regisss/math_qa huggingface dataset:
Problem: a side of beef lost 40 percent of its weight in processing . if the side of beef weighed 240 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 400 , c ) 737 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 60 / 100 ) * x = 240 = > x = ( 240 * 100 ) / 60 = 400 answer b"
Answer: b
Problem: 36 men can complete a piece of work in 18 days . in how days will 27 men can complete the work ?
Options: a ) 18 , b ) 20 , c ) 17 , d ) 24 , e ) 21
Rationale: "let the required number of days be x less men , more days ( indirect proportion ) 27 : 36 : : 18 : x 27 x = 36 * 18 x = ( 36 * 18 ) / 27 x = 24 days option is d"
Answer: d
Problem: a trader bought a car at 50 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 71 %
Rationale: "original price = 100 cp = 95 s = 95 * ( 180 / 100 ) = 112 100 - 171 = 71 % answer : e"
Answer: e
Problem: renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?
Options: a ) 4.8 , b ) 1.2 , c ) 4.4 , d ) 4.6 , e ) 4.7
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 8 = 5 / 24 suma can do it alone in 4.8 days . answer : a"
Answer: a
Problem: what is the sum of the odd integers from 35 to 65 , inclusive ?
Options: a ) 800 , b ) 550 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 50 . sum = mean ( # of elements ) there are 16 odd numbers between 35 - 65 inclusive . 16 * 50 = 800 a"
Answer: a
Problem: excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 20 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 11 min
Rationale: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( 18 / 54 ) x 60 = 20 min answer : a"
Answer: a
Problem: a worker can load one truck in 6 hours . a second worker can load the same truck in 5 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.7 , b ) 2.9 , c ) 3.1 , d ) 3.3 , e ) 3.5
Rationale: "the workers fill the truck at a rate of 1 / 6 + 1 / 5 = 11 / 30 of the truck per hour . then the time to fill one truck is 30 / 11 which is about 2.7 hours . the answer is a ."
Answer: a
Problem: which is equal to 11 ?
Options: a ) 1.1 , b ) - 11 , c ) 11 / 11 , d ) 11 / 1 , e ) 1 / 11
Rationale: "11 / 1 is equal to 11 . answer : d"
Answer: d
Problem: the speed of a train is 102 kmph . what is the distance covered by it in 30 minutes ?
Options: a ) 50 kmph , b ) 51 kmph , c ) 41 kmph , d ) 61 kmph , e ) 21 kmph
Rationale: "102 * 30 / 60 = 51 kmph answer : b"
Answer: b
Problem: a rectangular of certain dimensions is chopped off from one corner of a larger rectangle as shown . ab = 8 cm and bc = 4 cm . the perimeter of the figure abcpqra ( in cm ) is :
Options: a ) 24
b ) 28
c ) 36
d ) 48
e ) none of these
Rationale: solution required perimeter = ( ab + bc + cp + pq + qr + ra ) = ab + bc + ( cp + qr ) + ( pq + ra ) = ab + bc + ab + bc = 2 ( ab + bc ) = [ 2 ( 8 + 4 ) ] cm = 24 cm . answer a
Answer: a
Problem: 20 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 20 * 10 / 40 = 5 answer is e"
Answer: e
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 110 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,210
Rationale: "10 / 100 p = 110 > > p = 110 * 100 / 10 = 1100 1100 - 110 = 990 answer : b"
Answer: b
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 9 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 9 , b ) - 1 , c ) 0 , d ) 1 , e ) 9
Rationale: "when x = 1 and when x = - 9 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 9 ) f ( 0 ) = - 9 the answer is a ."
Answer: a
Problem: in a trapezium abcd , ab is parallel to dc , ab = 3 * dc , and the diagonals of the trapezium intersect at o . the ratio of the area of ∆ ocd to the area of ∆ oab is :
Options: a ) 1 : 9
b ) 1 : 3
c ) 3 : 1
d ) 1 : 10
e ) can not be determined
Rationale: triangles are similar , so ratio will be 1 : 9 a
Answer: a
Problem: when 1 / 10 percent of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 495 , e ) 694
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 6,000 ? 2 ) what is 1 / 10 of 6,000 ? to calculate 1 / 10 percent of 6,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 6,000 = 1 / 1,000 x 6,000 = 6 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 5,000 . to do this we simply multiply 1 / 10 by 6,000 . 1 / 10 x 6,000 = 600 the answer to part 1 is 6 , and the answer to part 2 is 600 . their difference is 600 – 6 = 694 . answer e ."
