regisss/math_qa huggingface dataset:
Problem: john purchased 1365 large bottles at $ 1.89 per bottle and 720 small bottles at $ 1.42 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.73 , e ) $ 1.76
Rationale: ( 1365 * 1.89 + 720 * 1.42 ) / ( 1365 + 720 ) = ~ 1.73 option ( d )
Answer: d
Problem: a train 100 meters long completely crosses a 300 meters long bridge in 15 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 96 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 45 = 400 / 15 * 18 / 5 = 96 answer : b"
Answer: b
Problem: ( 500 + 200 + 100 ) ã — 4 ã — ( 3 + 4 ) = ?
Options: a ) 52000 , b ) 32400 , c ) 22400 , d ) 22800 , e ) 24200
Rationale: "( 500 + 200 + 100 ) ã — 4 ã — ( 3 + 4 ) = ? or , ? = 800 ã — 4 ã — 7 = 22400 answer c"
Answer: c
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent e ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . e = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Problem: if the wheel is 10 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 16.8 , b ) 26 , c ) 14 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 10 * x = 1056 = > x = 16.8 answer : a"
Answer: a
Problem: the perimeter of a semi circle is 126 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 98 , d ) 24.5 , e ) 13
Rationale: "36 / 7 r = 126 = > r = 24.5 answer : d"
Answer: d
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 15 kmph . what time will they take to be 50 km apart ?
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: "to be ( 10 + 15 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 25 * 50 = 2 hrs answer is b"
Answer: b
Problem: r is the set of positive even integers less than 101 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 101 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , 36 , 64 , and 100 are even integers ( less than 101 ) that are in both sets . solution : five answer : d"
Answer: d
Problem: a fill pipe can fill 1 / 4 of cistern in 16 minutes in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 48 min , b ) 36 min , c ) 25 min , d ) 30 min , e ) 50 min
Rationale: "1 / 4 of the cistern can fill in 16 min 3 / 4 of the cistern can fill in = 16 * 4 * 3 / 4 = 48 min answer is a"
Answer: a
Problem: how many three digit numbers e are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples e - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 35 % and its breadth is decreased by 21 % ?
Options: a ) 4.65 % increase , b ) 5.65 % increase , c ) 6.65 % increase , d ) 6.65 % decrease , e ) 7.65 % increase
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 35 % = 135 b decrease by 21 % = 79 135 * 79 = 10665 6.65 % increase answer : c"
Answer: c
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 3 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 56.6 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 3 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 3 or 45 * 18 - 45 * x + 36 * x = 3 * 100 or 9 x = - 3 * 100 + 45 * 18 x = 510 / 9 = 56.6 % b"
Answer: b
Problem: a and b began business with rs . 2000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 455 , e ) 361
Rationale: "( 2 * 8 + 1 * 4 ) : ( 4 * 8 + 5 * 4 ) 5 : 13 13 / 18 * 630 = 455 answer : d"
Answer: d
Problem: if 70 % of a number exceeds 28 % of it by 39.9 , then find the number ?
Options: a ) 65 , b ) 67 , c ) 100 , d ) 95 , e ) 33
Rationale: "use the elimination method to find the correct option . of all the options only 95 fits 70 % of 95 = 66.5 28 % of 95 = 26.6 66.5 - 26.6 = 39.9 required number is 95 . answer : d"
Answer: d
Problem: 40 onions on a scale weigh 7.68 kg . when 5 onions are removed from the scale , the average weight of the 35 onions is 190 grams . what is the average weight ( in grams ) of the 5 onions which were removed ?
Options: a ) 200 , b ) 202 , c ) 204 , d ) 206 , e ) 208
Rationale: "35 * 190 = 6650 . the other 5 onions weigh a total of 1030 grams . the average weight is 1030 / 5 = 206 grams . the answer is d ."
Answer: d
Problem: evaluate : 6402.5 + 640.25 + 64.025 + 6.4025 + 0.64025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 7113.81775 , e ) 6891.59775
Rationale: "6402.5 640.25 64.025 6.4025 + 0.64025 - - - - - - - - - - - - - - - 7113.81775 answer is d ."
Answer: d
Problem: mudit ' s age 16 years hence will be thrice his age 4 years ago . find mudit ' s present age ?
Options: a ) 14 , b ) 19 , c ) 27 , d ) 18 , e ) 15
Rationale: explanation : let mudit ' s present age be ' m ' years . m + 16 = 3 ( m - 4 ) = > 2 m = 28 = > m = 14 years . answer : a
Answer: a
Problem: the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1540 respectively . what is the rate of interest ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: 1540 - 1400 = 140 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 140 ) / ( 1400 ) = 10 % the answer is e .
