2 + 5 = 7 3 + 4 = 7 4 + 3 = 7 5 + 2 = 7 6 + 1 = 7 each combination has 1 / 36 of probability of occurrence , or in total 6 / 36 for the six combinations , which is 1 / 6 . in order to get the probability of this occurring twice in a row we multiply 1 / 6 * 1 / 6 and we get 1 / 36 . the answer is b ."
Answer: b
Problem: one fast typist type some matter in 2 hrs and another slow typist type the same matter in 3 hrs . if both do combine in how much time they will take to finish .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: fast ' s 1 hr work = 1 / 2 slow ' s 1 hr work = 1 / 3 1 / 2 + 1 / 3 = 5 / 6 they ll finish in 6 / 5 hrs = 1 1 / 5 = = > 1 hr 12 mins answer : c
Answer: c
Problem: how many internal diagonals does a nonagon ( nine sided polygon ) have ?
Options: a ) 25 , b ) 27 , c ) 40 , d ) 56 , e ) 80
Rationale: "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 9 no . of diagonals = 9 ( 9 - 3 ) / 2 = 27 ans b"
Answer: b
Problem: if a lends rs . 3200 to b at 12 % per annum and b lends the same sum to c at 14.5 % per annum then the gain of b in a period of 5 years is ?
Options: a ) 157.78 , b ) 157.98 , c ) 400 , d ) 420 , e ) 430
Rationale: "( 3200 * 2.5 * 5 ) / 100 = > 400 answer : c"
Answer: c
Problem: country x taxes each of its citizens an amount equal to 12 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.12 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,800 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,200 - - > x = 56,000 . answer : b ."
Answer: b
Problem: in a kilometer race , a beats b by 54 meters or 12 seconds . what time does a take to complete the race ?
Options: a ) 212 , b ) 190 , c ) 277 , d ) 181 , e ) 122
Rationale: "time taken by b run 1000 meters = ( 1000 * 12 ) / 54 = 222 sec . time taken by a = 224 - 12 = 212 sec . answer : a"
Answer: a
Problem: find the average of all prime numbers between 60 and 90
Options: a ) 45 , b ) 55 , c ) 69 , d ) 65 , e ) 77
Rationale: "prime numbers between 60 and 90 are 67 , 71 , 73 , 79 , 83 , 89 required average = ( 67 + 71 + 73 + 79 + 83 + 89 ) / 6 = 462 / 6 = 77 answer is e"
Answer: e
Problem: 5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope . the letter is said to be put in correct position if for example letter 1 goes into envelope 1 . now what is the probability that all letters be put into wrong envelopes ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 11 / 120 , d ) 11 / 30 , e ) 76 / 120
Rationale: this q is based on derangement , a permutation in which all elements are in the wrong position . number of derangements = n ! ( 12 ! − 13 ! + 14 ! + . . . + ( ( − 1 ) n ) n ! ) n ! ( 12 ! − 13 ! + 14 ! + . . . + ( ( − 1 ) n ) n ! ) . . of course it can be derived but thats not required . . since there are 5 letters and 5 envelopes : - derangements = 5 ! ( 12 ! − 13 ! + 14 ! − 15 ! ) derangements = 5 ! ( 12 ! − 13 ! + 14 ! − 15 ! ) = > 120 ( 1 / 2 − 1 / 6 + 1 / 24 − 1 / 120 ) = 60 − 20 + 5 − 1 = 44.120 ( 1 / 2 − 1 / 6 + 1 / 24 − 1 / 120 ) = 60 − 20 + 5 − 1 = 44 . total possible ways = 5 ! = 120 . therefore required prob , p = 44 / 120 = 11 / 30 . ans d
Answer: d
Problem: a rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3600
Rationale: "area = ( l + b – d ) d ( 70 + 60 – 10 ) 10 = > 1200 m 2 1200 * 3 = rs . 3600 answer : e"
Answer: e
Problem: the distance from city a to city b is 220 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 44 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the time it takes bob to drive to city b is 220 / 40 = 5.5 hours . alice needs to take less than 5 hours for the trip . alice needs to exceed a constant speed of 220 / 5 = 44 miles per hour . the answer is a ."
Answer: a
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 18 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 42 % , d ) 18 % , e ) 8.5 %
Rationale: "instead of using complex calculations and remembering formulae , why dont u directly get to weighted average . 3 parts of 10 % + 1 part of x ( unknown ) % = 4 parts of 18 % = > x % = 72 % - 30 % = 42 % ans c it is ."