Answer: e
Problem: if there are 200 questions in a 3 hr examination . among these questions are 10 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 17.14286 min , b ) 62 min , c ) 70.1346 min , d ) 74 min , e ) 76.1346 min
Rationale: x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 190 x + 10 * 2 x = 180 x = 180 / 210 x = 0.72 time taken for type a problem = 10 * 2 * 0.857143 = 17.14286 min answer : a
Answer: a
Problem: working individually , jane can bake cakes for 4 hours and roy can bake cakes in 5 hours . if jane and roy work together but independently at the task for 2 hours , at which point roy leaves , how many remaining hours will it take jane to complete the task alone ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 4 , d ) 1 / 4 , e ) 1 / 5
Rationale: in first 2 hrs roy will finish 2 / 5 = 2 / 5 of work and jane will finish 2 / 4 work so total 2 / 5 + 1 / 2 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now jane will take ( 1 / 10 ) * 4 = 2 / 5 hrs to finish it . so answer is b .
Answer: b
Problem: the arithmetic mean of set x is zero . if y = { - 2.22 ; - 1.96 ; - 1.68 ; 1.62 ; 1.94 ; 2.16 } is the subset of x consisting of all those elements in x which are more than two but less than 3 standard deviations away from the arithmetic mean of x , what could be equal to the standard deviation of x ?
Options: a ) 0.54 , b ) 0.77 , c ) 0.82 , d ) 0.97 , e ) 1.62
Rationale: this is a fairly straightforward question that can be solved quickly by just applying the options we are provided with mean , m = 0 and y = { - 2.22 ; - 1.96 ; - 1.68 ; 1.62 ; 1.94 ; 2.16 } is the subset of s y consists of all those elements in x that are more than 2 but less than 3 xds away from the arithmetic mean of x if an element is 1 xd away from the mean , we can write it as either m + xd or m - xd similarly , if an element is 2 xds away from the mean , we can write it as either m + 2 * xd or m - 2 * xd so , if these elements lie within 2 and 3 xds of mean , m = 0 we can find which one of these values of xd satisfies each value within y only xd = 0.77 does answer : b
Answer: b
Problem: what is the sum of odd integers from 25 to 85 , inclusive ?
Options: a ) 1,705 , b ) 1,500 , c ) 1,240 , d ) 1,120 , e ) 1,100
Rationale: number of odd integers = ( 85 - 25 ) / 2 + 1 = 60 / 2 + 1 = 31 sum of odd integers = ( 25 + 85 ) / 2 * 31 = 1705 answer a
Answer: a
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 25 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.95 * 25 = $ 248.75 . answer is b .
Answer: b
Problem: evaluate the sum 1 - 2 + 3 - 4 + 5 - 6 + . . . + 997 - 998 + 999 - 1000
Options: a ) - 500 , b ) - 1000 , c ) - 999 , d ) - 1001 , e ) 500500
Rationale: one groups the first two terms and each successive two terms to obtain a sum of 500 expressions each of which is - 1 . the answer is - 500 correct answer a
Answer: a
Problem: a line has a slope of 3 / 4 and intersects the point t ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point t of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Problem: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8337 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 6947.5
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8337 ( 100 / 120 ) = rs . 6947.5 answer : e"
Answer: e
Problem: two drivers began their journey with the same amount of petrol in their cars at the same time . the only difference is that the first driver � s car could drive 4 hours in that amount of petrol and the second one could drive 5 hours . however , they only drove for some time and found that the amount of petrol that was left in one of the cars was 4 times the petrol left in the other one . for how long had they driven at this point of time ?
Options: a ) 3.75 hours , b ) 5.45 hours , c ) 7.10 hours , d ) 4.75 hours , e ) 3.33 hours
Rationale: a 3.75 hours while you can solve it as you like , a simple mathematical equation can be used to find out . let m be the amount of petrol initially . let n be the time for which they drove . according to the question , the amount of petrol used by first car in n hours = mn / 4 the amount of petrol used by second car in n hours = mn / 5 hence , the amount of petrol left in the first car = ( m - mn / 4 ) the amount of petrol left in the second car = ( m - mn / 5 ) as per the details given in the question , we can form the below equation : m - mn / 5 = 4 ( m - mn / 4 ) n = 15 / 4 or 3.75 hours . hence , both the drivers have driven the car for 3.75 hours at that particular time .
Answer: a
Problem: the ratio of two numbers is 5 : 9 . if each number is decreased by 5 , the ratio becomes 5 : 11 . find the numbers .
