regisss/math_qa huggingface dataset:
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 22 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 210 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 22 = 330 m . let the length of the platform be x m . then , ( x + 330 ) / 36 = 15 = > x = 210 m . answer : b"
Answer: b
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.55 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 7 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.55 9.9 - 45 x + 36 x = 8.55 9 x = 1.35 x = 0.15 the answer is e ."
Answer: e
Problem: the average age of a , b and c is 29 years . if the average age of a and c is 32 years , what is the age of b in years ?
Options: a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 23
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 29 ã — 3 â € “ 32 ã — 2 = 87 â € “ 64 = 23 years e"
Answer: e
Problem: the number of sailors on a ship is 88 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 47 : 25 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1 / 88 * officer sailor / officer = 1.88 / 1 = 188 / 100 = 47 / 25 answer will be c"
Answer: c
Problem: if each side of a square is increased by 6 % , find the percentage change in its area ?
Options: a ) 10.68 % , b ) 8.72 % , c ) 9.28 % , d ) 12.36 % , e ) 11.91 %
Rationale: "let each side of the square be a , then area = a x a new side = 106 a / 100 = 53 a / 50 new area = ( 53 a x 53 a ) / ( 50 x 50 ) = ( 2809 a ² / 2500 ) increased area = = ( 2809 a ² / 2500 ) - a ² increase % = [ ( 309 a ² / 2500 ) x ( 1 / a ² ) x 100 ] % = 12.36 % answer : d"
Answer: d
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 300 m , its area is ?
Options: a ) 3000 sq m
b ) 1878 sq m
c ) 2789 sq m
d ) 26811 sq m
e ) 29762 sq m
Rationale: 5 x + 12 x + 13 x = 300 = > x = 10 a = 50 , b = 120 , c = 130 s = ( 50 + 120 + 130 ) / 2 = 150 3000 sq m answer : a
Answer: a
Problem: a coin is tossed 7 times . what is the probability of getting exactly 6 heads ?
Options: a ) 7 / 32 , b ) 3 / 64 , c ) 5 / 64 , d ) 3 / 128 , e ) 7 / 128
Rationale: "the number of possible outcomes is 2 ^ 7 = 128 there are 7 ways to get exactly 6 heads . p ( exactly 6 heads ) = 7 / 128 the answer is e ."
Answer: e
Problem: approximately how many cubic feet of water are needed to fill a circular swimming pool that is 60 feet across and 6 feet deep ?
Options: a ) 900 , b ) 4000 , c ) 10000 , d ) 17000 , e ) 25000
Rationale: "answer should be d . v = \ pir ^ 2 h = \ pi * 30 ^ 2 * 6 = approximately 17000"
Answer: d
Problem: how many integer values r are there for x such that 1 < 3 x + 5 < 17 ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: 1 < 3 x + 5 < 17 = > - 4 < 3 x < 12 = > - 4 / 3 < x < 4 x can take integer values r - 1,0 , 1 , 2 , 3 answer d
Answer: d
Problem: find the missing value : 8597 - ? = 7429 - 4358
Options: a ) 5526 , b ) 5426 , c ) 5326 , d ) 5226 , e ) none of them
Rationale: "let 8597 - x = 7429 - 4358 . then , x = ( 8597 + 4358 ) - 7429 = 12955 - 7429 = 5526 . answer is a ."
Answer: a
Problem: if m and n are positive integers and n ≠ 1 , then mn ( n − 1 ) is
Options: a ) m - n , b ) m + n , c ) mn , d ) mn ^ 2 - mn , e ) mn ^ 2
Rationale: "mn ( n - 1 ) = mn ^ 2 - mn answer : d"
Answer: d
Problem: two numbers are in the ratio of 5 : 7 . if 20 is subtracted from each number , they are in the ratio of 5 : 9 . what are the two numbers ?
Options: a ) 35 , 49 , b ) 40 , 56 , c ) 45 , 63 , d ) 50 , 70 , e ) 55 , 77
Rationale: "( 5 x - 20 ) : ( 7 x - 20 ) = 5 y : 9 y 5 x - 20 = 5 y 7 x - 20 = 9 y 140 - 100 = 45 y - 35 y 40 = 10 y y = 4 5 x - 20 = 20 x = 8 the two numbers are 5 x and 7 x which are 40 and 56 . the answer is b ."
