regisss/math_qa huggingface dataset:
Problem: the sum of all two digit numbers divisible by 6 is
Options: a ) 910 , b ) 510 , c ) 710 , d ) 610 , e ) 810
Rationale: "required numbers are 12 , 18,24 . . . . . 96 this is an a . p . in which a = 12 , d = 6 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 6 n - 6 = 96 6 + 6 n = 96 6 n = 96 - 6 n = 90 / 6 then n = 15 . required sum = n / 2 ( a + l ) = 15 / 2 ( 12 + 96 ) = 810 answer is e ."
Answer: e
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 182 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 182 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 182 m ) / ( w + m ) = 180 170 w + 182 m = 180 w + 180 m 2 m = 10 w m = 5 w m / w = 5 / 1 the ratio of men to women is 5 to 1 . b"
Answer: b
Problem: ages of two persons differ by 14 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 13,27 , c ) 16,32 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 14 ) = > 3 ( x - 6 ) = ( x + 14 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 8 = > x = 13 so other person age is x + 14 = 27 answer : option b"
Answer: b
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 400 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 80 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 400 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 400 ) * 100 / 500 = 80 % answer : option e"
Answer: e
Problem: convert 2.3 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "2.3 hectares in ares 1 hectare = 100 ares therefore , 2.3 hectares = 2.3 × 100 ares = 230 ares . answer - d"
Answer: d
Problem: jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the number ' s sum will be 13 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21
Rationale: both dice addition result is 13 = ( 6 + 7 ) probability that the number on first die is 6 = 1 / 6 probability that the number on second die is 7 = 1 / 7 probability that both dice addition result is 13 = 1 / 6 * 1 / 7 = 1 / 42 d
Answer: d
Problem: calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 9 , 12 , 15 and 18 seconds ?
Options: a ) 186 , b ) 130 , c ) 180 , d ) 181 , e ) 120
Rationale: "lcm of 9 , 12 , 15 and 18 is 180 lcm = 180 answer : c"
Answer: c
Problem: if a = 105 and a ^ 3 = 21 * 25 * 315 * b , what is the value of b ?
Options: a ) 35 , b ) 7 , c ) 45 , d ) 49 , e ) 54
Rationale: first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 315 = 3 * 3 * 5 * 7 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 3 * 5 * 7 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 3 * 7 ^ 2 b = 7 correct answer b .
Answer: b
Problem: boy sells a book for rs . 540 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 450 , c ) 550 , d ) 590 , e ) 660
Rationale: "cost price = 540 / 90 x 100 = 600 to gain 10 % = 600 x 10 / 100 = 60 sp = cp + gain = 600 + 60 = 660 answer : e"
Answer: e
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 16 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 3 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 3 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 16 . ans . a ."
Answer: a
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 723 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 21897 , c ) 28799 , d ) 30000 , e ) 32782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 723 p = 30000 answer : d"
Answer: d
Problem: if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 2 : 5 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.2 a = 0.08 b â ‡ ” a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 â ˆ ´ a : b = 2 : 5 . answer b"
Answer: b
Problem: a person want to give his money of $ 1800 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 700 , b ) $ 600 , c ) $ 900 , d ) $ 500 , e ) $ 400
Rationale: "b ' s share = 1800 * 3 / 9 = $ 600 answer is b"
Answer: b
Problem: in what time will a train 240 metres long cross an electric pole , if its speed be 126 km / hr ?
Options: a ) 6.75 sec , b ) 6.85 sec , c ) 6.55 sec , d ) 6.44 sec , e ) 7.85 sec
Rationale: "solution speed = ( 126 x 5 / 18 ) m / sec = 35 m / sec time taken = ( 240 / 35 ) sec = 6.85 sec . answer b"
Answer: b
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 7 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 78.40 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80
Rationale: correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.07 ( $ 1120 ) = $ 78.40 . the correct answer is b .
Answer: b
Problem: how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 200 m in length ?
