regisss/math_qa huggingface dataset:
Problem: the circumferences of two circles are 132 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2996 sq m , b ) 2897 sq m , c ) 4312 sq m , d ) 5768 sq m , e ) 8470 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 132 and 2 ∏ l = 352 s = 132 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 66 ^ 2 / ∏ ^ 2 - 132 ^ 2 / ∏ ^ 2 } = 66 ^ 2 / ∏ - 132 ^ 2 / ∏ = ( 66 - 132 ) ( 66 + 132 ) / ∏ = ( 110 ) ( 242 ) / ( 22 / 7 ) = 8470 sq m answer : e"
Answer: e
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and dinley have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and dinley submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 22 , b ) 21 , c ) 35 , d ) 37 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 16000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 70000 < = > v = 35 answer : c ) 35"
Answer: c
Problem: when positive integer w is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation that can be formed w is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b
Answer: b
Problem: a certain box has 11 cards and each card has one of the integers from 1 to 11 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 11 cards ?
Options: a ) 1 / 11 , b ) 2 / 11 , c ) 2 / 33 , d ) 4 / 55 , e ) 5 / 66
Rationale: the average of the numbers is 6 the total number of ways to choose 2 cards from 11 cards is 11 c 2 = 55 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } the probability is 4 / 55 the answer is d .
Answer: d
Problem: if a 2 + b 2 + c 2 = 281 and ab + bc + ca = 4 , then a + b + c is
Options: a ) 16 , b ) 18 , c ) 22 , d ) 17 , e ) 20
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 281 and ab + bc + ca = 4 , ( a + b + c ) ^ 2 = 281 + 2 ( 4 ) = 289 = 17 ^ 2 therefore : a + b + c = 17 answer : d"
Answer: d
Problem: pradeep has to obtain 25 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are
Options: a ) 840 , b ) 600 , c ) 800 , d ) 1000 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 25 % of x = 185 + 25 = > 25 / 100 x = 210 x = ( 210100 / 25 ) x = 840 . answer : a"
Answer: a
Problem: how many digits will be there to the right of the decimal point in the product of 98 and . 08216 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 7 , e ) 8
Rationale: "product of 98 and . 08216 is 8.05168 . therefore number of digits to right of decimal point is 5 answer is a ."
Answer: a
Problem: 9 men went to a theater . 8 of them spent rs . 3 each over their tickets and the ninth spent rs . 2 more than the average expenditure of all the 9 . determine the total money spent by them ?
Options: a ) 29 , b ) 29.25 , c ) 31 , d ) 31.23 , e ) 32
Rationale: average of 9 = x 9 x = 8 * 3 + x * 2 x = 3.25 total = 9 * 3.25 = 29.25 b
Answer: b
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 48 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 10 , e ) 12
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 48 = 6 k + 4 p = > k = 6 , p = 3 total red ' s in bag a will be 2 k = 12 e"
Answer: e
Problem: a runs 1 2 / 3 times as fast as b . if a gives b a start of 80 m , how far must the winning post be so that a and b might reach it at the same time ?
Options: a ) 200 m , b ) 300 m , c ) 270 m , d ) 160 m , e ) 150 m
Rationale: explanation : ratio of the speeds of a and b = 5 : 1 = 5 : 3 thus , in race of 5 m , a gains 2 m over b . 2 m are gained by a in a race of 5 m . 80 m will be gained by a in race of 5 / 2 x 80 m = 200 m winning post is 200 m away from the starting point . answer is a
Answer: a
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 18 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 468 , b ) 444 , c ) 676 , d ) 767 , e ) 663
Rationale: "1 h - - - - - 3 ? - - - - - - 60 12 h rs = 18 + 21 = 39 t = 12 d = 39 * 12 = 468 answer : a"
Answer: a
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 6 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 6 ) = multiply and divide by 2 ^ 3 = 2 ^ 3 / ( 2 ^ 3 * 2 ^ 3 * 5 ^ 6 ) = 2 ^ 3 / 10 ^ 6 = > non zero digits are 8 = > ans a"
Answer: a
Problem: if the perimeter and diagonal of a rectangle are 14 and 5 cms respectively , find its area .