Answer: c
Problem: the average salary / head of all the workers in a workshop is rs . 700 , if the average salary / head of 5 technician is rs . 800 and the average salary / head of the rest is rs . 650 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 19 , c ) 17 , d ) 16 , e ) 15
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 800 + 650 ( y - 5 ) = 700 y ⇒ 4000 + 650 y - 3250 = 700 y ⇒ 50 y = 750 ∴ y = 15 so total number of workers = 15 e
Answer: e
Problem: there are 9 executives , including the ceo and cfo , that are asked to form a small team of 5 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 85 , b ) 87 , c ) 89 , d ) 91 , e ) 93
Rationale: "the total number of ways to form a team of 5 is 9 c 5 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 3 = 35 . the number of ways to form an acceptable team is 126 - 35 = 91 . the answer is d ."
Answer: d
Problem: there are 720 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 120 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 720 . hence , we have m + f = 720 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 720 / 3 = 240 solving the three equations yields the solution f = 240 , m = 480 , and d = 240 . the number of female democratic participants equals half the female participants equals 240 / 2 = 120 . answer : c"
Answer: c
Problem: in the first 20 overs of a cricket game , the run rate was only 4.2 . what should be the rate in the remaining 30 overs to reach the target of 250 runs ?
Options: a ) 6.25 , b ) 6.28 , c ) 6.11 , d ) 5.53 , e ) 6.21
Rationale: "required run rate = [ 250 - ( 4.2 * 20 ) ] / 30 = 166 / 30 = 5.53 answer : d"
Answer: d
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 45000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 80
Rationale: "0.036 * 10 ^ 5 can be written as 3600 45000 * 10 ^ ( - 3 ) can be written as 45 required = 3600 / 45 = 80 answer : e"
Answer: e
Problem: if the wheel is 10 cm then the number of revolutions to cover a distance of 1200 cm is ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 19 , e ) 10
Rationale: "2 * 22 / 7 * 10 * x = 1200 = > x = 19 answer : d"
Answer: d
Problem: in an apartment building that has 441 units , 4 out of every 7 units are currently rented , including 1 / 5 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 45 , b ) 70 , c ) 100 , d ) 105 , e ) 140
Rationale: "rented = 4 / 7 * 441 = 252 . rented two - bedroom = 6 / 7 * 252 = 216 ; rented one - bedroom = 1 / 7 * 252 = 36 or 252 - 216 = 36 ) . rented one - bedroom units are 1 / 5 of all one - bedroom : 1 / 5 * { all one bedroom } = 36 - - > { all one - bedroom } = 180 . { all two - bedroom } = 441 - 180 = 261 . two - bedroom not rented = 261 - 216 = 45 . answer : a ."
Answer: a
Problem: john was 35 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 8 of john ' s . how old is betty ?
Options: a ) 24 , b ) 35 , c ) 28 , d ) 30 , e ) 32
Rationale: "assume betty ' s age on marriage = x years . john ' s age on marriage = 35 john ' s age after 5 years = 40 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 40 ) = 35 therefore betty ' s current age = 35 option b"
Answer: b
Problem: the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 4800 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 3840 , b ) rs . 5270 , c ) rs . 6275 , d ) rs . 6720 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 4800 ( 100 / 125 ) = rs . 3840 . answer : a"
Answer: a
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 675 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 15 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 675 3 b 2 = 675 b 2 = 225 b = 15 m . answer : option d"
Answer: d
Problem: in a sports club with 30 members , 16 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 16 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 16 - x ) + ( 19 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"
Answer: a
Problem: two trains 50 m and 120 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 14.8 sec , c ) 6.12 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 50 + 120 = 170 m . required time = 170 * 9 / 250 = 6.12 = 6.12 sec . answer : c"
Answer: c
Problem: a large field of 500 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 205 , b ) 215 , c ) 225 , d ) 260 , e ) 270
Rationale: "average of the two areas = 500 / 2 = 250 one - fifth of the average of the two areas = 250 / 5 = 50 ⇒ difference of the two areas = 50 let area of the smaller part = x hectares . then , area of the larger part = x + 50 hectares . = > x + x + 50 = 500 = > 2 x = 450 = > x = 225 answer : c"
Answer: c
Problem: a small college reduced its faculty by approximately 25 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 260 , c ) 224 , d ) 254 , e ) 302
Rationale: "if x is the original number of faculty members , then after 25 % reduction in faculty members number is . 75 x but we are given . 75 x = 195 x = 260 so the original number of faculty members is 260 correct answer - b"
Answer: b
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 3.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1918
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.5 * 2 ) 2 * 3.5 = > 959 959 * 2 = rs . 1918 answer : e"
Answer: e
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 39 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 150 = 390 m . time taken = 390 / 10 = 39 sec . answer : c"
Answer: c
Problem: a bag making machine can make 20 bags per hour . if the company adjusts the machine to produce twice the amount per hour to satisfy expected rise in demand . how many bags can the machine make in the next 5 days if it works 10 hours a day ?