Answer: b
Problem: a train 500 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "length = speed * time speed = l / t s = 500 / 10 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : e"
Answer: e
Problem: a retailer sold 2 houses at each $ 15000 . on 1 st house he got 20 % profit and on 2 nd house he loss 5 % then find his net profit or loss ?
Options: a ) 10 % , b ) 9 % , c ) 14 % , d ) 15 % , e ) 12 %
Rationale: "a = 20 % b = - 5 % profit % = 20 - 5 + ( - 100 / 100 ) = 14 % answer is c"
Answer: c
Problem: ages of two persons differ by 16 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 16,32 , d ) 18,34 , e ) 19,32
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 16 ) = > 3 ( x - 6 ) = ( x + 16 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 10 = > x = 14 . so other person age is x + 16 = 30 answer : option b"
Answer: b
Problem: the sum of two consecutive numbers is 452 . the greatest among these three number is :
Options: a ) 226 , b ) 228 , c ) 229 , d ) 230 , e ) 200
Rationale: "let the numbers be x , x + 1 then , x + ( x + 1 ) = 452 2 x = 450 x = 225 greatest number , ( x + 1 ) = 226 answer : a"
Answer: a
Problem: a car travels uphill at 30 km / hr and downhill at 90 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 39 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 90 = 5 / 9 ; avg speed = 150 / ( 10 / 3 + 5 / 9 ) = 39 kmph answer : b"
Answer: b
Problem: six 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 7776 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 = 46656 ways . hence the probability is 6 / 46656 = 1 / 7776 answer : b"
Answer: b
Problem: a present value of a machine is $ 700 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 567
Rationale: "p = $ 700 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 700 * 9 / 10 * 9 / 10 = $ 567 answer is e"
Answer: e
Problem: if xy denotes x is raised to the power y , find the last two digits of 19413843 + 19614181
Options: a ) 67 , b ) 97 , c ) 55 , d ) 32 , e ) 62
Rationale: "1721 ^ 3856 unit digit = 1 ^ 2 = 1 10 th digit = 5 * 6 = 30 = 0 means last two digit = 1 and 1982 ^ 4181 unit digit = 1 10 th digit = 8 * 2 = 16 mean last two digit = 61 hence , 61 + 1 = 62"
Answer: e
Problem: two trains 200 m and 180 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 132 sec , c ) 192 sec , d ) 273.6 sec , e ) none
Rationale: "solution relative speed = ( 45 - 40 ) kmph = 5 kmph = ( 5 x 5 / 18 ) m / sec = ( 25 / 18 ) m / sec time taken = ( 380 x 18 / 25 ) sec = 273.6 sec . answer d"
Answer: d
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "in 24 liters , red = 5 / 8 * 24 = 15 and blue = 9 so , 15 / ( 9 + x ) = 3 / 5 or , x = 16 ( answer d )"
Answer: d
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 33 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 22 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: 262.85 ( 33 ) + 3 , 104.35 x = 1 , 399.45 ( 33 + x ) solve the equation . 262.85 ( 33 ) + 3 , 104.35 x = 1 , 399.45 ( 33 + x ) 8 , 674.05 + 3 , 104.35 x = 46181.85 + 1 , 369.45 x 8 , 674.05 + 1 , 704.9 x = 46181.85 1 , 704.9 x = 37 , 507.8 x = 22 answer is b .
Answer: b
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 7800 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 7800 ] – [ 3 1 / 3 % of rs . 7800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 7800 = 1 / 6 % of rs . 7800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 7800 ] = rs . 13 . answer is b ."