Options: a ) 18.6 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec
Rationale: "a 18.6 sec d = 110 + 200 = 310 m s = 60 * 5 / 18 = 50 / 3 t = 310 * 3 / 50 = 18.6 sec answer is a"
Answer: a
Problem: excepting ‘ seldom ’ which means – rarely , infrequently and not often , is the antonym .
Options: a ) 22 , b ) 278 , c ) 267 , d ) 176 , e ) 971
Rationale: answer : d
Answer: d
Problem: if y is the smallest positive integer such that 7350 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 6 * 7350 = 44 , 100 , which is a square of 210 c"
Answer: c
Problem: simplify : 0.6 * 0.6 + 0.6 * 0.6
Options: a ) 0.52 , b ) 0.42 , c ) 0.48 , d ) 0.64 , e ) 0.46
Rationale: "given exp . = 0.6 * 0.6 + ( 0.6 * 6 ) = 0.36 + 0.1 = 0.46 answer is e ."
Answer: e
Problem: two pipes a and b can fill a tank in 24 minutes and 32 minutes respectively . if both the pipes are opened simultaneously , after how much time should b be closed so that the tank is full in 18 minutes ?
Options: a ) 7 minute , b ) 9 minute , c ) 10 minute , d ) 8 minute , e ) 11 minute
Rationale: pipe a will work for 18 minutes . suppose pipe b is closed after x minutes than we have 18 / 24 + x / 32 = 1 x = 8 minute . answer : d
Answer: d
Problem: the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 179.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"
Answer: b
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 280 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 7 = 280 ) 100 % - - - - - > 700 ( 100 * 7 = 700 ) answer : option b"
Answer: b
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 990 grams per kg , what is his percent ?
Options: a ) 1.01 % , b ) 25 % , c ) 22 % , d ) 29 % , e ) 45 %
Rationale: "990 - - - 10 100 - - - ? = > 1.01 % answer : a"
Answer: a
Problem: a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 30 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 200,000 , e ) $ 205,000
Rationale: "30 % of 1000 = 300 worked for 30 hours payment @ 5 / hr total payment = 300 * 30 * 5 = 45000 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 45000 + 100000 + 40000 + 15000 = 200000 hence , answer is d"
Answer: d
Problem: 50 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 660
Rationale: "5 x / 10 - x / 3 = 110 1 x / 6 = 110 x = 660 answer : e"
Answer: e
Problem: the bases of a hemisphere and a cone are equal . if their heights are also equal then ratio between their curved surface area is —
Options: a ) 1 : √ 2
b ) √ 2 ∶ 1
c ) 1 : 2
d ) 2 : 1
e ) none of these
Rationale: both having same radius and the heights are same . so height of cone is same as the radius . 2 π r ^ 2 / π rl 2 r / √ ( r ^ 2 + h ^ 2 ) , where π r gets cancelled on both sides and l ^ 2 = r ^ 2 + h ^ 2 2 r / √ ( 2 r ^ 2 ) , r = h 2 / √ 2 √ 2 / 1 answer : b
Answer: b
Problem: the average age of a , b and c is 26 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 21
Rationale: "c 20 age of b = age of ( a + b + c ) – age of ( a + c ) = 26 × 3 – 29 × 2 = 78 – 58 = 20 years"
Answer: c
Problem: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 25 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water 70 l syrup . to make 25 % syrup solution , the result solution must have 112.5 l syrup and 37.5 l syrup . therefore we are taking 32.5 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 32.5 l syrup in 69.6 l solution we started by multiplying 10 now to get to the result we need to divide by 32.5 = > amount of solution to be replaced with water = ( 69.6 / 32.5 ) = 2.14 . correct option : c"
Answer: c
Problem: in what time will a train 175 m long cross an electric pole , it its speed be 180 km / hr ?