Options: a ) 30 , 19 , b ) 21 , 37 , c ) 15 , 34 , d ) 15 , 27 , e ) none of these
Rationale: "explanation : let the two numbers be 5 x and 9 x . ( 5 x - 5 ) / ( 9 x - 5 ) = 5 : 11 ( 5 x - 5 ) * 11 = ( 9 x - 5 ) * 5 55 x – 55 = 45 x – 25 10 x = 30 x = 3 therefore , the numbers are 15 and 27 . answer : d"
Answer: d
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 11 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 190 , c ) 132 , d ) 170 , e ) 60
Rationale: "c 132 sum = ( n x n ) + n hence , 11 x 11 = 121 + 11 = 132"
Answer: c
Problem: the average height of 12 girls out of a class of 20 is 161 cm . and that of the remaining girls is 158 cm . the average height of the whole class is :
Options: a ) 142.3 cms , b ) 162.3 cms , c ) 160.5 cms , d ) 142.8 cms , e ) 159.8 cms
Rationale: "explanation : average height of the whole class = ( 12 × 161 + 8 × 158 / 20 ) = 159.8 cms answer e"
Answer: e
Problem: find out the c . i on rs . 9000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 550.87 , b ) 506.07 , c ) 506.04 , d ) 506.03 , e ) 306.01
Rationale: "a = 9000 ( 51 / 50 ) 3 = 9550.87 9000 - - - - - - - - - - - 550.87 answer : a"
Answer: a
Problem: the length of rectangle is thrice its breadth and its perimeter is 56 m , find the area of the rectangle ?
Options: a ) 432 , b ) 212 , c ) 252 , d ) 992 , e ) 147
Rationale: "2 ( 3 x + x ) = 56 l = 21 b = 7 lb = 21 * 7 = 147 answer : e"
Answer: e
Problem: in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is
Options: a ) 3 hr . , b ) 5 hr . , c ) 2 hr . , d ) 7 hr . , e ) 1 hr .
Rationale: "e 1 hr . let the duration of the flight be x hours . then , 600 / x - 600 / 0.5 x = 200 - - > 600 / x - 1200 / ( 2 x + 1 ) = 200 - - > x ( 2 x + 1 ) = 3 - - > 2 x ^ 2 + x - 3 = 0 - - > ( 2 x + 3 ) ( x - 1 ) = 0 - - > x = 1 hr ."
Answer: e
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2200 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 19,800 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2200 triples to $ 6600 , in 28 years , it will again triple to $ 6600 * 3 = $ 19,800 answer b"
Answer: b
Problem: a rocket soars for 12 seconds at 150 meters per second . it then plummets 600 meters in 3 seconds . what is the average speed of the rocket in meters per second ?
Options: a ) 140 , b ) 150 , c ) 155 , d ) 160 , e ) 175
Rationale: when soaring , the rocket travels a total distance of 1800 m ( 150 m / s for 12 s ) while plummeting the rockets travel distance of 600 m in 3 s the total distance traveled is 2400 m ( 1800 + 600 ) the time taken to travel this distance is 15 s ( 12 + 3 ) average speed = 2400 / 15 = 160 ans : ( option d )
Answer: d
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers w are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a
Answer: a
Problem: a no . when divided by 224 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "224 + 43 = 267 / 17 = 12 ( remainder ) e"
Answer: e
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours x will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) x = 5 . , d ) x = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double x = 6 hrs . . so closest to that option is 5 ."
Answer: c
Problem: the product of two numbers is 168 and the sum of these two numbers is 26 . what is the largest of these two numbers ?
Options: a ) 22 , b ) 77 , c ) 88 , d ) 12 , e ) 62
Rationale: "let the numbers be x and ( 26 – x ) . therefore , x ( 26 – x ) = 168 x 2 – 26 x + 168 = 0 ( x – 14 ) ( x – 12 ) = 0 x = 14 or x = 12 so , the numbers are 14 and 12 . answer : d"
Answer: d
Problem: a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 700.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.40 , b ) $ 10.00 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 700 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 700 / 70 = 10 b"
Answer: b
Problem: in a survey of 330 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 37 / 66 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 276 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 330 we have to find not part time and not uninsured . in other words not part time and insured = x / 330 = ( 276 - 104 + 13 ) / 330 = 37 / 66 answer is a ."