Options: a ) 12 cm 2
b ) 16 cm 2
c ) 20 cm 2
d ) 24 cm
e ) none of these
Rationale: in a rectangle , ( perimeter ) 2 / 4 = ( diagonal ) 2 + 2 × area ⇒ ( 14 ) 2 / 4 = 5 ( 2 ) + 2 × area 49 = 25 + 2 × area ∴ area = 49 − 25 / 2 = 24 / 2 = 12 cm 2 answer a
Answer: a
Problem: a train 110 m long is running with a speed of 50 km / h . in how many seconds will the train pass a man who is running at 5 km / h in the direction opposite to that in which the train is going ?
Options: a ) 6.1 , b ) 7.2 , c ) 8.3 , d ) 9.4 , e ) 10.5
Rationale: "the speed of the train relative to the man = 50 + 5 = 55 km / h . 55000 m / h * 1 h / 3600 s = ( 550 / 36 ) m / s ( 110 m ) / ( 550 / 36 m / s ) = ( 110 * 36 ) / 550 = 36 / 5 = 7.2 seconds the answer is b ."
Answer: b
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in h hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of h ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * h = 1 = > x = 1 / h when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / h = 4 / 3 = > 1 / h = ( 8 - 3 ) / 6 = 5 / 6 = > h = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Problem: if two - third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .
Options: a ) 90 seconds , b ) 150 seconds , c ) 60 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: 2 / 3 filled in 100 seconds 1 / 3 filled in 50 secs then 2 / 3 + 1 / 3 = 100 + 50 seconds = 150 seconds answer : b
Answer: b
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 14
Rationale: "for unit digit of a ^ 2 to be 9 . . . unit digit of a has to be 3 or 7 . . . now for unit digit of ( a + 1 ) ^ 2 to be 4 . . unit digit of a has to be 1 or 7 . . . . from the above two conditions , unit value of a has to be 7 , which will satisfy both the conditions . . . now id unit digit of a is 7 , unit digit of ( a + 2 ) ^ 2 hast to be 1 . answer : a"
Answer: a
Problem: if the cost price is 81 % of selling price then what is the profit percentage .
Options: a ) 22.45 , b ) 23.45 , c ) 32.45 , d ) 23.54 , e ) 23.55
Rationale: selling price = rs 100 : then cost price = rs 81 : profit = rs 19 . profit = { ( 19 / 81 ) * 100 } % = 23.45 % answer is b .
Answer: b
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 5000 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 16 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 5000 ) x 100 = 9.6 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 9.6 % x ( 100 / 60 ) = 16 % the correct answer is ( b ) ."
Answer: b
Problem: in company j , the total monthly payroll for the 15 factory workers is $ 30000 and the total monthly payroll for the 30 office workers is $ 75000 . by how much does the average ( arithmetic mean ) monthly salary of an office worker exceed that of a factory worker in this company ?
Options: a ) $ 450 , b ) $ 500 , c ) $ 600 , d ) $ 650 , e ) $ 750
Rationale: the average monthly salary of a factory worker is : $ 30000 / 15 = $ 2000 . the average monthly salary of an office worker is : $ 75000 / 30 = $ 2500 . the difference in average salary is : $ 2500 - $ 2000 = $ 500 . the answer is b .
Answer: b
Problem: the average mark of the students of a class in a particular exam is 70 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ?