Options: a ) 7.5 , b ) 6.5 , c ) 5.5 , d ) 4.5 , e ) 3.5
Rationale: "speed = 180 * 5 / 18 = 50 m / sec time taken = 175 / 50 = 3.5 sec . answer : e"
Answer: e
Problem: 80 % of the population of a village is 64000 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 80000 , d ) 29973 , e ) 12312
Rationale: "x * ( 80 / 100 ) = 64000 x = 800 * 100 x = 80000 answer : c"
Answer: c
Problem: the sum of 33 consecutive integers is 3333 . what is the greatest integer in the set ?
Options: a ) 113 , b ) 115 , c ) 117 , d ) 119 , e ) 121
Rationale: "let x be the first integer in the set , then x + 32 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 32 ) = 33 x + 32 * 33 / 2 = 33 ( x + 16 ) then x + 16 = 101 x = 85 the largest integer in the set is 85 + 32 = 117 the answer is c ."
Answer: c
Problem: the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ?
Options: a ) 128 cm 2 , b ) 36.0 cm 2 , c ) 105 cm 2 , d ) 25 cm 2 , e ) 135 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 5.0 * 42 / 2 = 105 cm 2 answer : c"
Answer: c
Problem: find the probability that the number drawn is a factor of 50 .
Options: a ) 1 / 25 , b ) 1 / 50 , c ) 3 / 25 , d ) 3 / 50 , e ) 7 / 50
Rationale: "the factors of 50 are 1 , 2 , 5 , 10 , 25 , 50 therefore , required probability = 6 / 100 = 3 / 50 . answer : d"
Answer: d
Problem: company c sells a line of 20 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000
Rationale: the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b .
Answer: b
Problem: the total age of a and b is 12 year more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 24 , c ) data inadequate , d ) none of these , e ) 34
Rationale: "solution ( a + b ) - ( b + c ) = 12 ⇔ a - c = 12 . answer a"
Answer: a
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 867 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 19 m
b ) 17 m
c ) 10 m
d ) 12 m
e ) 18 m
Rationale: answer : option b explanation : let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 867 3 b 2 = 867 b 2 = 289 = 172 ( b > 0 ) b = 17 m . answer : option b
Answer: b
Problem: in a fuel station the service costs $ 1.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 293.85 $ , e ) 312.12 $
Rationale: "service cost of 3 van and 2 truck = 1.05 * ( 3 + 2 ) = 5.25 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.6 = 288.6 total cost = fuel + service = 288.6 + 5.25 = 293.85 answer is d"
Answer: d
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 34 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 136
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 34 / 100 40 x + 700 = 34 x + 1220 6 x = 820 x = 136 lts correct option : e"
Answer: e
Problem: a car runs 375 km in 3 hours . what ' s the car ' s speed ?
Options: a ) 124 , b ) 125 , c ) 126 , d ) 127 , e ) none
Rationale: solution : 375 ÷ 3 = 125 answer b
Answer: b
Problem: two men a and b working together complete a piece of work which it would have taken them respectively 12 and 18 days to complete if they worked separately . they received rs . 149.25 as their payment . find the share of a in the amount they received ?
Options: a ) rs . 89.55 , b ) rs . 59.70 , c ) rs . 85.56 , d ) rs . 88.56 , e ) none of these
Rationale: lcm of 12 and 18 is 36 no of untits of a is 3 units no of units of b is 2 units then 5 - - > 149.25 3 - - - > ? ( 3 * 149.25 ) / 5 = 89.55 answer : a
Answer: a
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 1 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 4 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 1 - - > e : l = 3 : 1 = 12 : 4 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 4 : 9 . answer : b ."
Answer: b
Problem: the compound ratio of 7 : 6 , 3 : 2 and 4 : 5 ?
Options: a ) 7 : 5 , b ) 1 : 87 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: 7 / 6 * 3 / 2 * 4 / 5 = 7 / 5 7 : 5 answer : a
Answer: a
Problem: how many times digit 5 is used while writing numbers from 1 to 500 ?