Answer: a
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 896 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 99 % , e ) 11.6 %
Rationale: "896 - - - 104 100 - - - ? = > 11.6 % answer : e"
Answer: e
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 numbers will be even ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 2 , e ) 12 / 21
Rationale: probability that the number on first die is even = 3 / 6 [ because 3 out of 6 faces are even ] probability that the number on second die is even = 3 / 7 [ because 3 out of 7 faces are even ] probability that both dice result in odd numbers = ( 3 / 6 ) * ( 3 / 7 ) = 3 / 14 answer : option a
Answer: a
Problem: what will be the compound interest on a sum of rs . 26000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.22 , b ) s . 10823.20 , c ) s . 10123.20 , d ) s . 10123.29 , e ) s . 10528.13
Rationale: "explanation : amount = [ 26000 * ( 1 + 12 / 100 ) 3 ] = 26000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 36528.13 - 26000 ) = rs . 10528.13 answer : e"
Answer: e
Problem: which number need to add to 859622 to get a no . exactly divisible by 456 ?
Options: a ) 345466 , b ) 465767 , c ) 565676 , d ) 645469 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent r of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is r = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Problem: a cistern is filled by pipe a in 10 hours and the full cistern can be leaked out by an exhaust pipe b in 12 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 10 - 1 / 12 ) hrs = 1 / 60 = 60 hrs answer : b"
Answer: b
Problem: here is 15 dots . if you select 3 dots randomly , what is the probability that 3 dots make a triangle ?
Options: a ) 440 / 455 , b ) 412 / 455 , c ) 434 / 455 , d ) 449 / 455 , e ) 438 / 455
Rationale: total ways of selecting 3 dots out of 15 is 15 c 3 = 455 if 3 dots are collinear then triangle may not be formed . now look at the above diagram . if we select any 3 dots from the red lines they may not form a triangle . they are 3 x 5 c 3 = 30 . if we select the three letters from blue lines , they may not form a triangle . they are in total 5 ways . also there are 6 others lines which do n ' t form a triangle . also another two orange lines . total = 30 + 5 + 6 + 2 = 43 . so we can form a triangle in 455 - 43 = 412 . so answer could be 412 / 455 . answer : b
Answer: b
Problem: in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 8 * 1 + 3 * 2 = 14 books . the 7 students who borrowed at least three books borrowed 40 - 14 = 26 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 26 - 18 = 8 books . the answer is a ."
Answer: a
Problem: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 9.25 , b ) 11.75 , c ) 13.25 , d ) 15.75 , e ) 17.25
Rationale: "let x be the length of the size 8 shoe . then 0.3 x = 9 / 4 x = 90 / 12 = 15 / 2 inches the size 15 shoe has a length of 15 / 2 + 7 / 4 = 37 / 4 = 9.25 inches the answer is a ."
Answer: a
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11 , 60 and 61 ?
Options: a ) 6.5 , b ) 12.5 , c ) 28 , d ) 30.5 , e ) 40
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 ans . d"
Answer: d
Problem: a man spends 50 % of his income on food , 15 % on children education and 50 % of the remaining on house rent . what percent of his income he is left with ?
Options: a ) 17.5 % , b ) 16 % , c ) 15.4 % , d ) 12.6 % , e ) 13.5 %
Rationale: "let the total income be x then , income left = ( 100 - 50 ) % of x - [ 100 - ( 50 + 15 ) ] % of x = 50 % of 35 % of x = 17.5 % of x answer is a"
Answer: a
Problem: a car covers a distance of 624 km in 3 hours . find its speed ?
Options: a ) 104 , b ) 277 , c ) 298 , d ) 269 , e ) 208
Rationale: 624 / 3 = 208 kmph answer : e
Answer: e
Problem: it was calculated that 50 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 20 days . , b ) 15 days . , c ) 22 days . , d ) 30 days . , e ) 18 days .
Rationale: "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 50 ) now : no . of workers = 25 one day work = 25 * 1 / ( 10 * 50 ) the total no . of days required to complete the work = ( 50 * 10 ) / 25 = 20 answer : a"
Answer: a
Problem: at a supermarket , the ratio of the number of shampoos to the number of soaps is 8 to 5 , and the ratio of the number of drinks to the number of shampoos is 3 to 4 . if the ratio of the soaps to the number of cereals is 9 to 2 , what is the ratio of the number of drinks to the number of cereals ?