Answer: e
Problem: on a certain planet where people usually tend to live for more than a century , the ratio of present ages of father and son is 7 : 4 . 10 years later , the ratio of their ages will be 5 : 3 . what is the sum of their present ages ?
Options: a ) 220 , b ) 200 , c ) 140 , d ) 80 , e ) 60
Rationale: the ratio of present ages of father and son is 7 : 4 , so suppose the present ages are 7 x and 4 x , respectively . 10 years later , the ages of father and son , respectively , shall be 7 x + 10 and 4 x + 10 . the ratio of ages 10 years later is given to be 5 : 3 . this means ( 7 x + 10 ) / ( 4 x + 10 ) = 5 / 3 solving we get x = 20 . so present age of father is 7 x = 140 and present age of son is 4 x = 80 . the sum of present ages is thus 220 . ans a
Answer: a
Problem: a certain candy manufacturer reduced the weight of candy bar m by 40 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?
Options: a ) 66.66 , b ) 62.5 , c ) 58 , d ) 60 , e ) 62
Rationale: "assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.6 oz new price of candy = 1 / 0.6 = 1.6666 price increase 66.66 % a"
Answer: a
Problem: weights of two friends ram and shyam are in the ratio 1 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: solution : given ratio of ram and shayam ' s weight = 1 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 1 / 5 or , x = 16 % . answer : option d
Answer: d
Problem: the average of first 20 prime numbers is ?
Options: a ) 9.5 , b ) 8.6 , c ) 9.3 , d ) 9.6 , e ) 9.8
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 / 8 = 77 / 8 = 9.6 ( approx ) answer is d"
Answer: d
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = − 2 , y = 1 , and z = 4 ?
Options: a ) 20 , b ) 24 , c ) 30 , d ) 32 , e ) 48
Rationale: "4 * 1 * 4 - ( - 2 * 1 * 16 ) = 16 + 32 = 48 ans : e"
Answer: e
Problem: a train of 35 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 9 , e ) 3.6
Rationale: "d = 35 * 60 + 1500 = 3600 m t = 3600 / 60 * 18 / 5 = 216 sec = 3.6 mins answer : e"
Answer: e
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent q of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before q = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Problem: the difference of two numbers is 11 and one - fifth of their sum is 9 . find the numbers
Options: a ) 28,22 , b ) 28,17 , c ) 27,17 , d ) 26,17 , e ) 28,19
Rationale: if two numbers are x , y x - y = 11 - - ( i ) & ( x + y ) / 5 = 9 - - ( ii ) solving ( i ) & ( ii ) , x = 28 , y = 17 answer : b
Answer: b
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 18000 left with him . find salary . .
Options: a ) $ 10800 , b ) $ 18000 , c ) $ 180000 , d ) $ 1800 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 18000 , = [ 1 - 9 / 10 ] * total salary = $ 18000 , total salary = $ 18000 * 10 = $ 180000 , correct answer ( c )"
Answer: c
Problem: bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 12 left in his pocket . what was the value of n ?
Options: a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer b if he had 44 , then he spent 11 at hardware store now he was left with 33 $ he spent 9 dollars on cleaning , thus he remained with 24 $ he then spent 1 / 2 of 24 , or 12 , and was left with 12 . hence , the only option that can be right is b"
Answer: b
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 3520 cm is ?
Options: a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 40
Rationale: "2 * 22 / 7 * 14 * x = 3520 = > x = 40 answer : e"
Answer: e
Problem: what will be the compound interest on a sum of rs . 15000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.22 , b ) s . 5823.20 , c ) s . 9123.20 , d ) s . 7256.20 , e ) s . 6073.92
Rationale: "explanation : amount = [ 15000 * ( 1 + 12 / 100 ) 3 ] = 15000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 35123.20 - 15000 ) = rs . 6073.92 answer : e"
Answer: e
Problem: if 13 = 13 w / ( 1 - w ) , then ( w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 3
Rationale: 13 - 13 w = 13 w 26 w = 13 w = 1 / 2 2 w * 2 = 1 / 2 * 2 = 1 answer : c
Answer: c
Problem: on dividing 15968 by a certain number , the quotient is 89 and the remainder is 37 . find the divisor .
Options: a ) 170 , b ) 179 , c ) 37 , d ) 67 , e ) 32
Rationale: "divisor = ( dividend – remainder / quotient ) = ( 15968 - 37 ) / 89 = 179 answer b 179"
Answer: b
Problem: 58 , 52 , 46 , 40 , 34 , . . . ?