Options: a ) 103 , b ) 98 , c ) 94 , d ) 105 , e ) 100
Rationale: "in 1 to 100 there are 20 in 100 to 200 there are 20 in 200 to 300 there are 20 in 300 to 400 there are 20 in 400 to 500 there are 20 so total is 100 correct option : e"
Answer: e
Problem: there are 50 students in a class . if 14 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 129 , e ) 11
Rationale: "number of students absent on a particular day = 14 % of 50 i . e . , 14 / 100 × 50 = 7 therefore , the number of students present = 50 - 7 = 43 students . answer : a"
Answer: a
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 31 kmph . of how many minutes does the train stop per hour ?
Options: a ) 18.6 , b ) 27 , c ) 12 , d ) 121 , e ) 28
Rationale: "explanation : t = 14 / 45 * 60 = 18.6 answer : option a"
Answer: a
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 2 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 15 , c ) 17 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 2 breaks = . 3 / 2 = . 15 hrs = 15 m so answer is b ) 15 mins"
Answer: b
Problem: 5358 x 71 = ?
Options: a ) 273762 , b ) 283758 , c ) 383298 , d ) 273258 , e ) 380418
Rationale: "e 5358 x 71 = 5358 x ( 70 + 1 ) = 5358 x 50 + 5358 x 1 = 375060 + 5358 = 380418"
Answer: e
Problem: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 1 km / h , how many hours will the swimmer take to swim against the current for 6 km ?
Options: a ) 1.2 , b ) 1.4 , c ) 1.6 , d ) 1.8 , e ) 2
Rationale: the swimmer can swim against the current at a speed of 4 - 1 = 3 km / h . the time it will take is 6 / 3 = 2 hours . the answer is e .
Answer: e
Problem: in a group of 90 students , 30 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 33 , d ) 27 , e ) 31
Rationale: "number of students taking history = h = 30 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 90 - 59 = 31 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 30 + 32 + 31 - x or x = 3 now , number of students taking only history will be h - x or 36 - 3 = 33 answer : - c"
Answer: c
Problem: calculate how long it will take a swimmer to swim a distance of 12 km against the current of a river which flows at 1.2 km / hr , given that he can swim in still water at 5 km / h
Options: a ) 3.26 , b ) 3.16 , c ) 2.34 , d ) 3.98 , e ) 3.17
Rationale: "swim in still water at = 5 speed of river = 1.2 us = 5 - 1.2 = 3.8 distance = 12 t = 12 / 3.8 = 3.16 answer : b"
Answer: b
Problem: the ratio of the volumes of two cubes is 1331 : 2197 . what is the ratio of their total surface areas ?
Options: a ) 121 : 169 , b ) 169 : 122 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 1331 : 3 √ 2197 = 11 : 13 ratio of surface areas = 11 ^ 2 : 13 ^ 2 = 121 : 169 answer : option a"
Answer: a
Problem: find the value of ( 100 + 20 / 90 ) × 90
Options: a ) 4520 , b ) 9100 , c ) 9150 , d ) 8120 , e ) 9020
Rationale: "( 9000 + 20 ) / 90 * 90 = 9020 answer : e"
Answer: e
Problem: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 112 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 125 , d ) 267 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 112 x = 125 answer : c"
Answer: c
Problem: a train which has 500 m long , is running 100 kmph . in what time will it cross a person moving at 10 kmph in same direction ?
Options: a ) 20 sec , b ) 25 sec , c ) 30 sec , d ) 35 sec , e ) 40 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 500 / ( ( 100 - 10 ) ( 5 / 18 ) = 500 / 90 * ( 5 / 18 ) = 500 / 25 = 20 sec answer : a"
Answer: a
Problem: how many multiples of 3 are there between 15 and 246 ?