Answer: b
Problem: a train 200 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 12 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 200 m at ( 50 / 3 ) m / sec = ( 200 x 3 / 50 ) sec = 12 sec . answer d"
Answer: d
Problem: evaluate : 40 - 12 ÷ 6 × 2 =
Options: a ) a ) 24 , b ) b ) 36 , c ) c ) 48 , d ) d ) 60 , e ) e ) 72
Rationale: "according to order of operations , 12 ÷ 6 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 6 × 2 = 2 × 2 = 4 hence 40 - 12 ÷ 6 × 2 = 40 - 4 = 36 correct answer is b ) 36"
Answer: b
Problem: in town x , 96 percent of the population are employed , and 24 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 75 % , e ) 52 %
Rationale: "total employed people 96 % , out of which 24 are employed males , hence 72 % are employed females . ( employed females ) / ( total employed people ) = 72 / 96 = 3 / 4 = 75 % answer : d ."
Answer: d
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 4 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 16
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 4 ( pir ^ 2 ) pir ^ 2 = 8 pir r = 8 answer : d"
Answer: d
Problem: in an entrance exam , 3 marks is awarded for every correct answer and ( - 1 ) for every wrong answer . if a student gets 38 marks after attempting all questions , find the number of questions answered correctly if the total questions were 70 .
Options: a ) 38 , b ) 40 , c ) 27 , d ) 43 , e ) 56
Rationale: explanation : let x be the number of questions answered correctly . hence , number of questions whose answer were wrong = ( 70 – x ) 3 * x + ( 70 – x ) * ( - 1 ) = 38 4 x = 38 + 70 = 108 x = 27 answer c
Answer: c
Problem: a meal cost $ 35.50 adn there was no tax . if the tip was more than 5 pc but less than 8 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 38 , e ) 36 - 37
Rationale: 5 % ( 35.5 ) = 1.775 8 % ( 35.5 ) = 2.84 total amount could have been 35.5 + 1.775 and 35.5 + 2.84 = > could have been between 37.275 and 38.34 = > approximately between 37 and 38 answer is b . d
Answer: d
Problem: r is the set of positive odd integers less than 10 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none
b ) two
c ) four
d ) five
e ) seven
Rationale: squares < 10 { 1 , 4,9 } s = { 1,9 } r = { 1,3 , . . . . . 10 } hence b .
Answer: b
Problem: in a certain kindergarten , every child has got either a dog or a cat or both . 18 children have got dogs only and 6 children have got both dogs and cats . if there are 30 children in the kindergarten , how many of them have cats ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 20
Rationale: a : only cats b : both cats and dogs c : only dogs as per question , a + b + c = 30 c = 18 b = 6 , so a = 6 . hence , a + b = 12 . answer is b
Answer: b
Problem: if 45 % of z is 90 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 150
Rationale: ( 45 / 100 ) z = ( 90 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 90 / 100 ) * ( 3 / 4 ) x i . e . z = ( 90 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.5 ) x = ( 150 / 100 ) x i . e . z is 150 % of x answer : option e
Answer: e
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 - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - seventh of his earnings for the entire year , what is the value of n ?
Options: a ) 31 / 4 , b ) 33 / 4 , c ) 29 / 4 , d ) 27 / 4 , e ) 25 / 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 7 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 7 ( 11 + n ) 11 + 2 n / 10 = 11 + n / 7 = > 77 + 14 n = 110 + 10 n = > 4 n = 33 n = 33 / 4 answer : b"
Answer: b
Problem: a lady builds 7 cm length , 18 cm width , and 3 cm height box using 9 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 42
b ) 45
c ) 47
d ) 49
e ) 56
Rationale: number of cubes required = volume of box / volume of cube = 7 * 18 * 3 / 9 = 42 cubes answer : a
Answer: a
Problem: solve the quickfire maths brain teaser â ˆ š 49 % = ?
Options: a ) 30 % , b ) 40 % , c ) 70 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 49 % = > â ˆ š 49 / â ˆ š 100 = > 7 / 10 = > 70 / 100 = > 70 % c"
Answer: c
Problem: the compound ratio of 1 : 4 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 3 : 10 , e ) 1 : 4
Rationale: "1 / 4 * 3 / 2 * 4 / 5 = 3 / 10 = 3 : 10 answer : d"
Answer: d
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 6 € ( 4 € 5 ) =
Options: a ) 480 , b ) 120 , c ) 160 , d ) 240 , e ) 360
Rationale: working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 6 € 40 = 2 * 6 * 40 = 480 hence , answer is a
Answer: a
Problem: a is a working partner and b is a sleeping partner in a business . a puts in 50,000 and b 60,000 . a gets 12.5 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the share of a in profit of 8800 .