Options: a ) 2,000 , b ) 1,000 , c ) 400 , d ) 50 , e ) 1,500
Rationale: 20 * 2 = 40 bags per hour . 5 days * 10 hours * 40 bags per hour = 2,000 bags . answer is option a .
Answer: a
Problem: 0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance z between any two of the tick marks ?
Options: a ) 1 / 70 , b ) 1 / 35 , c ) 2 / 35 , d ) 1 / 12 , e ) 1 / 7
Rationale: divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . z = 1 / 35 answer is b .
Answer: b
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 3 : 5 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 2 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 1 : 2 , b ) 2 : 2 , c ) 2 : 5 , d ) 2 : 6 , e ) 2 : 7
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 3 x / 8 , and fraction of zinc in alloy _ 1 = 5 x / 8 . similarly , fraction of copper in alloy _ 2 = 6 y / 8 , and fraction of zinc in alloy _ 2 = 2 y / 8 . mixing them , we get copper = 3 x / 8 + 6 y / 8 ; zinc = 5 x / 8 + 2 y / 8 . so , 3 x + 6 y = 5 x + 2 y - > 2 x = 4 y - > x / y = 2 / 4 = 1 / 2 so , they must be mixed in the ratio 1 : 2 answer : a"
Answer: a
Problem: david obtained 76 , 65 , 82 , 67 and 85 marks ( out in 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) 79
Rationale: "add all those marks and divide it by 5 becz they gave us 5 subjects for finding average marks we need to divide them add them 76 + 65 + 82 + 67 + 85 / 5 = 375 / 5 = 75 answer : d"
Answer: d
Problem: 51 + 52 + 53 + . . . . . . . . . + 100 ) is equal to
Options: a ) 3775 , b ) 3779 , c ) 3629 , d ) 3729 , e ) 3719
Rationale: "51 + 52 + 53 + . . . . . . . . . . . + 100 = ( 1 + 2 + 3 + . . . . + 100 ) - ( ! + 2 + 3 + . . . . . . + 50 ) = = ( 5050 - 1275 ) = 3775 answer ; a"
Answer: a
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 2952400 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 2952400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 29524 so we have 1 , 3 , 9 , 27 . . . . . 2652400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 29524 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 29524 x - 2 = 1 - 3 ^ n - 59048 = 1 - 3 ^ n - 59049 = - 3 ^ n 59049 = 3 ^ n ( negatives cancel out ) 59049 can also be re written as 3 ^ 10 therefore ; 3 ^ 10 = 3 ^ n thus n = 10 ( c )"
Answer: c
Problem: a company decreased the price of its main product by 20 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 3.0 , b ) 7.0 , c ) 5.0 , d ) 2.0 , e ) 1.0
Rationale: "for the total revenue to remain the same when the price is one fifth , the number of products sold must five times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 20 % = 5.0 answer : c"
Answer: c
Problem: in how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 1152 , b ) 1987 , c ) 2012 , d ) 1856 , e ) 2546
Rationale: "number of ways = 2 * 4 ! * 4 ! = 1152 answer is a"
Answer: a
Problem: the average of first five multiples of 3 is :
Options: a ) 3 , b ) 9 , c ) 12 , d ) 15 , e ) 17
Rationale: "solution average = 3 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 45 / 5 = 9 answer b"
Answer: b
Problem: the average age of an adult class is 40 years . 17 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 17 x 32 = ( y + 17 ) x 36 â ‡ ’ 40 y + 544 = 36 y + 612 â ‡ ’ 4 y = 68 â ˆ ´ y = 17 d"
Answer: d
Problem: a train requires 12 seconds to pass a pole while it requires 27 seconds to cross a stationary train which is 300 mtrs long . find the speed of the train .
Options: a ) 60 kmph , b ) 75 kmph , c ) 80 kmph , d ) 85 kmph , e ) 72 kmph
Rationale: "in 12 s the train crosses the pole and in 27 sec the train crosses one more stationary train in 15 sec the train travels a distance of 300 mtrs speed = 300 / 15 = 20 m / s = 20 ( 3600 / 1000 ) = 20 * 18 / 5 = 72 kmph answer : e"
Answer: e
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?