Options: a ) 20 , b ) 22 , c ) 28 , d ) 27 , e ) 32
Rationale: "each number is 6 less than the previous number . 58 - 6 = 52 52 - 6 = 46 46 - 6 = 40 40 - 6 = 34 34 - 6 = 28 answer : c"
Answer: c
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 4 times , what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 1 / 16 , e ) 1 / 32
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 16 answer : d
Answer: d
Problem: if rs . 460 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) rs . 575 , b ) rs . 595 , c ) rs . 590 , d ) rs . 580 , e ) rs . 585
Rationale: "80 = ( 460 * 4 * r ) / 100 r = 4.34 % i = ( 460 * 6 * 4.34 ) / 100 = 120 460 + 120 = 580 answer : d"
Answer: d
Problem: a train passes a station platform in 50 sec and a man standing on the platform in 15 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 500 , c ) 550 , d ) 525 , e ) 171
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 15 = 225 m . let the length of the platform be x m . then , ( x + 225 ) / 50 = 15 = > x = 525 m . answer : d"
Answer: d
Problem: a trained covered x km at 70 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22.25 , b ) 99 , c ) 26.25 , d ) 66 , e ) 887
Rationale: "total time taken = x / 70 + 2 x / 20 hours = 4 x / 35 hours average speed = 3 x / ( 4 x / 35 ) = 26.25 kmph answer : c"
Answer: c
Problem: a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :
Options: a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881
Rationale: answer : c ) 1200
Answer: c
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 420 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "3 x = 420 x = 140 therefore , the salesman sold 140 kg in the morning and 2 ⋅ 140 = 280 kg in the afternoon . so answer is d ."
Answer: d
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1000 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 20625 , e ) none of these
Rationale: solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1000 × 20.625 ) = 20625 . answer d
Answer: d
Problem: the probability that a can solve the problem is 2 / 3 and b can solve it is 3 / 4 . if both of them attemp the problem , then what is the probability that the problem get solved ?
Options: a ) 9 / 12 , b ) 10 / 12 , c ) 11 / 12 , d ) 1 , e ) 2
Rationale: explanation : the event is defined as : a solves the problem and b does not solve the problem or a does n ' t solve the problem and b solves the problem or a solves the problem and b solves the problem numerically this is equivalent to : ( 2 / 3 ) x ( 1 / 4 ) + ( 1 / 3 ) x ( 3 / 4 ) + ( 2 / 3 ) x ( 3 / 4 ) = 11 / 12 answer : c
Answer: c
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 11 days . c alone will finish the job in
Options: a ) 41.25 days , b ) 30.25 days , c ) 60.25 days , d ) 71.25 days , e ) 51.25 days
Rationale: explanation : 11 = ( 15 * x ) / ( 15 + x ) 165 + 11 x = 15 x 4 x = 165 x = 41.25 answer : option a
Answer: a
Problem: on a map , 1 inch represents 28 miles . how many x xxinches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "x inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Problem: tim has 13 10 - dollar bills , 11 5 - dollar bills , and 17 one - dollar bills . if tim needs to pay exactly $ 128 , what is the least number of bills he will need to use ?
Options: a ) 68 , b ) 66 , c ) 565 , d ) 16 , e ) 35
Rationale: 128 is the total sum of money . as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils 128 - 120 = 8 so now we need to get 8 from either 5 dollar bills or 1 dollar bills 8 - 5 ( use only 1 5 dollar bill ) = 3 so we can get 3 from using 3 $ 1 bills . hence 16 ( 12 + 1 + 3 ) answer is d
Answer: d
Problem: if in a race of 130 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 26 m , c ) 11 m , d ) 10 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 130 * 5 ) / 25 = 26 m hence , a beats b by 26 m . answer b"
Answer: b
Problem: the average of 10 consecutive integers is 25 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 19 , b ) 19.5 , c ) 20 , d ) 20.5 , e ) 21
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is d ."
Answer: d
Problem: if 0.75 : x : : 5 : 11 , then x is equal to :
Options: a ) 1.12 , b ) 1.65 , c ) 1.2 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 11 ) x = 8.25 / 5 = 1.65 answer : b"
Answer: b
Problem: an empty fuel tank is filled with brand z gasoline . when the tank is 3 / 4 empty , it is filled with brand x gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand x gasoline . at this time , what percent of the gasoline in the tank is brand z ?