Options: a ) 128 , b ) 94 , c ) 89 , d ) 76 , e ) 60
Rationale: "it should be mentioned whether 15 and 246 are inclusive . if 15 and 246 are inclusive , then the answer is ( 246 - 15 ) / 3 + 1 = 78 . if 15 and 246 are not inclusive , then the answer is ( 243 - 18 ) / 3 + 1 = 76 . since oa is d , then we have not inclusive case ."
Answer: d
Problem: the area of a square land is a square feet and the perimeter is p feet . if 5 a = 10 p + 45 , what is the perimeter of the land , in feet ?
Options: a ) 18
b ) 56
c ) 40
d ) 36
e ) 64
Rationale: you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with b you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 5 a = 10 p + 45 or a = 2 p + 9 - - > eliminate b and e now pick d ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking d indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )
Answer: d
Problem: a cube of edge 16 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 13.65 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 16 * 16 * 16 cm ^ 3 rise in water level = volume / area = 16 * 16 * 16 / 20 * 15 = 13.65 cm answer is c"
Answer: c
Problem: find the value of ( 45 + 23 / 89 ) × 89
Options: a ) 4028 , b ) 4026 , c ) 4248 , d ) 4538 , e ) 9028
Rationale: "= ( 45 + 23 / 89 ) × 89 = ( 4005 + 23 ) / 89 × 89 = 4028 / 89 × 89 = 4028 answer is a ."
Answer: a
Problem: the average age of father and his two sons is 24 years . 5 years ago , the average age of the two sons was 15 years . if the difference between the ages of the two sons is 4 years , what is the present age of the father ?
Options: a ) 45 , b ) 32 , c ) 47 , d ) 48 , e ) 49
Rationale: the total present age of father and two sons is 3 x 24 = 72 yrs the total present age of sons is ( 15 + 5 ) x 2 = 40 years so , present age of father is 72 â € “ 40 = 32 yrs answer b
Answer: b
Problem: a caterer ordered 225 ice - cream bars and 125 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.52 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: let price of a sundae = s price of ice cream bar = . 6 $ 225 * . 6 + 125 * s = 200 = > 125 * s = 65 = > s = 0.52 answer a
Answer: a
Problem: what is the remainder when 3 ^ 26 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 26 has the form 4 k + 2 , so the units digit of 3 ^ 26 is 9 . the remainder when dividing by 5 is 4 . the answer is e ."
Answer: e
Problem: 15.06 * 0.00001 = ?
Options: a ) 15060000 , b ) 0.0001506 , c ) 0.01506 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 7 digits should be there . option b"
Answer: b
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 50 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220050
Rationale: "( 555 + 445 ) * 2 * 110 + 50 = 220000 + 50 = 220050 e"
Answer: e
Problem: if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 5 have ?
Options: a ) 30 , b ) 40 , c ) 45 , d ) 50 , e ) 56
Rationale: when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is a . 5 * 6 = 30
Answer: a
Problem: if 20 % of a number = 300 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 1800 , e ) 1820
Rationale: "let the number x . then , 20 % of x = 300 x = ( 300 * 100 ) / 20 = 1500 120 % of x = ( 120 / 100 * 1500 ) = 1800 . answer : d"
Answer: d
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 5 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 3 , e ) 5 / 2
Rationale: "b work 1 / 8 * 5 = 5 / 8 remaining work = 1 - 5 / 8 = 3 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take remaining work is done in = 8 / 3 * 1 / 4 = 2 / 3 days answer : b"
Answer: b
Problem: a contractor undertook to do a certain piece of work in 6 days . he employed certain number of men , but 5 of them being absent from the very first day , the rest could finish the work in 10 days . the number of men originally employed were :
Options: a ) 12 , b ) 10 , c ) 13 , d ) 11 , e ) none of these
Rationale: explanation : let there be x men at the beginning . less men , more days ( indirect proportion ) 12 : 6 : : x : ( x - 5 ) 12 ( x - 5 ) = 6 x < = > 6 x = 60 x = 10 answer : b
Answer: b
Problem: a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 7 points if you must draw exactly 5 “ low ” cards ?