Options: a ) 4 : 3 , b ) 15 : 6 , c ) 45 : 16 , d ) 15 : 4 , e ) 27 : 5
Rationale: sh : soaps = 8 : 5 drinks : sh = 3 : 4 = > 6 : 8 drinks : sh : soaps = 6 : 8 : 5 soaps : cer = 9 : 2 = > 9 * 5 : 2 * 5 = 45 : 10 now , drinks : sh : soaps = > 6 * 9 : 8 * 9 : 5 * 9 = 54 : 72 : 45 drinks : sh : soaps : cer = 54 : 72 : 45 : 10 drinks : cer = 54 : 10 = > 27 : 5 e
Answer: e
Problem: xy = 1 then what is ( 5 ^ ( x + y ) ^ 2 ) / ( 5 ^ ( x - y ) ^ 2 )
Options: a ) 2 , b ) 625 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 5 ^ 4 = 625 answer b"
Answer: b
Problem: gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 8 w 10 + 5 x = 8 ( x + 1 ) x = 2 / 3 ratio of gold with copper = 1 : 2 / 3 = 3 : 2 answer is a"
Answer: a
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 400 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 400 / 3 = 133.33 sq m l b = 133.33 i . e . , l * l / 3 = 133.33 l ^ 2 = 400 > l = 20 . c"
Answer: c
Problem: a baker charges n dollars for a birthday cake . next week , she intends to earn 320 dollars selling cakes . if she were to reduce the price of the cake by 20 percent , she would have to sell two more cakes to earn the same amount of revenue . how many cakes does she intend to sell next week ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: we ' re told that by selling cakes at n dollars / cake , a baker will make $ 320 . reducing the price by 20 % and selling 2 more cakes will also make her $ 320 . we ' re asked for the original number of cakes that the baker intends to sell . $ 320 is a rather interesting number . based on the answer choices , we ' re almost certainly dealing with integer values for the number of cakes and the price per cake . as such , 6 is probably not going to be part of the solution ( either as 4 and 6 cakes or as 6 and 8 cakes ) . as such , we can avoid answers b and c . . . . let ' s test answer d : 8 cakes if . . . . original cakes = 8 8 ( n ) = $ 320 , so n = $ 40 / cake 20 % off = $ 8 off = 40 - 8 = $ 32 / cake + 2 more cakes = 8 + 2 = 10 cakes 10 ( 32 ) = $ 320 this is an exact match for what we were told , so this must be the answer . final answer : d
Answer: d
Problem: a sum of money deposited at c . i . amounts to rs . 1820 in 4 years and to rs . 2402 in 5 years . find the rate percent ?
Options: a ) 30 % , b ) 31 % , c ) 34 % , d ) 19 % , e ) 50 %
Rationale: "1820 - - - 582 100 - - - ? = > 31 % answer : b"
Answer: b
Problem: an assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 52 , e ) 56
Rationale: "the time to produce the first 60 cogs is 60 / 30 = 2 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 3 hours = 40 cogs per hour . the answer is a ."
Answer: a
Problem: if the cost price of 44 chocolates is equal to the selling price of 24 chocolates , the gain percent is :
Options: a ) 83.55 % , b ) 83.33 % , c ) 80 % , d ) 83.39 % , e ) 84.33 %
Rationale: explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 24 chocolates = rs . 24 ; s . p . of 24 chocolates = rs . 44 . . ' . gain % = 20 * 100 / 24 = 83.33 % answer : b
Answer: b
Problem: 90 percent of your marbles are a solid color . 5 percent of your marbles are solid yellow . what percentage of your marbles are a solid color other than yellow ?
Options: a ) 5 , b ) 15 , c ) 85 , d ) 90 , e ) 95
Rationale: 90 percent are solid colors including solid yellow . 5 percent are solid yellow . 90 % - 5 % = 85 % , so 85 percent are a solid color other than yellow = > ( c )
Answer: c
Problem: when m divided by 288 , the remainder is 47 . find the remainder when the same m is divided by 24 ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 26
Rationale: 23 option d
Answer: d
Problem: the length of rectangle is thrice its breadth and its perimeter is 112 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 588 sq m , e ) 525 sq m
Rationale: "2 ( 3 x + x ) = 112 l = 42 b = 14 lb = 42 * 14 = 588 answer : d"
Answer: d
Problem: in measuring the sides of a rectangle , one side is taken 5 % in excess and the other 4 % in deficit . find the error percent in the area , calculate from the those measurements .
Options: a ) 0.9 % , b ) 0.8 % , c ) 0.3 % , d ) 0.2 % , e ) 0.5 %
Rationale: "explanation : let x and y be the sides of the rectangle then correct area = = error % = answer : b ) 0.8 %"
Answer: b
Problem: we have a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 144 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 216 , b ) b 196 , c ) c 170 , d ) d 140 , e ) e 121
Rationale: "l = 144 / 12 = 12 ft w = 72 / 12 = 6 ft area of paper = 72 area of cube = 12 * side ^ 2 side of cube = 6 v of cube = 216"
Answer: a
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 7 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 34 , d ) d . 18 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 34 hours c"
Answer: c
Problem: if k is an integer and 0.00010101 x 10 ^ k is greater than 1000 , what is the least possible value of k ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "0.00010101 * 10 ^ k > 1000 we need to move the decimal point to the right 7 places to get 1010.1 this is equivalent to multiplying by 10 ^ 7 . the answer is b ."