Options: a ) 20 , b ) 15 , c ) 10 , d ) 12 , e ) 25
Rationale: "let the number of students who wrote the exam be x . total marks of students = 70 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 70 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 20 x = > x = 10 answer : c"
Answer: c
Problem: what is the smallest positive integer nn such that √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
Rationale: "sol : let ' s factorize 6480 and we get 6480 = 3 ^ 4 * 2 ^ 4 * 5 now we need to see for what minimum value of n √ n * 6480 = a ^ 3 where a is an integer so from 6480 we already have 2 ^ 4 * 3 ^ 4 * 5 * n √ n = ( 2 ^ 2 ) ^ 3 * ( 3 ^ 2 ) ^ 3 * ( 5 ) ^ 3 why cause a is an integer which will need to be have the same factors which are in lhs solving for n √ n = ( 2 ^ 6 * 3 ^ 6 * 5 ^ 3 ) / 2 ^ 4 * 3 ^ 4 * 5 and we get n √ n = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 or n = 2 ^ 4 * 3 ^ 4 * 5 ^ 4 or 30 ^ 4 answer is e"
Answer: e
Problem: what will be the fraction of 12 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 3 / 25 , e ) none of these
Rationale: "explanation : 12 * 1 / 100 = 3 / 25 . option d"
Answer: d
Problem: at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 20 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 23 , c ) 2 / 5 , d ) 8 / 14 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 20 % of 60 = 12 total new books = 28 fraction = 16 / 28 = 8 / 14 ans : d"
Answer: d
Problem: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is ?
Options: a ) 26 , b ) 28 , c ) 80 , d ) 26 , e ) 21
Rationale: "let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c"
Answer: c
Problem: a rectangle having length 120 cm and width 50 cm . if the length of the rectangle is increased by ten percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 7.69 % , e ) none of these
Rationale: "explanation : solution : ( 10 / ( 120 + 10 ) * 100 ) % = 7.69 % answer : d"
Answer: d
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 39 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 31 degrees , d ) 34 degrees , e ) 74 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 39 tu + w + th = 192 - 39 = 153 f = 184 – 153 = 31 answer : c"
Answer: c
Problem: it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 3 mile / hour , what is the speed with which joey returns ?
Options: a ) 1 , b ) 6 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 2 miles an hour let the other half be x miles an hour now , avg speed = 3 mile an hour 2 * 2 * x / 2 + x = 3 4 x = 3 x + 6 = > x = 6 b"
Answer: b
Problem: a man is 16 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 14 years , c ) 16 years , d ) 18 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 16 . = > 2 ( x + 2 ) = ( x + 16 + 2 ) = > 2 x + 4 = x + 18 = > x = 14 years option b"
Answer: b
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 50 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 15 - 2.5 = 12.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.5 - 2.5 = 10 km / hr answer is a ."
Answer: a
Problem: a man ' s speed with the current is 21 km / hr and the speed of the current is 4.3 km / hr . the man ' s speed against the current is
Options: a ) 9.2 , b ) 10.3 , c ) 11.5 , d ) 12.4 , e ) 13
Rationale: "man ' s rate in still water = ( 21 - 4.3 ) km / hr = 16.7 km / hr . man ' s rate against the current = ( 16.7 - 4.3 ) km / hr = 12.4 km / hr . answer : d"
Answer: d
Problem: three cubes of metal whose edges are 9 , 12 and 15 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 21 cm , b ) 19 cm , c ) 32 cm , d ) 18 cm , e ) 28 cm
Rationale: "93 + 123 + 153 = a 3 = > a = 18 answer : d"
Answer: d
Problem: martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for 85 cents , and zachary buys a pencil and an eraser for 45 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )
Options: a ) 300 , b ) 315 , c ) 330 , d ) 345 , e ) 360
Rationale: pencil + notebook = 80 notebook + eraser = 85 pencil + eraser = 45 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 210 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 210 ) = 315 the answer is b .
Answer: b
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 25 % . what is the selling price of the cycle ?
Options: a ) s . 1050 , b ) s . 1160 , c ) s . 1190 , d ) s . 1202 , e ) s . 1204
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 25 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1050 . answer : a"
Answer: a
Problem: 1 + 3 = 2 2 + 3 = 10 3 + 3 = 30 4 + 3 = 68 5 + 3 = ? ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: 1 ^ 3 + 3 - 2 = 2 , 2 ^ 3 + 3 - 1 = 10 , 3 ^ 3 + 3 - 0 = 30 , 4 ^ 3 + 3 + 1 = 68 , 5 ^ 3 + 3 + 2 = 130 answer : c
Answer: c
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 90 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 240 , c ) 360 , d ) 495 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 90 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 90 = 405 . total area = 90 + 405 = 495 answer : d ."
Answer: d
Problem: what is the difference between the place value of 2 in the numeral 7669 ?