Options: a ) 3500 , b ) 4600 , c ) 5400 , d ) 4800 , e ) none of these
Rationale: the amount a gets for managing = 12.5 % of rs . 8800 = 1100 remaining profit = 8800 – 1100 = 7700 this is to be divided in the ratio 5 : 6 . share of a = 5 / 11 of 7700 = 3500 ⇒ total share of a = 3500 + 1100 = 4600 . answer b
Answer: b
Problem: the number x of cars sold each week varies with the price y in dollars according to the equation x = 800000 – 50 y . what would be the total weekly revenue , in dollars , from the sale of cars priced at $ 12000 ?
Options: a ) 50,000 , b ) 750,000 , c ) 850,000 , d ) 7 , 500,000 , e ) 2,400 , 000,000
Rationale: number of cars sold = x = 800000 - 50 y y = 12000 x = 800000 - 600000 = 200000 revenue from 50000 cars = 12000 * 200000 = 2400000000 answer e
Answer: e
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 20 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 10800 , e ) 3600
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 20 ã — 4 ã — 270 â ‡ ” x = 20 x 4 x 270 / 6 = 3600 . answer e"
Answer: e
Problem: the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 111 cm . what was the actual average height of the students in the class ?
Options: a ) 174 cm , b ) 173 cm , c ) 172 cm , d ) 171 cm , e ) 170 cm
Rationale: "the total height was 40 cm too much . the average height should be reduced by 40 cm / 20 = 2 cm the answer is b ."
Answer: b
Problem: john was thrice as old as tom 6 years ago . john will be 2 times as old as tom in 4 years . how old is tom today ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 4 = 2 ( t + 4 ) ( 3 t - 12 ) + 4 = 2 t + 8 t = 16 the answer is c .
Answer: c
Problem: mary and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 800 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 2000 , b ) $ 6000 , c ) $ 4000 , d ) $ 1333 , e ) $ 3000
Rationale: explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 7 : 3 . i . e . , 70 % of 2 x would go to mary and 30 % of 2 x would go to mike . hence , mary would get ( 70 - 30 ) % of 2 x more than mike or 40 % of 2 x = $ 800 i . e . , ( 40 / 100 ) * 2 x = 800 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . the correct choice is ( e )
Answer: e
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds w in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out w : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much t does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) t = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Problem: in an intercollegiate competition that lasted for 3 days , 115 students took part on day 1 , 80 on day 2 and 100 on day 3 . if 50 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 40 took part on all three days , how many students took part only on day 3 ?
Options: a ) 20 , b ) 35 , c ) 40 , d ) 55 , e ) 60
Rationale: "day 1 & 2 = 50 ; only day 1 & 2 ( 50 - 40 ) = 10 , day 2 & 3 = 70 ; only day 2 & 3 ( 70 - 40 ) = 30 , only day 3 = 100 - ( 10 + 30 + 40 ) = 20 answer : a"
Answer: a
Problem: a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 401 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ?
Options: a ) 44001 , b ) 44000 , c ) 40400 , d ) 40401 , e ) can not be determined
Rationale: "explanatory answer the shape of the area used for growing cauliflower has remained a square in both the years . let the side of the square area used for growing cauliflower this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cauliflower last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cauliflower grown has increased by 401 , the area would have increased by 401 sq ft because each cauliflower takes 1 sq ft space . hence , x 2 - y 2 = 401 ( x + y ) ( x - y ) = 401 . 401 is a prime number and hence it will have only two factors . i . e . , 401 and 1 . therefore , 401 can be expressed as product of 2 numbers in only way = 401 * 1 i . e . , ( x + y ) ( x - y ) = 401 * 1 so , ( x + y ) should be 401 and ( x - y ) should be 1 . solving the two equations we get x = 201 and y = 200 . therefore , number of cauliflower produced this year = x 2 = 2012 = 40401 alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , b and c . as 44001,44000 and 40400 are not the square of any number . check choice d : if this year ' s produce is 40401 , last year ' s produce would have been 40401 - 401 = 40000 40000 is the square of 200 . so , 40401 is the answer . choice d ."