Answer: b
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 30 kg , b ) 31 kg , c ) 37 kg , d ) 39 kg , e ) 41 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 . b ' s weight = 31 kg b )"
Answer: b
Problem: a car is purchased on hire - purchase . the cash price is $ 22 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 515 , d ) $ 528 , e ) $ 537
Rationale: "explanation : cash price = $ 22 000 deposit = 10 % ã — $ 22 000 = $ 2200 loan amount = $ 22000 â ˆ ’ $ 2200 number of payments = 60 = $ 19800 i = p * r * t / 100 i = 11880 total amount = 19800 + 11880 = $ 31680 regular payment = total amount / number of payments = 528 answer : d"
Answer: d
Problem: 5 is added to a certain number , the sum is multiplied by 2 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 44 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 63 , d ) 30 , e ) 45
Rationale: "let number is x . when 5 added to it , = ( x + 5 ) 2 multiplied to sum , = 2 * ( x + 5 ) now , = [ { 2 * ( x + 5 ) } / 5 ] and , = [ { 2 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 2 * ( x + 5 ) } / 5 ] - 5 = half of 44 [ ( 2 x + 10 ) / 5 ) = 22 + 5 2 x + 10 = 27 * 5 2 x - 135 - 10 x = 125 / 2 = 62.5 = 63 so , required number is : 63 . answer : c"
Answer: c
Problem: the ratio between the sale price and the cost price of an article is 9 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 3 : 6 , d ) 2 : 0 , e ) 2 : 1
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 9 x . then , gain = rs . 2 x required ratio = 2 x : 7 x = 2 : 7 answer : b"
Answer: b
Problem: find the number which when multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: let the number be x . then , 15 x - x = 196 < = > 14 x = 196 < = > x = 14 . answer : a
Answer: a
Problem: one night a certain hotel rented 3 / 4 of its rooms . including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 20 , b ) 33 1 / 3 , c ) 35 , d ) 40 , e ) 80
Rationale: consider total # of rooms to be 100 ; as 3 / 5 of the rooms are air conditioned then # of rooms that are air conditioned is 3 / 5 * 100 = 60 ; 3 / 4 rooms were rented - - > 1 / 4 * 100 = 25 were not rented ; 2 / 3 of air conditioned rooms were rented - - > 1 / 3 * 60 = 20 air conditioned room were not rented ; 20 / 25 = 4 / 5 = 80 % . answer : e .
Answer: e
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 72 seconds . what is the length of each train ( in meters ) ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 72 seconds , the relative difference in distance traveled is 72 * 25 / 9 = 200 meters this distance is twice the length of each train . the length of each train is 200 / 2 = 100 meters the answer is d ."
Answer: d
Problem: 80 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 81
Rationale: "explanation : 80 + 5 * 12 / ( 180 / 3 ) = 80 + 5 * 12 / ( 60 ) = 80 + ( 5 * 12 ) / 60 = 80 + 1 = 81 . answer : e"
Answer: e
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio t of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio t of ann ' s time to bob ' s time is 3 : 2 . answer : b .
Answer: b
Problem: if 6 x = 10 y = 14 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 213 , b ) 58 , c ) 84 , d ) 122 , e ) 168
Rationale: answer = d = 122 6 x = 10 y = 14 z 3 x = 5 y = 7 z 3 ( 5 * 7 ) = 5 ( 3 * 7 ) = 7 ( 3 * 5 ) addition = 35 + 21 + 15 = 71 answer would be multiple of 71 which is 213 answer : a
Answer: a
Problem: tough and tricky questions : percents . over the course of a year , a certain microbrewery increased its beer output by 20 percent . at the same time , it decreased its total working hours by 30 percent . by what percent did this factory increase its output per hour ?
Options: a ) 171.4 , b ) 171.5 , c ) 171.6 , d ) 171.7 , e ) none of the above
Rationale: lets assume the initial production was 100 litres of beer for 100 hr . with the 20 % increase the total amount of beer production will be 120 litres and with 30 % decrease in total hours will be reduced to 70 hr . 100 hr - - - - > 100 lts 1 hr - - - - - > 1 lts 70 hr - - - - - > 120 lts 1 hr - - - - - > 1.714 lts total increase in production for 1 hr = 171.4 % answer a
Answer: a
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 8 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let t = usual time = distance / usual speed t + 8 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 32 the answer is d ."