Options: a ) 160 , b ) 165 , c ) 180 , d ) 190 , e ) 540
Rationale: answer : option ' e ' 600 - 60 = 540
Answer: e
Problem: machine a and machine b are each used to manufacture 770 sprockets . it takes machine a 10 hours longer to produce 770 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "machine b : takes x hours to produce 770 sprockets machine a : takes ( x + 10 ) hours to produce 770 sprockets machine b : in 1 hour , b makes 770 / x sprockets machine a : in 1 hour , a makes 770 / ( x + 10 ) sprockets equating : 1.1 ( 770 / ( x + 10 ) ) = 770 / x 847 / ( x + 10 ) = 770 / x 847 x = 770 x + 7700 77 x = 7700 x = 100 a makes 770 / ( 110 ) = 7 sprockets per hour answer : b"
Answer: b
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 370 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 100 , d ) rs . 350 , e ) none of these
Rationale: z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 740 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 37 3.7 z = 370 , z = 100 answer : . c
Answer: c
Problem: village x has a population of 70000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 14 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 70000 - 1200 p = 42000 + 800 p 2000 p = 28000 p = 14 answer is a ."
Answer: a
Problem: a , b , c can do a piece of work in 11 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by b and c on alternate days ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: a + b 1 day work = 1 / 11 + 1 / 20 = 31 / 220 a + c 1 day work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 days = 31 / 220 + 6 / 55 = 55 / 220 = 1 / 4 1 / 4 work is done by a in 2 days whole work will be done in 2 * 4 = 8 days answer is c
Answer: c
Problem: a group of men decided to do a work in 8 days , but 3 of them became absent . if the rest of the group did the work in 10 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 25 , e ) 18
Rationale: "original number of men = 3 * 10 / ( 10 - 8 ) = 15 answer is a"
Answer: a
Problem: x , y , and z are different prime numbers . the product x ^ 2 * y ^ 2 * z ^ 2 is divisible by how many different positive numbers ?
Options: a ) 9 , b ) 18 , c ) 27 , d ) 36 , e ) 45
Rationale: "the exponents of x ^ 2 * y ^ 2 * z ^ 2 are 2 , 2 , and 2 . the number of factors is ( 2 + 1 ) ( 2 + 1 ) ( 2 + 1 ) = 27 the answer is c ."
Answer: c
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 36 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 36 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 36 lets say x machines are used to attain the desired rate , thus x / 36 + x / 36 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + x ) / 36 = 1 / 2 2 x / 36 = 1 / 2 x = 9 . qa = 9 ( answer d )"
Answer: d
Problem: ? x 24 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 1730 , e ) 534
Rationale: "let y x 24 = 173 x 240 then y = ( 173 x 240 ) / 24 = 173 x 10 = 1730 answer : d"
Answer: d
Problem: in how many no . between 10 and 20 exactly two of the digits is 1 ?
Options: a ) 25 , b ) 35 , c ) 10 , d ) 1 , e ) 15
Rationale: "it ' s simple can be solved by elimination of answer choices . option a and b are too large , not possible . even ce are large to have correct choice . ans : d"
Answer: d
Problem: a man sells a car to his friend at 11 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 25561.80 , b ) rs . 37500.80 , c ) rs . 50561.80 , d ) rs . 60000 , e ) none of these
Rationale: explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 11 % . now s . p = rs . 45000 and loss = 11 % c . p . rs . [ 100 / 89 ã — 45000 ] = rs . 50561.80 . correct option : c
Answer: c
Problem: given that 268 x 74 = 19532 , find the value of 2.68 x . 74 .