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 6 ! / 5 ! which represents ( 6 * 5 * 4 * 3 * 2 * 1 ) / ( 5 * 4 * 3 * 2 * 1 ) which simplifies to just 6 , giving you answer a ."
Answer: a
Problem: one gear of pulley rotates at a speed of 3 rev / sec another gear roates at 5 rev / sec . if both start together after how many seconds will they be together again
Options: a ) 3 sec , b ) 5 sec , c ) 15 sec , d ) 20 sec , e ) 25 sec
Rationale: 3 rotates 3 , 6,9 , 12,15 5 rotates 5 , 10,15 ans is 15 answer : c
Answer: c
Problem: a group of n students can be divided into equal groups of 3 with 1 student left over or equal groups of 6 with 1 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 46 , c ) 49 , d ) 53 , e ) 86
Rationale: "3 x + 1 = 6 y + 1 . . . . . . . . . . . ie : 3 x - 6 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = 4 and thus n = 13 if y = 4 thus x is = 8 and thus n = 25 13 + 25 = 38 e"
Answer: e
Problem: one type of liquid contains 10 % of water and the second type of liquid contains 15 % of water . a glass is filled with 5 parts of 1 st liquid and 2 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?
Options: a ) 5.6 % , b ) 11.4 % , c ) 15.6 % , d ) 21.3 % , e ) 18.9 %
Rationale: "required percentage = ( 10 % of 5 + 15 % of 2 ) / 5 + 2 * 100 = 0.8 / 7 * 100 = 11.4 % answer is b"
Answer: b
Problem: a cylindrical can has a radius of 3 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi
b ) 64 pi
c ) 96 pi
d ) 144 pi
e ) 576 pi
Rationale: they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 24 = 144 pi answer is d .
Answer: d
Problem: mala and usha shared their water from a bottle . if mala and usha both drank for the same amount of time , but usha only drank 2 / 10 of the total bottle , what was the ratio of mala and usha speed ?
Options: a ) 1 : 4 , b ) 2 : 5 , c ) 4 : 1 , d ) 3 : 5 , e ) 2 : 3
Rationale: the answer is suppose to be c . 4 : 1 . it ' s from the gmatprep answer : option c
Answer: c
Problem: the floor of a rectangular room is 18 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 126 m 2 , c ) 136 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 22 ã — 16 = 352 m 2 area of the inner rectangle = 18 ã — 12 = 216 m 2 required area = ( 352 â € “ 216 ) = 136 m 2 answer c"
Answer: c
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 84 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 24
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 84 thus m = 672 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 672 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 24 ans : e"
Answer: e
Problem: a box contains 21 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) 31 / 88
Rationale: "solution p ( none is defective ) = 17 c 2 / 21 c 2 = 57 / 88 . p ( at least one is defective ) = ( 1 - 57 / 88 ) = 31 / 88 . answer e"
Answer: e
Problem: p , q and r together earn rs . 1710 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 40 , b ) s . 60 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1710 / 9 = 190 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 190 = 60 = > amount earned by r in 1 day = 60 answer : option b"
Answer: b
Problem: simple interest on a certain sum at a certain annual rate of interest is 1 / 9 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 5 , b ) 8 , c ) 3 1 / 3 , d ) 2 2 / 3 , e ) none of these
Rationale: explanation : let sum = x . then , s . i . = x / 9 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 9 ? r ^ 2 = 100 / 9 r = 10 / 3 = 3 1 / 3 . hence , time = 3 1 / 3 % . answer : c
Answer: c
Problem: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 32 . find the profit percentage ?