Options: a ) 41 % , b ) 42 % , c ) 43 % , d ) 43.75 % , e ) 44 %
Rationale: "work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 2 3 rd step : brand z is ( 3 / 4 ) * ( 1 / 2 ) + 1 / 2 = 7 / 8 4 th step : brand z is ( 1 / 2 ) * ( 7 / 8 ) = 7 / 16 = 43.75 % answer ( d )"
Answer: d
Problem: there are 9 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 24 , b ) 25 , c ) 28 , d ) 32 , e ) 36
Rationale: "9 c 2 = 36 the answer is e"
Answer: e
Problem: what is the value of â ˆ š 25 % ?
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 45 % , e ) 68 %
Rationale: "explanation : br > â ˆ š 25 % = â ˆ š 25 / â ˆ š 100 = 5 / 10 = 50 / 100 = 50 % correct answer is b ) 50 %"
Answer: b
Problem: in how many years rs 160 will produce the same interest at 8 % as rs . 500 produce in 4 years at 8 %
Options: a ) 13 , b ) 13.5 , c ) 11.5 , d ) 12.5 , e ) 12
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 500 , time 4 years and rate 8 % , it will be rs . 160 then we can get the time as time = ( 100 * 160 ) / ( 160 * 8 ) = 12.5 option d"
Answer: d
Problem: of 15 applicants for a job , 7 had at least 4 years ' experience , 9 had degrees , and 1 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 2
Rationale: "15 - 1 = 14 14 - 7 - 9 = - 2 then 2 are in the intersection between 4 years experience and degree . answer : e"
Answer: e
Problem: simple interest on a certain sum of money for 5 years at 8 % per annum is half the compound interest on rs . 8000 for 2 years at 15 % per annum . the sum placed on simple interest is
Options: a ) rs . 3225 , b ) rs . 2580 , c ) rs . 8000 , d ) rs . 1290 , e ) none
Rationale: solution c . i . = rs [ 8000 x ( 1 + 15 / 100 ) â ² - 8000 ] rs . ( 8000 x 115 / 100 x 115 / 100 - 8000 ) = rs . 2580 . sum = rs . [ 1290 x 100 / 5 x 8 ] = rs . 3225 . answer a
Answer: a
Problem: for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 80 color copies at print shop y than at print shop x ?
Options: a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140
Rationale: "the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 80 * $ 1.50 = $ 120 the answer is a ."
Answer: a
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,8 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 8 = 16 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 16 = 1 / 2 the answer is c ."
Answer: c
Problem: three cubes of metal whose edges are 9 , 12 and 24 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 28
b ) 77
c ) 66
d ) 18
e ) 25.3
Rationale: 93 + 123 + 243 = a 3 = > a = 25.3 answer : e
Answer: e
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr the distance travelled downstream in 12 minutes is :
Options: a ) 2 km , b ) 2.6 km , c ) 3.6 km , d ) 4 km , e ) none
Rationale: sol . speed downstream = ( 15 + 3 ) kmph = 18 kmph . distance travelled = [ 18 * 12 / 60 ] km = 3.6 km . answer c
Answer: c
Problem: two cubes each with side b are joined to form a cuboids . what is the surface area of this cuboids ?
Options: a ) 12 b ^ 2
b ) 10 b ^ 2
c ) 6 b ^ 2
d ) 4 b ^ 2
e ) 2 b ^ 2
Rationale: l = 2 b ; b = b ; h = b ; surface area = 2 * ( lb + bh + hl ) = 2 * ( 2 b ^ 2 + b ^ 2 + 2 b ^ 2 ) = 10 b ^ 2 answer : b
Answer: b
Problem: bob is attempting to feed his pets . he feeds his pets as follows : - no dog receives more food than any other dog - no cat receives any less food than any other cat - the cats , as a group , receive exactly as much food as a single dog if bob has 7 dogs and 4 cats , approximately what percentage of the food bag does a cat receive ?
Options: a ) 25.0 % , b ) 8.3 % , c ) 3.1 % , d ) 2.7 % , e ) 1.0 %
Rationale: c . each cat gets 1 / 4 as much food as a dog . a dog gets 1 / 8 of the food . 1 / 4 of 1 / 8 is 1 / 32 , which is about 3.1 % , so the answer is c .
Answer: c
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) 2 , c ) - 2 , d ) 1 , e ) - 10
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , 7 ) should satisfy the equation . hence x = t and y = 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( 7 - 5 ) / ( 4 - 2 ) = 1 imo option d is correct answer ."
Answer: d
Problem: what is the least number of square tiles required to pave the floor of a room 11 m 50 cm long and 1 m 50 cm broad ?