Options: a ) 1.9532 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9532 answer a"
Answer: a
Problem: if a = { 1 , 3 , 5 } , b = { 3 , 5 , 6 } . find a ∪ b
Options: a ) { 1,5 } , b ) { 1,3 , 5,6 } , c ) { 2,6 } , d ) { 8,9 } , e ) { 4,12 }
Rationale: "a = { 1 , 3,5 } b = { 3 , 5,6 } therefore , correct answer : a ∪ b = { 1 , 3 , 5 , 6 } b"
Answer: b
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 3 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 64
Rationale: "let the numbers be 1 x and 3 x . then , their l . c . m = 3 x . so , 3 x = 48 or x = 16 . the numbers are 16 and 48 . hence , required sum = ( 16 + 48 ) = 64 . answer : e"
Answer: e
Problem: after a storm deposits 115 billion gallons of water into the city reservoir , the reservoir is 80 % full . if the original contents of the reservoir totaled 245 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 115 billion gallons , volume of water in the reservoir = 245 + 115 = 360 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 360 / 0.8 = 450 billion gallons therefore percentage of reservoir that was full before the storm = ( 245 / 450 ) * 100 = 54.4 % option c"
Answer: c
Problem: the sum of the ages of 5 children born at the intervals of 2 years each is 50 years . what is the age of the youngest child ?
Options: a ) 6 , b ) 18 , c ) 10 , d ) 99 , e ) 38
Rationale: let x = the youngest child . each of the other four children will then be x + 2 , x + 4 , x + 6 , x + 8 . we know that the sum of their ages is 50 . so , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 therefore the youngest child is 6 years old answer : a
Answer: a
Problem: an inspector rejects 0.08 % of the meters as defective , how many meters he examine to reject 2 meteres
Options: a ) 1200 , b ) 2400 , c ) 1400 , d ) 2500 , e ) none of these
Rationale: explanation : it means that 0.08 % of x = 2 = > ( 8 / 100 × 100 × x ) = 2 = > x = 2 × 100 × 100 / 8 = > x = 2500 option d
Answer: d
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 36 / 49 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 7 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 36 / 49 = ( 6 / 7 ) * ( 6 / 7 ) therefore probability that the next one she draws is pink = 1 / 7 option ( a )"
Answer: a
Problem: increasing the original price of a certain item by 30 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 69.0
Rationale: "we ' re told that the original price of an item is increased by 30 % and then that price is increased by 30 % . . . . if . . . . starting value = $ 100 + 30 % = 100 + . 30 ( 100 ) = 130 + 30 % = 130 + . 30 ( 130 ) = 130 + 39 = 169 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 59 / 100 = 69 % final answer : e"
Answer: e
Problem: the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 15 , what is the perimeter of the garden , in feet ?
Options: a ) 28 , b ) 36 , c ) 40 , d ) 56 , e ) 64
Rationale: "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 15 ( p ^ 2 ) / 16 = 2 p + 15 p ^ 2 = 32 p + 240 p ^ 2 - 32 p - 240 = 0 p ^ 2 - 40 p + 6 p - 240 = 0 p ( p - 40 ) + 6 ( p + 40 ) = 0 ( p - 40 ) ( p + 6 ) = 0 p = 40 or - 6 discarding negative value , p = 40 answer is c"
Answer: c
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 370 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 740 , e ) 720
Rationale: explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 370 ) = 2 + 2 ( extra ) = > 2 x - 740 = x = > x = 740 . answer : d
Answer: d
Problem: if the perimeter of a rectangular garden is 900 m , its length when its breadth is 190 m is ?
Options: a ) 338 m , b ) 778 m , c ) 200 m , d ) 260 m , e ) 971 m
Rationale: "2 ( l + 190 ) = 900 = > l = 260 m answer : d"
Answer: d
Problem: two pipes can fill a tank in 20 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 ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 20 + v / 15 - v / 10 = v / 60 per minute the tank will be filled in 60 minutes . the answer is e ."
Answer: e
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 200 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 200 meters , thus the circumference is 200 + 200 = 400 meters . answer : d ."
Answer: d
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 11 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 11 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 11 hence x = 13 . answer is c"
Answer: c
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 9 , 0 ) , ( 1 , 2 ) and ( 9 , 2 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 5 , b ) 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 8
Rationale: if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 5 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 5 , 1 ) is 1 / 5 . the answer is d .
Answer: d
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - third of his earnings to charity . if the worker ' s charitable contributions totaled one - eighth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 33 / 25 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 3 = 1 / 8 ( 11 x + nx ) ; 11 / 10 + n / 3 = 1 / 8 ( 11 + n ) 33 + 10 n / 30 = 11 + n / 8 = > 264 + 80 n = 330 + 30 n = > 50 n = 66 n = 66 / 50 = 33 / 25 answer : d ."