Options: a ) 80 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 60 %
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 160 ( 32 * 5 ) profit percentage = ( 160 - 100 ) / 100 * 100 = 60 % answer : e"
Answer: e
Problem: a fraudulent dairy guy declares to market his dairy at price range but he combined it with water and therefore benefits 25 % . the percentage of water in the combination is :
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 35 % , e ) 60 %
Rationale: explanation : - > if capability price of 1 l of milk = rs . 1 and s . price of 1 l of combination = rs . 1 benefits = 20 % capability price of 1 l of combination = [ ( 100 / 100 + 25 ) * 1 ] = rs . 100 / 125 = rs . 4 / 5 - > from the rule of allegation i . capability price of 1 l of water = 0 ii . capability price of 1 l of milk = 1 iii . ( p ) = 4 / 5 iv . d – m = 1 – 4 / 5 = 1 / 5 v . m – c = 4 / 5 – 0 = 4 / 5 ratio of milk to water = 4 / 5 : 1 / 5 = 4 : 1 % of water in the combination = ( 1 / 5 x 100 ) % = 20 % answer : a
Answer: a
Problem: 49 ã — 49 = 7 ^ ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) none of these
Rationale: 49 ã — 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) = 7 ? or 7 ( 4 ) = 7 ? or , ? = 4 answer a
Answer: a
Problem: a batsman in his 12 th inning makes a score of 60 and their by increasing his average by 4 . what is his average after the 12 th inning ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "11 x + 60 = 12 ( x + 4 ) x = 12 + 4 = 16 answer : b"
Answer: b
Problem: find the ones digit of 73 ^ 351
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 351 will be the same as the units digit of 3 ^ 351 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 351 = 348 + 3 = ( multiple of 4 ) + 3 , then the units digit of 3 ^ 351 will be the third number in the pattern thus 7 . answer : d ."
Answer: d
Problem: 5 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 66 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 30 , e ) 45
Rationale: let number is x . when 5 added to it , = ( x + 5 ) 7 multiplied to sum , = 7 * ( x + 5 ) now , = [ { 7 * ( x + 5 ) } / 5 ] and , = [ { 7 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 66 [ ( 7 x + 35 ) / 5 ) = 33 + 5 7 x + 35 = 38 * 5 x = 155 / 7 x = 22.14 = 22 so , required number is : 22 . answer : c
Answer: c
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 17 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 30.22 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 65.23
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 17 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 17 solve for x x = $ 30.22 correct answer b"
Answer: b
Problem: if a trader sold two cars each at rs . 325475 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 ) 1.74 % , c ) 1.84 % , d ) 1.97 % , e ) 2.25 %
Rationale: "sp of each car is rs . 325475 , 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 % = 1.44 % answer : e"
Answer: e
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 5 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 487 , c ) 481 , d ) 729 , e ) 600
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 5 = 480 answer : e"
Answer: e
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 60 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 50 , b ) 75 , c ) 92 , d ) 136 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 60 - 40 ) / ( 40 - 36 ) = 20 / 4 = 5 / 1 = number of microtron stocks / number of dynaco stocks so for every 5 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 5 ) th i . e . 300 / 6 = 50 must be dynaco stock . answer ( a )"
Answer: a
Problem: in township k , 1 / 5 of the housing units are equipped with cable television . if 1 / 10 of the housing units , including 1 / 3 of those that are equipped with cable television , are equipped with videocassette recorders , what fraction of the housing units have neither cable television nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: let total housing units = 5 x . as per question , equipped with cable tv = x equipped with vcr = x / 2 , which includes x / 3 ctv . so , only vcr = x / 2 - x / 3 = x / 6 . so , cable tv + vcr = x + x / 6 = 7 x / 6 no cable tv and vcr = 5 x - 7 x / 6 = 23 x / 6 . fraction = 23 x / ( 6 * 5 x ) = 23 / 30 . hence , a
Answer: a
Problem: every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` hen ' ' ?
Options: a ) 69 , b ) 72 , c ) 75 , d ) 78 , e ) 81
Rationale: "` ` hen ' ' = ( 8 + 5 + 14 ) * 3 = 81 . the answer is e ."