Options: a ) 724 , b ) 804 , c ) 69 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1150 cm & 150 cm = 50 cm . area of each tile = ( 50 x 50 ) cm 2 ∴ required number of tiles = [ 1150 x 150 / 50 x 50 ] = 69 . answer c"
Answer: c
Problem: in a cricket match , 5 batsmen a , b , c , d and e scored an average of 36 runs . d scored 5 more than e ; e scored 8 fewer than a ; b scored as many as d and e combined ; and b and c scored 107 between them . how many runs did e score ?
Options: a ) 62 , b ) 45 , c ) 28 , d ) 20 , e ) 25
Rationale: explanation : total runs scored = ( 36 x 5 ) = 180 . let the runs scored by e be x . then , runs scored by d = x + 5 ; runs scored by a = x + 8 ; runs scored by b = x + x + 5 = 2 x + 5 ; runs scored by c = ( 107 - b ) = 107 - ( 2 x + 5 ) = 102 - 2 x . so , total runs = ( x + 8 ) + ( 2 x + 5 ) + ( 102 - 2 x ) + ( x + 5 ) + x = 3 x + 120 . therefore 3 x + 120 = 180 3 x = 60 x = 20 . answer : option d
Answer: d
Problem: a property decreases in value every year at the rate of 6 1 / 4 % of its value at the beginning of the year its value at the end of 3 years was rs . 21093 . find its value at the beginning of the first year ?
Options: a ) 25600.24 , b ) 25600.27 , c ) 25600.28 , d ) 25600.21 , e ) 25600.29
Rationale: 6 1 / 4 % = 1 / 16 x * 15 / 16 * 15 / 16 * 15 / 16 = 21093 x = 25600.24 answer : a
Answer: a
Problem: the speed at which a man can row a boat in still water is 24 kmph . if he rows downstream , where the speed of current is 8 kmph , what time will he take to cover 40 metres ?
Options: a ) 4.49 seconds , b ) 8.89 seconds , c ) 26 seconds , d ) 12 seconds , e ) 16 seconds
Rationale: "speed of the boat downstream = 24 + 8 = 32 kmph = 32 * 5 / 18 = 8.89 m / s hence time taken to cover 40 m = 40 / 8.89 = 4.49 seconds . answer : a"
Answer: a
Problem: a manufacturing company has 15 % cobalt , 25 % led and 60 % of copper . if 5 kg of led is used in a mixture how much copper we need to use
Options: a ) 12 kg , b ) 13 kg , c ) 22 kg , d ) 14 kg , e ) 15 kg
Rationale: 25 % = 5 kg 100 % = 20 kg 60 % of 20 kg = 12 kg 12 kg answer : a
Answer: a
Problem: in a simultaneous throw of pair of dice . find the probability of getting the total more than 7 ?
Options: a ) 12 / 5 , b ) 5 / 12 , c ) 6 / 4 , d ) 2 / 3 , e ) 4 / 7
Rationale: "here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option b"
Answer: b
Problem: the smallest number which when diminished by 15 , is divisible 10 , 15 , 25 , 30 and 35 is :
Options: a ) 1008 , b ) 1055 , c ) 1022 , d ) 1032 , e ) 1048
Rationale: "required number = ( l . c . m . of 10 , 15 , 25 , 30 , 35 ) + 15 = 1050 + 15 = 1055 answer : option b"
Answer: b
Problem: the length of the longest tape in cm which can be used to measure exactly , the length 7 m ; 3 m 85 cm ; and 12 m 95 cm is :
Options: a ) 37 , b ) 35 , c ) 34 , d ) 36 , e ) 38
Rationale: "the three lengths in cm are 700 , 385 & 1295 . hcf of 700 , 385 & 1295 is 35 . hence , the answer is 35 cm . answer : b"
Answer: b
Problem: a rectangular box measures internally 1.6 m long , 1 m broad and 60 cm deep . the number of cubical blocks each of edge 20 cm that can be packed inside the box is
Options: a ) 30
b ) 60
c ) 120
d ) 150
e ) none
Rationale: sol . number of blocks = 160 x 100 x 60 20 x 20 x 20 ] = 120 . answer c
Answer: c
Problem: two pipes can fill a tank in 12 minutes and 15 minutes . an outlet pipe can empty the tank in 10 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 12 + v / 15 - v / 10 = 3 v / 60 = v / 20 per minute the tank will be filled in 20 minutes . the answer is a ."
Answer: a
Problem: an article with cost price of 192 is sold at 25 % profit . what is the selling price ?