Answer: d
Problem: an inspector rejects 0.08 % of the meters as defective . how many will be examine to project ?
Options: a ) 2000 , b ) 2300 , c ) 2700 , d ) 2500 , e ) 250
Rationale: let the number of meters to be examined be x . then , 0.08 % of x = 2 [ ( 8 / 100 ) * ( 1 / 100 ) * x ] = 2 x = [ ( 2 * 100 * 100 ) / 8 ] = 2500 answer is d .
Answer: d
Problem: a can do a piece of work in 15 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 8 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 * 5 = 1 / 2 remaining work = 1 â ˆ ’ 1 / 2 = 1 / 2 a can finish work = 15 â ˆ — 1 / 2 = 7.5 days answer is c"
Answer: c
Problem: a couple decides to have 3 children . if they succeed in having 3 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 1 girl and 2 boys ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 1 , e ) 1 / 4
Rationale: sample space = 2 ^ 3 = 8 favourable events = { bgg } , { bgb } , { bbb } , { ggg } , { gbg } , probability = 5 / 8 = 5 / 8 . ans ( c ) .
Answer: c
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 60 / r years . if pat ' s parents invested $ 7,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 20 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 14000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 60 / r years , then for r = 6 it ' ll double in 60 / 6 = ~ 10 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 20 years investment will become $ 7,000 * 2 = $ 14,000 . answer : b"
Answer: b
Problem: find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 28 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 12 , 6,16 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 4 given , ( a + b ) + ( c - b ) = 21 = > a + c = 28 = > 3 x + 4 x = 28 = > x = 4 a , b , c are 3 x , 2 x , 4 x a , b , c are 12 , 8 , 16 . answer : c"
Answer: c
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 570 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 38 / 15 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 570 km time taken by eddy = 3 hours average speed of eddy = 570 / 3 = 190 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 190 / 75 = 38 / 15 answer c"
Answer: c
Problem: two trains 180 m and 360 m long run at the speed of 60 kmph and 30 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 21.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 30 = 90 kmph * 5 / 18 = 25 m / s distance covered in crossing each other = 180 + 360 = 540 m required time = 540 * 1 / 25 = 21.6 sec answer is a"
Answer: a
Problem: if 5 ^ 10 x 2 ^ 10 = 10 ^ n what is the value of n ?
Options: a ) 16 , b ) 14 , c ) 12 , d ) 10 , e ) 18
Rationale: "5 ^ 10 * 2 ^ 10 = 10 ^ n or 10 ^ 10 = 10 ^ n n = 10 d"
Answer: d
Problem: the average of 55 results is 28 and the average of other 28 results is 55 . what is the average of all the results ?
Options: a ) 37 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 83 result = sum of 55 result + sum of 28 result . = 30 x 20 + 20 x 30 = 3080 correct option : a"
Answer: a
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 90 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 98 , e ) 95
Rationale: "total score on 3 tests = 90 * 3 = 270 jerry wants the average to be = 92 hence total score on 4 tests should be = 92 * 4 = 368 score required on the fourth test = 368 - 270 = 98 option d"
Answer: d
Problem: 36 men can complete a piece of work in 18 days . in how many days will 9 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 88 , d ) 72 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 9 : 36 : : 18 : x x = 72 answer : d ) 72 days"
Answer: d
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 4,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.85 % , b ) 7.25 % , c ) 7.76 % , d ) 8.33 % , e ) 8.75 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 6000 = 1 / 12 which is about 8.33 % the answer is d ."