Answer: d
Problem: what is the units digit of ( 5 ! * 4 ! + 6 ! * 5 ! ) / 3 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 1
Rationale: "( 5 ! * 4 ! + 6 ! * 5 ! ) / 3 = 5 ! ( 4 ! + 6 ! ) / 3 = 120 ( 24 + 720 ) / 3 = ( 120 * 744 ) / 3 = 120 * 248 units digit of the above product will be equal to 0 answer d"
Answer: d
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 3 parts , respectively . this will give us in the final mixture ( 5 + 3 ) : ( 3 + 3 ) , which means 4 : 3 answer d .
Answer: d
Problem: if x is 11 percent greater than 70 , then x =
Options: a ) 77.7 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 70 = ( 70 * 0.11 ) = 7.7 11 % greater than 70 = 70 + 7.7 = 77.7 answer is clearly a ."
Answer: a
Problem: if an examination 63 % of the candidates in english , 65 % passed in mathematics , and 27 % failed in both subjects . what is the pass percentage ?
Options: a ) 55 % , b ) 60 % , c ) 65 % , d ) 75 % , e ) none .
Rationale: fail in english = 100 - 63 = 37 % fail in maths = 100 - 65 = 35 % so pass % = 100 - ( 37 + 35 - 27 ) = 55 % answer : a
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train ?
Options: a ) 250 meter , b ) 876 meter , c ) 167 meter , d ) 719 meter , e ) 169 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : a"
Answer: a
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 1 strokes ?
Options: a ) 1 / 2 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 so removed = 1 - 1 / 2 = 1 / 2"
Answer: a
Problem: fred and sam are standing 40 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 4 miles per hour and sam walks at a constant speed of 4 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 20 , d ) 30 , e ) 45
Rationale: "relative distance = 40 miles relative speed = 4 + 4 = 8 miles per hour time taken = 40 / 8 = 5 hours distance travelled by sam = 4 * 5 = 20 miles = c"
Answer: c
Problem: the average of first seven multiples of 5 is :
Options: a ) 20 , b ) 16 , c ) 15 , d ) 8 , e ) 10
Rationale: "explanation : ( 5 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 5 x 28 / 7 = 20 answer : a"
Answer: a
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot at the rate of 26.50 per metre is 5,300 , what is the length of the plot ( in metres ) ?
Options: a ) 40 , b ) 120 , c ) 50 , d ) data inadequate , e ) none of these
Rationale: "perimeter of the rectangular plot = [ ( b + 20 ) + b ] × 2 = 5300 / 26.5 = 200 = 200 ∴ ( 2 b + 20 ) 2 = 200 ⇒ b = 40 ⇒ l = 40 + 20 = 60 m answer e"
Answer: e
Problem: a , b and c are entered into a partnership . a invested rs . 6500 for 6 months , b invested rs . 8400 for 5 months and c invested for rs . 10000 for 3 months . a is a working partner and gets 5 % of the total profit for the same . find the share of c in a total profit of rs . 7400 ?
Options: a ) 2998 , b ) 1900 , c ) 2788 , d ) 2662 , e ) 1122
Rationale: 65 * 6 : 84 * 5 : 100 * 3 26 : 28 : 20 c share = 74000 * 95 / 100 = 7030 * 20 / 74 = > 1900 answer : b
Answer: b
Problem: if 25 men do a work in 96 days , in how many days will 40 men do it ?
Options: a ) 66 , b ) 53 , c ) 55 , d ) 60 , e ) 61
Rationale: "25 * 96 = 40 * x x = 60 days answer : d"
Answer: d
Problem: there are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 8 and for second = 7 so total methods = 8 * 7 = 56 answer : d"
Answer: d
Problem: the expression ( 12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 ) will be a perfect square for p equal to
Options: a ) 0.28 , b ) 0.26 , c ) 1 , d ) 0 , e ) 2
Rationale: explanation : 12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 = ( 12.86 ) 2 + 12.86 × p + ( 0.14 ) 2 this can be written as ( 12.86 + 0.14 ) 2 = 132 , if 12.86 × p = 2 × 12.86 × 0.14 i . e . , if p = 2 × 0.14 = 0.28 hence , p = 0.28 . answer : option a
Answer: a
Problem: if the sample interest on a sum of money 20 % per annum for 2 years is $ 400 , find the compound interest on the same sum for the same period at the same rate ?