Options: a ) 560 , b ) 240 , c ) 329 , d ) 443 , e ) 544
Rationale: "let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 xkilograms . so , the total is x + 2 x = 3 x this must be equal to 360 . 3 x = 360 x = 360 / 3 x = 120 therefore , the salesman sold 120 kg in the morning and 2 ⋅ 120 = 240 kg in the afternoon ."
Answer: b
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 30 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) 62 sec
Rationale: "relative speed = 30 + 30 = 60 km / hr . 60 * 5 / 18 = 50 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 50 = 60 sec . answer : d"
Answer: d
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number f of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) f = 90 , d ) f = 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 130 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 260 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 130 total = 130 + 130 = 260 answer ( d )"
Answer: d
Problem: on dividing a number by 5 , we get 2 as quotient and 0 as remainder . on dividing the same number by 4 , what will be the remainder ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "number = 5 * 2 + 0 = 10 4 ) 10 ( 2 8 - - - - - - - - 2 required number = 2 . answer : c"
Answer: c
Problem: two tains of equal lengths take 10 seconds and 16 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 12.3 , e ) 18
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 16 ] m / sec = 7.5 m / sec . relative speed = ( 12 + 7.5 ) = m / sec = 19.5 m / sec . ∴ required time = ( 120 + 120 ) / 19.5 secc = 12.3 sec . answer d"
Answer: d
Problem: how many paying stones , each measuring 2 m * 1 m are required to pave a rectangular court yard 30 m long and 16 m board ?
Options: a ) 240
b ) 18
c ) 26
d ) 17
e ) 12
Rationale: 30 * 16 = 2 * 1 * x = > x = 240 answer : a
Answer: a
Problem: the circumferences of two circles are 268 meters and 380 meters . find the difference between the areas of the larger and the smaller circles .
Options: a ) 388.15 , b ) 2992 , c ) 4312.5 , d ) 2887.27 , e ) 5773.09
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 268 and 2 ∏ l = 380 s = 268 / 2 ∏ and l = 380 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1902 / ∏ 2 - 1342 / ∏ 2 } = 1902 / ∏ - 1342 / ∏ = ( 190 - 134 ) ( 190 + 134 ) / ∏ = ( 56 ) ( 324 ) / ( 22 / 7 ) = ( 18144 ) / ( 22 ) ( 7 ) = 5773.09 sq m . answer : e"
Answer: e
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind roe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of roe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . roe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d"
Answer: d
Problem: the difference between the local value and the face value of 3 in the numeral 62975143 is
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 5
Rationale: "explanation : ( local value of 3 ) - ( face value of 3 ) = ( 3 - 3 ) = 0 d )"
Answer: d
Problem: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 36 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: first , let ' s translate the expression 21 # 36 , using the definition given : 21 # 36 = 21 × 24 × 27 × 30 × 33 × 36 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 36 = 3 ^ 6 ( 7 × 8 × 9 × 10 × 11 × 12 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 36 = 3 ^ 6 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 × ( 2 ^ 2 × 3 ) ) let ' s group the prime bases : 21 # 36 = 2 ^ 6 × 3 ^ 9 × 5 × 7 × 11 the sum of the exponents is 6 + 9 + 1 + 1 + 1 = 18 the answer is c .
Answer: c
Problem: a grocer has a sale of rs . 435 , rs . 927 , rs . 855 , rs . 230 and rs . 562 for 5 consecutive days . how much sale must he have in the sixth day so that he gets an average sale of rs . 625 ?
Options: a ) rs 741 , b ) rs 5991 , c ) rs 6001 , d ) rs 6991 , e ) none of these
Rationale: "explanation : total sale for 5 days = rs . ( 435 + 927 + 855 + 230 + 562 ) = rs . 3009 . required sale = rs . [ ( 625 x 6 ) - 3009 ] = rs . ( 3750 - 3009 ) = rs . 741 . answer : a"
Answer: a
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm .
Options: a ) 335 cm 2 , b ) 885 cm 2 , c ) 285 cm 2 , d ) 247 cm 2 , e ) 725 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 13 ) = 247 cm 2 answer : d"
Answer: d
Problem: the monthly rent of a shop of dimension 10 feet × 8 feet is rs . 2400 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 56 , c ) 68 , d ) 360 , e ) 92
Rationale: "sol . monthly rent per square feet = 2400 / ( 10 * 8 ) = 30 & annual rent per square feet = 12 * 30 = 360 answer : d"
Answer: d
Problem: find compound interest on $ 12000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 4663.5 , b ) 4203.5 , c ) 4303.5 , d ) 4403.5 , e ) 4103.5
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 12000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 12000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 16663.50 . : . c . i . = rs . ( 16663.50 - 12000 ) = $ 4663.50 answer a ."
Answer: a
Problem: after decreasing 24 % in the price of an article costs rs . 320 . find the actual cost of an article ?
Options: a ) 400 , b ) 520 , c ) 651 , d ) 525 , e ) 421
Rationale: "cp * ( 76 / 100 ) = 320 cp = 4.21 * 100 = > cp = 421 answer : e"
Answer: e
Problem: in a group of 800 people , 1 / 5 play at least one instrument , 32 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 4 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: "p ( playing 2 or more instruments ) = 32 / 800 = 1 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 1 / 25 = 4 / 25 . answer b ."
Answer: b
Problem: teacher took exam for english , average for the entire class was 80 marks . if we say that 10 % of the students scored 95 marks and 20 % scored 90 marks then calcualte average marks of the remaining students of the class .
Options: a ) 60 , b ) 70 , c ) 65 , d ) 75 , e ) 80
Rationale: lets assume that total number of students in class is 100 and required average be x . then from the given statement we can calculate : ( 10 * 95 ) + ( 20 * 90 ) + ( 70 * x ) = ( 100 * 80 ) 70 x = 8000 - ( 950 + 1800 ) = 5250 answer : d x = 75 .
Answer: d
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 2000 more than d , what is b ' s share ?
Options: a ) a ) 4000 , b ) b ) 2900 , c ) c ) 2000 , d ) d ) 2393 , e ) e ) 2009
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 2000 = > x = 2000 . b ' s share = rs . 2 x = 2 * 2000 = rs . 4000 . answer : a"
Answer: a
Problem: what is the square root of 324 ?
Options: a ) a ) 18 , b ) b ) 9 , c ) c ) 45 , d ) d ) 62 , e ) e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 18 * 18 = 324 324 divided by x = 18 x = 18 ( a ) 18"
Answer: a
Problem: a and b together have rs . 1210 . if of a ' s amount is equal to of b ' s amount , how much amount does b have ?
Options: a ) 484 , b ) 460 , c ) 550 , d ) 664 , e ) none of them
Rationale: 4 / 15 a = 2 / 5 b a = ( 2 / 5 x 15 / 4 ) b a = 3 / 2 b a / b = 3 / 2 a : b = 3 : 2 . therefore , b ' s share = rs . ( 1210 x 2 / 5 ) = rs . 484 . answer is a .
Answer: a
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 10 weavers in 10 days ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "1 weaver can weave 1 mat in 4 days . 10 weavers can weave 10 mats in 4 days . 10 weavers can weave 25 mats in 10 days . the answer is d ."
Answer: d
Problem: if a trader sold two cars each at rs . 404415 and gains 15 % on the first and loses 15 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 2.02 % , c ) 1.04 % , d ) 2.25 % , e ) 3.40 %
Rationale: "explanation : sp of each car is rs . 404415 , he gains 15 % on first car and losses 15 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 15 ) ( 15 ) / 100 % = 2.25 % answer is d"
Answer: d
Problem: robert ate 10 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 10 - 5 = 5 . answer is d
Answer: d
Problem: if a + b = − 9 , and a = 30 / b , what is the value of a ^ 2 + b ^ 2 ?
Options: a ) 31 , b ) 21 , c ) 41 , d ) 61 , e ) 51
Rationale: "a ^ 2 + b ^ 2 should make you think of these formulas : ( a + b ) ( a + b ) = a ^ 2 + b ^ 2 + 2 ab we already know ( a + b ) = - 9 and a * b = 30 ( a + b ) ( a + b ) = ( - 9 ) ( - 9 ) = a ^ 2 + b ^ 2 + 2 * ( 30 ) a ^ 2 + b ^ 2 = 81 - 60 = 21 answer : b"
Answer: b
Problem: a basket contains 6 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "the total number of ways to choose 2 apples is 6 c 2 = 15 the number of ways that include the spoiled apple is 5 c 1 = 5 p ( the spoiled apple is included ) = 5 / 15 = 1 / 3 the answer is a ."