Answer: d
Problem: if 5 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 30 , c ) 36 , d ) 40 , e ) 60
Rationale: let the capacity of the tank = c ( 3 / 4 ) c + 5 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 5 = > ( 3 / 20 ) c = 5 = > c = ( 5 * 20 ) / 3 = 33.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 5 = 24.99 + 5 = 29.99 = 30 answer b
Answer: b
Problem: a retailer buys 120 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 210 , b ) 215 , c ) 212 , d ) 230 , e ) 320
Rationale: "let the market price of each pen be $ 1 then , cost price of 120 pens = $ 36 selling price of 120 pens = 99 % of $ 120 = $ 118.80 profit % = ( ( 82.80 * 100 ) / 36 ) % = 230 % answer d"
Answer: d
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 68 %
Options: a ) 14.11 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 68 / 100 = 50.40 so x = 14.11 answer : a"
Answer: a
Problem: on dividing number by 56 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: let x be the number and y be the quotient . then , x = 357 * y + 39 = ( 17 * 21 * y ) + ( 17 * 2 ) + 5 = 17 * ( 21 y + 2 ) + 5 . required remainder = 5 . answer : b
Answer: b
Problem: a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 1.60 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y . there are six possible numbers of pencils that fit that requirement : 1 pen : $ 0.35 and 5 pencils for $ 0.25 each . that ' s 1 pens and 5 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Problem: given that g and h are events such that q ( g ) = 0.30 q ( h ) = 0.9 q ( gnh ) = 0.9 find q ( g | h ) and q ( g | h )
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 6 , e ) 1 / 3
Rationale: here , g and h are events q ( g | h ) = q ( gnh ) / q ( h ) = 0.9 / 0.9 = 1 q ( g | h ) = q ( gnh ) / q ( g ) = 0.9 / 0.30 = 1 / 3 answer is c
Answer: c
Problem: 6000 − ( 105 ÷ 21.0 ) = ?
Options: a ) 6100 , b ) 5100 , c ) 550 , d ) 598 , e ) 5995
Rationale: "explanation : = 6000 − ( 105 / 21 ) = 6000 − 5 = 5995 option e"
Answer: e
Problem: a boats man can row in still water at speed of 7 km / hr . it takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km / hr . what is the distance between the two destinations ?
Options: a ) 40 , b ) 87 , c ) 126 , d ) 18 , e ) 91
Rationale: explanation : x = 7 km / hr ; y = 3 km / hr ds = 10 km / hr ; us = 4 km / hr distance ( d ) is same . therefore , if time taken for downstream is t hours , the time for upstream is ( t + 6 ) hours . 10 * t = 4 * ( t + 6 ) 6 t = 24 ; t = 4 hours d = 10 * 4 = 40 km answer : a
Answer: a
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 3 m + n ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 45 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 3 * 10 + 15 = 45 answer : d"
Answer: d
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 24 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 104 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 24 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 24 r 2 = ( 24 * 2 ) / 3 = 16 = > r = 4 rate = 4 % answer : option d"
Answer: d
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 76 . how tall is the fourth person ?
Options: a ) 76 , b ) 78 , c ) 80 , d ) 82 , e ) 84
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 76 ) = 304 x = 72 and the fourth person has a height of 72 + 10 = 82 inches the answer is d ."
Answer: d
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 65 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,960 , e ) $ 27,360
Rationale: for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.65 * 12000 = 12000 - 7800 x = 4200 earning becomes 9360 + 3 x = 9360 + 3 * 4200 = 21960 ans : d
Answer: d
Problem: how many prime numbers between 1 and 100 are factors of 7150 ?
Options: a ) 238 , b ) 100 , c ) 299 , d ) 270 , e ) 111
Rationale: "ans : 7 , 150 = 2 × 52 × 11 × 13 so there are 4 distinct prime numbers that are below 100 answer : b"
Answer: b
Problem: in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.8 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 228.9 $ , c ) 343.7 $ , d ) 395.05 $ , e ) 412.12 $
Rationale: service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.8 = 384.8 total cost = fuel + service = 384.8 + 10.25 = 395.05 answer is d
Answer: d
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 88 and rs . 80 respectively . the sum is :
Options: a ) 880 , b ) 1450 , c ) 1600 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 88 * 80 / ( 88 - 80 ) = rs . 880 . answer a"
Answer: a
Problem: machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 3 hours and machine y produces k bottles in 2 hours . how many hours does it take machines x and y , working simultaneously , to produce 12 k bottles ?