Options: a ) $ 460 , b ) $ 510 , c ) $ 440 , d ) $ 500 , e ) $ 550
Rationale: "rate = 20 % time = 2 years s . i . = $ 400 principal = 100 * 400 / 20 * 2 = $ 1000 amount = 1000 ( 1 + 20 / 100 ) ^ 2 = $ 1440 c . i . = 1440 - 1000 = $ 440 answer is c"
Answer: c
Problem: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is
Options: a ) 36 , b ) 40 , c ) 99 , d ) 13 , e ) 12
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b"
Answer: b
Problem: a man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km per hour . find the distance travelled on foot .
Options: a ) 26 km , b ) 32 km , c ) 30 km , d ) 28 km , e ) none
Rationale: total time = 7 hrs let the distance travelled by foot @ 8 kmph be x kms ? distance travlled by bicycle @ 16 kmph be ( 80 - x ) kms atq . 7 hr = x / 8 + ( 80 - x ) / 16 ? 7 = ( 2 x + 80 - x ) / 16 ? x = 32 kms answer : b .
Answer: b
Problem: after decreasing 24 % in the price of an article costs rs . 820 . find the actual cost of an article ?
Options: a ) 1400 , b ) 1079 , c ) 1200 , d ) 1023 , e ) 1523
Rationale: "cp * ( 76 / 100 ) = 820 cp = 10.78 * 100 = > cp = 1079 answer : b"
Answer: b
Problem: if x ^ 2 – x = 2 , then one possible value of x – 4 =
Options: a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 5
Rationale: x ^ 2 – x = 2 i . e . x ^ 2 – x - 2 = 0 i . e . x ^ 2 + x - 2 x - 2 = 0 i . e . ( x - 2 ) ( x + 1 ) = 0 i . e . x = 2 or - 1 i . e . x - 4 = 2 - 4 or - 1 - 4 i . e . x - 4 = - 2 or - 5 answer : option b
Answer: b
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 8 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.15 % , c ) 14.14 % , d ) 13.33 % , e ) 12.52 %
Rationale: ( 100 % + 8 % ) * ( 100 % - 19 % ) = 1.08 * . 81 = 0.8748 1 - 0.8748 = 12.52 % lost = - 12.52 % the answer is e the organization has lost 12.52 % of its total volunteers from fall to spring .
Answer: e
Problem: the side of a cube is 12 m , find the lateral surface area ?
Options: a ) 816
b ) 516
c ) 716
d ) 216
e ) 916
Rationale: lateral surface = 4 a ( power ) 2 4 × 12 ( power ) 2 = 4 × 144 = > 516 m ( power ) 2 answer is b .
Answer: b
Problem: a train passes a platform in 25 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 75 , b ) 25 , c ) 26 , d ) 23 , e ) 22
Rationale: speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 20 = > 300 + l = 15 × 25 = 375 = > l = 375 - 300 = 75 meter answer is a .
Answer: a
Problem: 5 + 8
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: b
Answer: b
Problem: how many integers between 324,700 and 418,600 have tens digit 1 and units digit 3 ?
Options: a ) 652 , b ) 827 , c ) 939 , d ) 1045 , e ) 1136
Rationale: "the integers are : 324,713 324,813 etc . . . 418,513 the number of integers is 4186 - 3247 = 939 the answer is c ."
Answer: c
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 250 . find the total worth of the stock ?
Options: a ) 12500 , b ) 20000 , c ) 20289 , d ) 20027 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 250 = > x = 12500 answer : a"
Answer: a
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 5 cm , and the point of contact is 7 cm above the ground , what is the radius of the other ball ?