Options: a ) 198 , b ) 200 , c ) 204 , d ) 240 , e ) 210
Rationale: "sp = 1.25 * 192 = 240 answer : d"
Answer: d
Problem: two pipes a and b can fill a tank in 50 hour and 75 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 15 hrs , b ) 20 hrs , c ) 25 hrs , d ) 30 hrs , e ) 32 hrs
Rationale: part filled by a in 1 hour = 1 / 50 part filled by b in 1 hour = 1 / 75 part filled by a + b in 1 hour = 1 / 50 + 1 / 75 = 1 / 30 both the pipes will together will fill the tank in 30 hours . answer is d
Answer: d
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 7 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 7 c + 3 . the minimum is 3 when c = 0 . the maximum is 45 when c = 6 . there are 7 such numbers . the answer is c ."
Answer: c
Problem: addison high school ’ s senior class has 160 boys and 200 girls . if 75 % of the boys attended the college and 40 % of the girls did not attend the college , what percentage of the total class attended college ?
Options: a ) 35 , b ) 64 , c ) 66.67 , d ) 60 , e ) 84
Rationale: number of boys attending the college : 0.75 * 160 = 120 number of girls not attending the college : 0.40 * 200 = 80 number of girls attending the college : 200 - 80 = 120 total attending = 120 + 120 = 240 total people = 160 + 200 = 360 % of people attending = 240 / 360 = 66.67 % . c is the correct answer
Answer: c
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 600 , b ) $ 700 , c ) $ 800 , d ) $ 900 , e ) $ 1000
Rationale: 0.1 x = 0.08 ( 2000 - x ) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a .
Answer: a
Problem: there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 3432 , then what was the price of the article initially ?
Options: a ) rs . 2000 , b ) rs . 4000 , c ) rs . 3000 , d ) rs . 5000 , e ) rs . 6000
Rationale: "let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 3432 for 114.4 - - - > 100 ; 2288 - - - > ? required price = ( 3432 * 100 ) / 114.4 = 30 * 100 = rs . 3000 . answer : c"
Answer: c
Problem: the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 40 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 16.66 % , e ) 26 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 90 gms because it weighs 10 % less . say , the cost price is $ 90 ( $ 1 / gm ) . since he gets a profit of 40 % , the selling price must be 90 + ( 40 / 100 ) * 90 = $ 126 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 126 , the mark up is simply 26 % . ans : e"
Answer: e
Problem: jaclyn buys $ 60 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 1187.5 , b ) 1234 , c ) 1289 , d ) 1425 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 60000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 1425 answer : d"
Answer: d
Problem: danny obtained 76 , 65 , 82 , 67 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 73
Rationale: average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 . answer : e
Answer: e
Problem: in the land of oz only one or two - letter words are used . the local language has 69 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 138
Rationale: "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 69 letters is 69 ; the number of 2 letter words ( xx ) that can be made from 69 letters is 69 * 69 , since each x can take 69 values . total : 69 + 69 * 69 . similarly : the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . the difference is ( 69 + 69 * 69 ) - ( 68 + 68 * 68 ) = 138 . answer : e ."
Answer: e
Problem: a candidate got 35 % of the votes and lost to the rival by 2400 votes . how many votes were cast ?
Options: a ) 7700 , b ) 8000 , c ) 8300 , d ) 8600 , e ) 8900
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 2400 10 % = 800 100 % of the votes = 8000 answer : b"
Answer: b
Problem: a bag contains 9 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 17 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 7 / 15
Rationale: "drawing two balls of same color from nine green balls can be done in 9 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 9 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 8 / 17 answer : a"
Answer: a
Problem: speed of a boat in standing water is 8 kmph and speed of the stream is 0.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 27.35 hours , b ) 26.35 hours , c ) 25.35 hours , d ) 24.35 hours , e ) 23.35 hours
Rationale: "speed upstream = 7.5 kmph speed downstream = 8.5 kmph total time taken = 105 / 7.5 + 105 / 8.5 = 26.35 hours answer is b"
Answer: b
Problem: a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .
Options: a ) rs . 3168 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 11 / 30 ) ã — 8640 ] = rs . 3168 answer : option a"
Answer: a
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.40 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.26 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.4 = 3 * x - - > x = $ 0.26 . answer : b .