Options: a ) 16 , b ) 20 , c ) 15 , d ) 72 / 5 , e ) 24
Rationale: x rate = k / 3 y rate = k / 2 k / 3 + k / 2 = 12 k / t solving t = 72 / 5 answer d
Answer: d
Problem: a family pays $ 800 per year for an insurance plan that pays 65 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 35 % of first 1000 $ in expense = 350 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 350 = 1150 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1500 $ ( since insurance plan will pay 100 % of amount that exceeds 1150 $ ) answer d"
Answer: d
Problem: by how much is 3 - fifth of 390 greater than 4 - seventh of 210 ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 114 , e ) 130
Rationale: explanation : 3 / 5 of 390 - 4 / 7 of 210 = 234 - 120 = 114 . answer : d
Answer: d
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 51 then sum is
Options: a ) rs . 5000 , b ) rs . 5100 , c ) rs . 5800 , d ) rs . 6000 , e ) rs . 6200
Rationale: p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 51 5100 answer : b
Answer: b
Problem: a box measuring 27 inches long by 15 inches wide by 6 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 90
b ) 180
c ) 210
d ) 240
e ) 864
Rationale: least number of cubes will be required when the cubes that could fit in are biggest . 3 is the biggest number that could divide all three , 27 , 15 and 6 . thus side of cube must be 3 , and total number of cubes = 27 / 3 * 15 / 3 * 6 / 3 = 90 ans a it is .
Answer: a
Problem: if x is 30 percent more than y and y is 50 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 65 % , d ) 125 % , e ) 60 %
Rationale: "z = 100 ; y = 50 so x = 65 x as % of z = 65 / 100 * 100 = > 65 % answer will be ( c )"
Answer: c
Problem: in an examination 35 % of the students passed and 481 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 740 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 481 65 x / 100 = 481 x = 481 * 100 / 65 = 740 answer is d"
Answer: d
Problem: a certain number of men can do a work in 20 days . if there were 4 men more it could be finished in 5 days less . how many men are there ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 20 , e ) 18
Rationale: "original number of workers = 4 * ( 20 - 5 ) / 5 = 12 men answer is b"
Answer: b
Problem: a farmer spent $ 38 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 41.80
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 38 = $ 15.2 on chicken feed , thus he spent the remaining 38 - 15.2 = $ 22.8 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 15.2 - - > x = $ 19 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 19 + 22.8 = $ 41.8 . answer : e ."
Answer: e
Problem: 10 men and 15 women together can complete a work in 7 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 350 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 7 15 women ' s 1 day work = ( 1 / 7 - 10 / 100 ) = 3 / 70 1 woman ' s 1 day work = 1 / 350 1 woman alone can complete the work in 350 days . answer : e"
Answer: e
Problem: a can do a work in 60 days . he works for 15 days and later b alone completes the work in 30 days . in what time will they together complete the work ?
Options: a ) 24 days , b ) 25 days , c ) 30 days , d ) 32 days , e ) none of these
Rationale: let a can do a work in = 1 / 60 days he does 15 days so work done by a in 15 days = ( 15 ) * ( 1 / 60 ) = 1 / 4 remaining work is = 1 - 1 / 4 = 3 / 4 b ' s one day work is = 1 / 30 so 3 / 4 work is done by b in = ( 3 / 4 ) * ( 1 / 30 ) = 1 / 40 days time require to complete the work is = 1 / 60 + 1 / 40 = 5 / 120 5 / 120 = 1 / 24 so 24 days require to complete the work together . answer : a
Answer: a
Problem: jerry and beth each drove from smallville to crown city by different routes . jerry drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than jerry to complete the trip . how many miles per hour was beth ' s average speed on this trip ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 75
Rationale: speed = distance / time distance for jerry = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for jerry + 5 = 20 + 5 = 25 miles time taken by beth = time taken by jerry + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer .
Answer: b
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 3 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 13 / 20
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 3 = 105 remaining work is 300 - 105 = 195 remaining fraction of work is = 195 / 300 = 13 / 20 answer e"
Answer: e
Problem: a certain company had a total annual expenditure of 1.47 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: given : total annual expenditure of 1.47 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 3.5 = 1470 therefore try to bring the numerator in terms of 1470 average salary = ( 1470 * 10 ^ 4 ) / 420 = 3.5 * 10 ^ 4 = 35,000 option c
Answer: c
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 12 hours , and machine с can finish the job in 8 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 15 / 4 , b ) 18 / 7 , c ) 21 / 8 , d ) 24 / 11 , e ) 28 / 13
Rationale: "the combined rate is 1 / 4 + 1 / 12 + 1 / 8 = 11 / 24 of the job per hour . the time to complete the job is 24 / 11 hours . the answer is d ."
Answer: d
Problem: the number 130 can be written as the sum of the squares of 2 different positive integers . what is the sum of these 2 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "11 ^ 2 + 3 ^ 2 = 130 - - > 11 + 3 = 14 . d"
Answer: d
Problem: if 10000 microns = 1 decimeter , and 1000000000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05
Rationale: given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b
Answer: b
Problem: pipe a can fill a tank in 24 minutes . pipe b can fill the same tank 6 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 32 / 7 minutes , c ) 192 / 7 minutes , d ) 3 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 24 minutes - - > the rate of a = 1 / 24 tank / minute ; pipe b can fill the same tank 6 times fasterthan pipe a - - > the rate of b = 1 / 24 + 6 / 24 = 7 / 24 tank / minute . their combined rate = 1 / 24 + 7 / 24 = 1 / 3 tank / minute ; therefore , a and b can fill the tank in 3 minutes . answer : d"
Answer: d
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 24 , what is the value of r - p ?
Options: a ) 28 , b ) 10 , c ) 30 , d ) 40 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 48 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 28 hence , the correct answer is a"
Answer: a
Problem: the ratio of three numbers is 6 : 7 : 5 and their sum is 108 . the second number of the three numbers is ?
Options: a ) 12 , b ) 42 , c ) 30 , d ) 36 , e ) none of these
Rationale: "explanation : 6 : 7 : 5 total parts = 18 18 parts - - > 108 1 part - - - - > 6 the second number of the three numbers is = 7 7 parts - - - - > 42 answer : option b"
Answer: b
Problem: a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room ?
Options: a ) 110 , b ) 124 , c ) 96 , d ) 117 , e ) 127
Rationale: "length = 6 m 24 cm = 624 cm width = 4 m 32 cm = 432 cm hcf of 624 and 432 = 48 number of square tiles required = ( 624 * 432 ) / ( 48 * 48 ) = 13 * 9 = 117 answer : d"
Answer: d
Problem: the average of first five prime numbers greater than 61 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 74.6 , d ) 32.8 , e ) 32.4
Rationale: "67 + 71 + 73 + 79 + 83 = 373 / 5 = 74.6 answer : c"
Answer: c
Problem: a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km
Options: a ) 200 km , b ) 222 km , c ) 224 km , d ) 248 km , e ) none of these
Rationale: "explanation : let time taken to travel the first half = x hr then time taken to travel the second half = ( 10 - x ) hr distance covered in the the first half = 21 x [ because , distance = time * speed ] distance covered in the the second half = 24 ( 10 - x ) distance covered in the the first half = distance covered in the the second half so , 21 x = 24 ( 10 - x ) = > 45 x = 240 = > x = 16 / 3 total distance = 2 * 21 ( 16 / 3 ) = 224 km [ multiplied by 2 as 21 x was distance of half way ] option c"
Answer: c
Problem: calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 9 , 10 , 14 and 18 seconds . ?
Options: a ) 636 , b ) 631 , c ) 633 , d ) 610 , e ) 630
Rationale: lcm of 9 , 10 , 14 and 18 is 630 lcm = 630 answer : e
Answer: e
Problem: the size of a flat - screen tablet is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 8 - inch flat - screen tablet than a square 7 - inch flat - screen tablet ?