Answer: a
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 60 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 102
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 60 = > 2 * ( 2 ) ^ 2 + y = 60 = > 8 + y = 60 = > y = 52 f ( 5 ) = 2 * ( 5 ) ^ 2 + 52 = 102 answer e"
Answer: e
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 884 in 4 years . the sum is :
Options: a ) s . 608 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 884 - 815 ) = rs . 69 . s . i . for 3 years = rs . ( 69 x 3 ) = rs . 207 . principal = rs . ( 815 - 207 ) = rs . 608 . answer : option a"
Answer: a
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 2 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 2 n = > 14 q + 4 = > remainder = > 4 for some integer q alternatively = > n = 2 > 2 n = > 4 = > 4 divided by 7 will leave a remainder 4 hence d"
Answer: d
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6900 ?
Options: a ) 4966 , b ) 6477 , c ) 7391 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6900 x 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 answer : c"
Answer: c
Problem: if 60 percent of 600 is 50 percent of x , then x = ?
Options: a ) 600 , b ) 720 , c ) 820 , d ) 800 , e ) 920
Rationale: "0.6 * 600 = 0.5 * x x = 6 / 5 * 600 = 720"
Answer: b
Problem: the length of the bridge , which a train 145 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 230 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 145 + x ) / 30 = 25 / 2 x = 230 m . answer : option a"
Answer: a
Problem: a $ 89.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 33 %
Rationale: "listed selling price of chair = 89.95 $ discounted selling price of chair = 59.95 $ discount = 89.95 - 59.95 = 30 $ % decrease in price of chair = ( 30 / 89.95 ) * 100 % = 33 % approx answer e"
Answer: e
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 390 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 3.9 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 390 â † ’ t = 3.9 answer d
Answer: d
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 12.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 4,100 , d ) $ 3,250 , e ) $ 4,500
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 12 = $ 6000 profit : 6000 - 1900 = $ 4100 option c is correct"
Answer: c
Problem: a certain rectangular window is three times as long as it is wide . if its perimeter is 32 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2
b ) 11 by 3
c ) 10.5 by 3.5
d ) 12 by 4
e ) 9 by 3
Rationale: 2 x + 2 y = 32 x + y = 16 x + 3 x = 16 4 x = 16 x = 4 answer d
Answer: d
Problem: a car averages 50 mph for the first 4 hours of a trip and averages 80 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: let the time for which car averages 80 mph = t 65 * ( t + 4 ) = 50 * 4 + 80 t = > 15 t = 60 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a
Answer: a
Problem: a sum of rs . 1000 at simple interest amounts to rs . 1192 in 4 years . the s . i . for 1 year is :
Options: a ) rs . 45 , b ) rs . 70 , c ) rs . 39 , d ) rs . 72 , e ) rs . 48
Rationale: s . i . for 4 years = rs . ( 1192 - 1000 ) = rs . 192 . s . i . for 1 year = rs . 192 / 4 = rs . 48 . answer : option e
Answer: e
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams . find the profit percent .
Options: a ) 12.11 , b ) 11.11 , c ) 13.11 , d ) 14.11 , e ) 15.11
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 900 100 + g / 100 + 0 = 1000 / 900 100 + g = 10 / 9 * 100 g = 11.11 answer : b"
Answer: b
Problem: if 0.5 % of a = 75 paise , then the value of a is ?
Options: a ) rs . 150 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 75 / 100 ∴ a = rs . ( 75 / 0.5 ) = rs . 150 correct option : a"
Answer: a
Problem: if | 4 x + 6 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 46 or 4 x + 6 = - 46 = > x = 10 or x = - 12 sum of both the values will be - 12 + 10 = - 2 answer is b"
Answer: b
Problem: ( √ 27 + √ 192 ) / √ 54 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 11 / ( 3 * √ 2 ) , e ) √ 2
Rationale: "( √ 27 + √ 192 ) / √ 54 = ( 3 √ 3 + 8 √ 3 ) / 3 √ 3 * 2 = 11 √ 3 / 3 √ 3 * 2 = 11 / ( 3 * √ 2 ) = 11 / ( 3 * √ 2 ) . hence , the correct answer is d ."
Answer: d
Problem: 60 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100.5 , b ) 200.5 , c ) 300.5 , d ) 350.5 , e ) 412.5
Rationale: "6 x / 10 - x / 3 = 110 4 x / 15 = 110 x = 412.5 answer : e"
Answer: e
Problem: a train traveling at 72 kmph crosses a platform in 32 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 280 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 32 = 640 m . so , length of platform = 640 - 360 = 280 m imo , answer a"
Answer: a