Answer: b
Problem: the largest four - digit number which is a perfect cube , is
Options: a ) 8000
b ) 9261
c ) 9999
d ) none of these
e ) can not be determined
Rationale: solution clearly , 9261 is a perfect cube satisfying the given property . answer b
Answer: b
Problem: a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "sol . let x = 6 q + 3 . then x 2 = ( 6 q + 3 ) 2 = 36 q 2 + 36 q + 9 = 6 ( 6 q 2 + 6 q + 1 ) + 3 . so , when x 2 is divided by 6 , remainder = 3 . answer d"
Answer: d
Problem: the contents of a certain box consist of 40 apples and 30 oranges . how many oranges must be added to the box so that exactly 40 % of the pieces of fruit in the box will be apples ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 30
Rationale: "apple = ( apple + orange + x ) * 0.4 40 = ( 30 + 40 + x ) * 0.4 x = 30 answer : e"
Answer: e
Problem: two numbers are in the ratio 5 : 8 and thier h . c . f is 4 . find the numbers .
Options: a ) 25 and 40 , b ) 20 and 32 , c ) 30 and 48 , d ) 15 and 24 , e ) 16 and 25
Rationale: explanation : let two numbers 5 x , 8 x their h . c . f = 4 therefore h . c . f is 4 i . e , x in this case . therefore the numbers are 5 x 4 = 20 8 x 4 = 32 answer : option b
Answer: b
Problem: a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 60 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 74 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 40 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.4 ) = 0.26 ( which means b would have covered 0.26 of the race length during the time in which a has covered 0.4 of the race length . therefore to win , b needs a headstart of ( 1 - 0.26 = ) 0.74 of the race length . so the answer is e"
Answer: e
Problem: a contract is to be completed in 46 days sad 117 men were said to work 8 hours a day . after 33 days , ( 4 / 7 ) of the work is completed . how many additional men may be employed so that the work may be completed in time , each man now working 9 hours a day ?
Options: a ) 91 , b ) 87 , c ) 85 , d ) 81 , e ) none of them
Rationale: remaining work = ( 1 - ( 4 / 7 ) = ( 3 / 7 ) remaining period = ( 46 - 33 ) days = 13 days let the total men working at it be x . less work , less men ( direct proportion ) less days , more men ( indirect proportion ) more hours per day , less men ( indirect proportion ) work ( 4 / 7 ) : ( 3 / 7 ) days 13 : 33 } : : 117 : x hrs / day 9 : 8 therefore ( 4 / 7 ) x 13 x 9 x x = ( 3 / 7 ) x 33 x 8 x 117 or x = ( 3 x 33 x 8 x 117 ) / ( 4 x 13 x 9 ) = 198 additional men to be employed = ( 198 - 117 ) = 81 . answer is d .
Answer: d
Problem: a person borrows 1000000 for 7 years at 3 % p . a . simple interest . he immediately lends it to another person at 5 % p . a . for 7 years . find his gain in the transaction per year .
Options: a ) 20068 , b ) 20050 , c ) 20000 , d ) 25000 , e ) 28000
Rationale: "gain in 7 years = [ ( 1000000 ã — 5 ã — 7 / 100 ) â ˆ ’ ( 1000000 ã — 7 ã — 3 / 100 ) ] = ( 350000 â € “ 210000 ) = 140000 â ˆ ´ gain in 1 year = ( 140000 / 7 ) = 20000 answer c"
Answer: c
Problem: 12 : 21 : : 31 : ?
Options: a ) 13 , b ) 14 , c ) 30 , d ) 31 , e ) 40
Rationale: "ans 13 reverse of 31 answer : a"
Answer: a
Problem: if ( n + 2 ) ! / n ! = 72 , n = ?
Options: a ) 7 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: ( n + 2 ) ! / n ! = 72 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 72 from here , we might just test the answer choices . since ( 9 ) ( 8 ) = 72 , we can see that n = 7 a
Answer: a
Problem: a room 5 m 55 cm long and 3 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor
Options: a ) 176 , b ) 170 , c ) 160 , d ) 179 , e ) 174
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . area of the room = ( 544 x 374 ) cm 2 . size of largest square tile = h . c . f . of 544 cm and 374 cm = 34 cm . area of 1 tile = ( 34 x 34 ) cm 2 . number of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer a 176"
Answer: a
Problem: the ages of two persons differ by 16 years . if 6 years agao , the elder one be 3 times as old as the younger one , find their present ages .
Options: a ) 20 years . , b ) 30 years . , c ) 40 years . , d ) 50 years . , e ) 60 years .
Rationale: "sol . let the age of the younger person be x years . then , age of the elder perosn = ( x + 16 ) years . ∴ 3 ( x - 6 ) = ( x + 16 - 6 ) ⇔ 3 x - 18 = x + 10 ⇔ 2 x = 28 ⇔ x = 14 hence , their present ages are 14 years and 30 years . answer b"
Answer: b
Problem: working at a constant rate , p can finish a job in 4 hours . q , also working at a constant rate , can finish the same job in 15 hours . if they work together for 3 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "each hour they complete 1 / 4 + 1 / 15 = 19 / 60 of the job . in 3 hours , they complete 3 ( 19 / 60 ) = 19 / 20 of the job . the time for p to finish is ( 1 / 20 ) / ( 1 / 4 ) = ( 1 / 5 ) hour = 12 minutes the answer is d ."