Options: a ) 7.6 , b ) 7.3 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 8 - inch flat - screen television the diagonal ( hypotenuse ) = 8 so , we can apply the pythagorean theorem to get x ² + x ² = 8 ² simplify : 2 x ² = 8 ² divide both sides by 2 to get : x ² = 8 ² / 2 since the area of the square = x ² , we can see that the area of this square is 8 ² / 2 square 7 - inch flat - screen television the diagonal ( hypotenuse ) = 7 so , we can apply the pythagorean theorem to get x ² + x ² = 7 ² simplify : 2 x ² = 7 ² divide both sides by 2 to get : x ² = 7 ² / 2 since the area of the square = x ² , we can see that the area of this square is 7 ² / 2 difference in areas = 8 ² / 2 - 7 ² / 2 = ( 8 ² - 7 ² ) / 2 = ( 64 - 49 ) / 2 = 15 / 2 = 7.5 d"
Answer: d
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1672 cm is ?
Options: a ) 22 , b ) 28 , c ) 19 , d ) 12 , e ) 88
Rationale: "2 * 22 / 7 * 14 * x = 1672 = > x = 19 answer : c"
Answer: c
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2016 ) = ?
Options: a ) 2017 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2016 ) = 2017 ans : a
Answer: a
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and six times as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 2 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 6 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 6 y + y + ( y - 12 ) = 100 8 y - 12 = 100 5 y = 112 y = 14 there are 14 blue balls . this is 12 more than the number of white balls , so z = 2 . that ' s the answer . just as a check , x = 84 , and 84 + 14 + 2 = 100 . answer = 2 , ( c )"
Answer: c
Problem: 75 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 48 , b ) 180 / 7 , c ) 50.4 , d ) 60 , e ) 90
Rationale: 75 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 75 ) * 100 = 48 square feet answer : option a
Answer: a
Problem: the radius of a sphere is increased by 10 % . the surface area increases by ?
Options: a ) 21 %
b ) 31 %
c ) 41 %
d ) 51 %
e ) none of these
Rationale: since 4 x pi x radius x radius = surface area . therefore , net % change in area = ( x + y + xy / 100 ) % = [ 10 + 10 + ( 10 x 10 ) / 100 ] % or 21 % . answer : a
Answer: a
Problem: there are 408 boys and 264 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 28 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 264 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 264 / 24 = 17 + 11 = 28 answer : a"
Answer: a
Problem: the speed at which a woman can row a boat in still water is 120 kmph . if she rows downstream , where the speed of current is 60 kmph , what time will he take to cover 500 metres ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: speed of the boat downstream = 120 + 60 = 180 kmph = 180 * 5 / 18 = 50 m / s hence time taken to cover 500 m = 500 / 50 = 10 seconds . answer : c
Answer: c
Problem: a company that ships boxes to a total of 15 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 9
Rationale: "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - d"
Answer: d
Problem: at a small company , 61 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 / 16 , b ) 1 / 3 , c ) 9 / 20 , d ) 47 / 61 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 61 and total married = 60 . total men = 100 - 61 = 39 and single men = 2 / 3 * 39 = 26 . married men = total men - single men = 39 - 26 = 13 . married women = total married - married men = 60 - 13 = 47 . fraction of women are married = married women / total women = 47 / 61 = 5 / 7 . ans d"
Answer: d
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 39 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 156 , c ) 144 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 39 4 / x = 1 / 39 = > x = 156 min . answer : b"
Answer: b
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 252 runs ?
Options: a ) 6.25 , b ) 6.22 , c ) 5.5 , d ) 6.39 , e ) 6.13
Rationale: "required run rate = [ 252 - ( 3.2 * 10 ) ] / 40 = 220 / 40 = 5.5 answer : c"
Answer: c
Problem: at what price must an article costing rs . 85.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 122.5 , b ) 142.5 , c ) 162.5 , d ) 182.5 , e ) 112.5
Rationale: "cp = 85.50 sp = 85.5 * ( 125 / 100 ) = 106.875 mp * ( 95 / 100 ) = 106.875 mp = 112.5 answer : e"
Answer: e