Answer: e
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 16 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 27 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 16 ) ( 3 / 2 ) = 24 minutes at the gym , and 24 + 16 = 40 minutes exercise , so ( 2 / 3 ) ( 40 ) = 27 minutes yoga . answer : c"
Answer: c
Problem: a cistern which could be filled in 8 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 90 hrs , e ) 40 hrs
Rationale: "1 / 8 - 1 / x = 1 / 10 = > 40 hrs answer : e"
Answer: e
Problem: a train travels from new york to chicago , a distance of approximately 270 miles , at an average rate of 30 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 10 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 270 / 30 = 9 hours . therefore , the train depart from new york at 7 : 00 - 9 hours = 10 : 00 in the morning , new york time . answer : c ."
Answer: c
Problem: in a certain pond , 35 fish were caught , tagged , and returned to the pond . a few days later , 35 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 875 , d ) 2500 , e ) 10 000
Rationale: "if x is total number of fish in the pond : 4 = 35 / x * 100 = > x = 875 so answer is c"
Answer: c
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 9 years . what is the sum ?
Options: a ) 42315 , b ) 42877 , c ) 44625 , d ) 38925 , e ) 22887
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 9 ) = rs . 44625 . answer : c"
Answer: c
Problem: average expenditure of a person for the first 3 days of a week is rs . 320 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 ) 360 , e ) none
Rationale: explanation : assumed mean = rs . 320 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 . 320 + rs . 40 = rs . 360 correct option : d
Answer: d
Problem: a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 30 percent , what is the discount rate on mysteries ?
Options: a ) 17.18 % , b ) 12 % , c ) 13 % , d ) 14 % , e ) 15 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.30 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.1718 = 17.18 a"
Answer: a
Problem: three numbers are in the ratio 2 : 3 : 5 and their average is 50 . the largest number is :
Options: a ) 30 , b ) 75 , c ) 27 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be 2 x , 3 x and 5 x , then , ( 2 x + 3 x + 5 x ) / 3 = 50 = > 10 x = 150 = > x = 15 . largest number 5 x = 5 * 15 = 75 answer : b"
Answer: b
Problem: in a certain school , the ratio of boys to girls is 5 to 13 . if there are 64 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 40 , c ) 45 , d ) 72 , e ) 117
Rationale: the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 64 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 64 . so 1 part corresponds to 64 / 8 = 8 and so 5 parts correspond to 5 * 8 = 40 . b
Answer: b
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 3 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 193
Rationale: "by the question , the equation would be 150 p - 83 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 193 . answer e for me ."
Answer: e
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 630 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 42 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 630 / 7 + 8 = 42 sec answer is c"
Answer: c
Problem: calculate the sum of first 60 natural numbers .
Options: a ) 1839 , b ) 2830 , c ) 1830 , d ) 1831 , e ) 1835
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 60 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 60 ) = ( 60 × 61 / 2 ) = 1830 . answer c"
Answer: c
Problem: buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of goats ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 2 goats answer : b
Answer: b
Problem: a batsman makes a score of 85 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 35
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 85 = 11 x x = 85 - 50 = 35 answer is e"
Answer: e
Problem: each of the three people individually can complete a certain job in 3 , 4 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 1 / 3 , b ) 9 / 20 , c ) 8 / 15 , d ) 5 / 12 , e ) 2 / 3
Rationale: the two slowest people work at rates of 1 / 4 and 1 / 6 of the job per hour . the sum of these rates is 1 / 4 + 1 / 6 = 5 / 12 of the job per hour . the answer is d .
Answer: d
Problem: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 80 per kg ?
Options: a ) 5 : 8 , b ) 4 : 7 , c ) 4 : 3 , d ) 9 : 5 , e ) 9 : 8
Rationale: ( 96 - 80 ) / ( 80 - 68 ) = 16 / 12 = 4 / 3 answer : c
Answer: c
Problem: if a man lost 4 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 2 , e ) 1
Rationale: "96 % - - - - 12 144 % - - - - ? 96 / 144 * 12 = 8 answer a"
Answer: a