Answer: d
Problem: a man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes . the area of the field is :
Options: a ) 18000 m 2
b ) 20000 m 2
c ) 19000 m 2
d ) 25000 m 2
e ) 15000 m 2
Rationale: length of the diagonal = distance covered in 3 min . at 4 km / hr . = ( 4000 / 60 * 3 ) = 200 m . therefore , area of the field = 1 / 2 * diagonal 2 = ½ * 200 * 200 = 20000 m 2 answer : b
Answer: b
Problem: how many positive integers less than 256 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 43 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . the numbers 244 and 248 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice d is correct here .
Answer: d
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much e does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) e = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Problem: two numbers are respectively 19 % and 40 % more than a third number . the percentage that is first of the second is ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: i ii iii 119 140 100 140 - - - - - - - - - - 119 100 - - - - - - - - - - - ? = > 15 % answer : a
Answer: a
Problem: the c . p of 5 books is equal to the s . p of 20 books . find his gain % or loss % ?
Options: a ) 35 % , b ) 20 % , c ) 5 % , d ) 25 % , e ) 75 %
Rationale: "explanation : 5 cp = 20 sp 20 - - - 15 cp loss 100 - - - ? = > 75 % loss answer : e"
Answer: e
Problem: for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 90 θ 33 ) θ 17 ) - ( 99 θ ( 33 θ 17 ) ) ?
Options: a ) 10 , b ) 8 , c ) 6 , d ) 4 , e ) 2
Rationale: "( ( 90 θ 33 ) θ 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 99 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; 7 - 3 = 4 . answer : d ."
Answer: d
Problem: convert the 10 / 36 m / s into kilometers per hour ?
Options: a ) 2.9 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1 kmph , e ) 5.7 kmph
Rationale: "10 / 36 m / s = 10 / 36 * 18 / 5 = 1 / 1 = 1 kmph . answer : d"
Answer: d
Problem: what is the remainder when 9 ^ 1 + 9 ^ 2 + 9 ^ 3 + . . . + 9 ^ 9 is divided by 3 ?
Options: a ) 0 , b ) 3 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 8 odd multiples of 3 , which yields remainder of 0 upon division by 3 . answer : a"
Answer: a
Problem: if the price of gasoline increases by 25 % and a driver intends to spend only 10 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 5 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.1 ( p * x ) y = ( 1.1 / 1.25 ) * x = 0.88 x which is a reduction of 12 % . the answer is d ."
Answer: d
Problem: a square was given . inside the square there are white tiles and black tiles . black tiles was among the diagonal of the square and dimensions of both white as well as black tiles is 1 cm x 1 cm . if there are 81 black tiles in the square . then find the no of white tiles in it .
Options: a ) 2399
b ) 1600
c ) 2679
d ) 1697
e ) 1711
Rationale: in a square , number of squares on the diagonal is equal to the tiles on a single row . if there are even number of square on a side , then total squares on the diagonal is 2 n - 1 , otherwise 2 n . as the total tiles on the diagonal are given as 81 , then number of tiles on a side = 2 n - 1 = 81 so n = 41 . so number of white tiles = 412 − 81 = 1681 − 81412 − 81 = 1681 − 81 = 1600 answer : b
Answer: b
Problem: if each edge of cube increased by 15 % , the percentage increase in
Options: a ) 30.25 , b ) 32.25 , c ) 38.25 , d ) 37.25 , e ) 41.25
Rationale: "100 × ( 115 ) / 100 × ( 115 ) / 100 = 132.25 = > 32.25 % answer is b ."
Answer: b
Problem: the average age of 16 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 12 th student is
Options: a ) 11 , b ) 66 , c ) 18 , d ) 16 , e ) 42
Rationale: "explanation : age of the 16 th student = [ 16 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 256 - 214 ) = 42 years . answer : e"
Answer: e
Problem: the difference between the place value and the face value of 8 in the numeral 856973 is
Options: a ) 973 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: "( place value of 8 ) - ( face value of 8 ) = ( 800000 - 8 ) = 799992 answer : option e"
Answer: e
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 6 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 360 km , d ) 540 km , e ) 600 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 6 h is 90 × 6 = 540 km ans . ( d )"
Answer: d