Options: a ) 10 cm , b ) 25 / 2 cm , c ) 35 / 3 cm , d ) 15 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 5 = 5 / r - 5 giving r = 35 / 3 . answer : c"
Answer: c
Problem: a couple spent $ 158.40 in total while dining out and paid this amount using a credit card . the $ 158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 115 , b ) $ 120 , c ) $ 125 , d ) $ 130 , e ) $ 135
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 158.40 x = 120 the correct answer is b ."
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 120 inches and the width is 108 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 125
b ) b 120
c ) c 70
d ) d 40
e ) e 10
Rationale: l = 120 / 12 = 10 ft w = 108 / 12 = 9 ft area of paper = 90 area of cube = 10 * side ^ 2 side of cube = 5 v of cube = 125
Answer: a
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 3 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 3 and m + 2 = 2 * ( n + k ) + 3 . by 1 st equation we have m - 2 n = 3 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 3 = 2 k + 1 - - - > k = 1 . the answer is , therefore , ( b ) ."
Answer: b
Problem: when positive integer x is divided by positive integer y , the remainder is 5 . if x / y = 96.2 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.2 and remainder is 5 so . 2 x y = 5 hence y = 25 ans d"
Answer: d
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 3.5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5040 , c ) 2889 , d ) 2870 , e ) 2799
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3.5 = 5040 . answer : b"
Answer: b
Problem: what is the greater of the two numbers whose product is 2048 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 90 , b ) b ) 32 , c ) c ) 64 , d ) d ) 70 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2048 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2048 / s = 64 . answer : c"
Answer: c
Problem: a can finish a work in 6 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 2 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 3 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 6 + 1 / 3 ) = 1 / 2 so in one day 1 / 2 work will be done answer : a"
Answer: a
Problem: a car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 50 miles per hour , how many hours long is the trip ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let t be the total time of the trip . 35 * 4 + 53 ( t - 4 ) = 50 t 3 t = 212 - 140 t = 24 the answer is e ."
Answer: e
Problem: 8 men , working 9 hours a day can complete a work in 24 days . how many hours a day must 12 men work to complete the same work in 16 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 9 * 24 = 1728 12 × 16 × ( x ) = 1728 x = 9 the answer is d ."
Answer: d
Problem: what percent of 13 is 13 percent of 1 ?
Options: a ) 0.001 , b ) 0.01 , c ) 1 , d ) 10 , e ) 101 .
Rationale: "13 % of 1 = ( 13 / 100 ) * 1 = 13 / 100 to determine what percentage of 13 this is : [ 13 ] [ / 100 * 13 ] * 100 = 1 % ans : c"
Answer: c
Problem: the volume of a cube is 1000 cc . find its surface .
Options: a ) 864 , b ) 556 , c ) 255 , d ) 600 , e ) 267
Rationale: "a 3 = 1000 = > a = 10 6 a 2 = 6 * 10 * 10 = 600 answer : d"
Answer: d
Problem: the speed of a boat in still water is 24 kmph . what is the speed of the stream if the boat can cover 64 km downstream or 32 km upstream in the same time ?
Options: a ) 8 kmph , b ) 6 kmph , c ) 7 kmph , d ) 5 kmph , e ) 4 kmph
Rationale: "x = the speed of the stream ( 24 + x ) / ( 24 - x ) = 2 / 1 24 + x = 48 - 2 x 3 x = 24 x = 8 km / hour if the speed of the stream is 8 km / hour , then the ' downstream ' speed of the boat is 24 + 8 = 32 km / hour and the ' upstream ' speed of the boat is 24 - 8 = 16 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 32 = 64 km downstream and 2 x 16 = 32 km / hour upstream . answer : a"
Answer: a
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number m is
Options: a ) 74 , b ) m = 75 , c ) m = 175 , d ) m = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 72 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 15 + 19 + 8 ) = 20 % basic astrophysics . 10 % of 360 ° is 72 ° . answer : e ."
Answer: e
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 36 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 36 = 6 k + 4 p = > k = 4 , p = 3 total red ' s in bag a will be 2 k = 8 e"
Answer: e
Problem: when asked what the time is , a person answered that the amount of time left is 1 / 2 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 4 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 2 x ⇒ x = 16 time is 4 pm answer : d"
Answer: d