Answer: d
Problem: the diameter of a garden roller is 1.4 m and it is 4 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 80 m 2 , b ) 84 m 2 , c ) 88 m 2 , d ) 86 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 4 = 88 m 2 answer c"
Answer: c
Problem: at a certain high school , the senior class is twice the size of the junior class . if 7 / 8 of the seniors and 1 / 2 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 4 , d ) 3 / 8 , e ) 5 / 16
Rationale: "start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 7 / 8 ) * 200 = 175 and ( 1 / 2 ) * 100 = 50 . 175 + 50 = 225 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 225 total students in japanese , so 225 students in japanese / 300 total students equals 3 / 4 of the students in both classes that study japanese . answer : a"
Answer: a
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 400 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the distance between the nest and the ditch is 400 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 400 = 12000 . d = st 12000 / 1.5 = t , i think we can take 12000 meters as 12 km , then only we get t = 8 . ( 1000 meters = 1 km ) d )"
Answer: d
Problem: what is the total cost of 2 sandwiches at $ 2.44 each and 4 sodas at $ 0.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.36 , d ) $ 10.08 , e ) $ 11.85
Rationale: "answer = c 2 * 2.44 + 4 * 0.87 = 2 ( 2.50 - 0.06 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.12 - 0.52 = 9 - 0.64 = 8.36"
Answer: c
Problem: average of 5 numbers is 12 . if one number is excluded the average becomes 10 . the excluded number is
Options: a ) 35 , b ) 20 , c ) 40 , d ) 30 , e ) 67
Rationale: explanation : number is ( 5 * 12 ) - ( 4 * 10 ) = 60 - 40 = 20 answer : option b
Answer: b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 200 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 1429 , c ) 1977 , d ) 2778 , e ) 2711
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 200 100 % - - - - ? = > rs . 1429 answer : b"
Answer: b
Problem: set a contains all the even numbers between 12 and 60 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 850 , b ) 1250 , c ) 1650 , d ) 2050 , e ) 2450
Rationale: "each term in set b is 50 more than the corresponding term in set a . the difference of the sums = 25 * 50 = 1250 . the answer is b ."
Answer: b
Problem: a worker earns $ 20 on the first day and spends $ 15 on the second day . the worker earns $ 20 on the third day and spends $ 15 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 90 ?
Options: a ) 28 , b ) 29 , c ) 31 , d ) 34 , e ) 36
Rationale: "every two days , the net total is $ 5 . after 28 days , the worker will have $ 70 . on day 29 , the worker will receive $ 20 for a net total of $ 90 . the answer is b ."
Answer: b
Problem: log 3 n + log 9 n what is 3 digit number n that will be whole number
Options: a ) 629 , b ) 729 , c ) 829 , d ) 929 , e ) 727
Rationale: "no of values n can take is 1 9 ^ 3 = 729 answer : b"
Answer: b
Problem: an employee ’ s annual salary was increased $ 15,000 . if her new annual salary now equals $ 90,000 , what was the percent increase ?
Options: a ) 15 % , b ) 16 2 ⁄ 3 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "new annual salary = $ 90,000 salary increase = $ 15,000 . original salary = $ 90,000 - $ 15,000 . = $ 75,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 20 % hence c ."
Answer: c
Problem: how many zeros does 50 ! end with ?
Options: a ) 20 , b ) 24 , c ) 25 , d ) 12 , e ) 32
Rationale: "according to above 50 ! has 50 / 5 + 50 / 25 = 10 + 2 = 12 trailing zeros . answer : d ."
Answer: d
Problem: when 1 + 2 = 23 , 2 + 3 = 65 , 3 + 4 = 127 , then 4 + 5 = ?
Options: a ) 209 , b ) 250 , c ) 265 , d ) 280 , e ) 225
Rationale: "1 + 2 = > 1 x 2 = 2 & 1 + 2 = 3 = > 2 & 3 = > 23 2 + 3 = > 2 ã — 3 = 6 & 2 + 3 = 5 = > 6 & 6 = > 65 3 + 4 = > 3 ã — 4 = 12 & 3 + 4 = 7 = > 12 & 7 = > 127 then 4 + 5 = > 4 ã — 5 = 20 & 4 + 5 = 9 = > 20 & 9 = > 209 answer : a"
Answer: a
Problem: paul sells encyclopedias door - to - door . he earns $ 150 on every paycheck , regardless of how many sets he sells . in addition , he earns commission as follows : commission sales 10 % $ 0.00 - $ 1000.00 5 % $ 1000.01 - - - > he does not earn double commission . that is , if his sales are $ 12000 , he earns 10 % on the first $ 10000 and 5 % on the remaining $ 2000 . his largest paycheck of the year was $ 1320 . what were his sales for that pay period ?
Options: a ) 13,400 , b ) 14,800 , c ) 16,400 , d ) 15,800 , e ) 19,600
Rationale: his pay check was $ 1320 . out of this , $ 150 was his fixed salary so the total commission he earned was $ 1320 - $ 150 = $ 1170 he earns 10 % on the sales of first $ 10,000 which gives a commission of $ 1000 . he earns 5 % on every subsequent dollar . since he earns another $ 170 , he must have had sales of another 170 * ( 100 / 5 ) = 3400 so his total sales must have been $ 10,000 + $ 3400 = $ 13,400 a
Answer: a