regisss/math_qa huggingface dataset:
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9 - sided polygon ) ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 6 = 1 / 3 . the answer is b ."
Answer: b
Problem: if 10 gallons of grape juice are added to 30 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 32.5 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 30 × 0.10 = 3 gallons of grape juice . 30 × 0.90 = 27 gallons of other components . if we add 10 gallons of grape juice , we will end up with 13 gallons of grape juice and 36 gallons of other components , and we will have a total of 40 gallons of the mixture . so 13 / 40 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 32,5 % . the correct answer is choice ( d )"
Answer: d
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 12 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32
Rationale: "3.456789 ^ 12 has 6 * 12 = 72 decimal places . 10 ^ 48 moves the decimal place to the right 48 places . ( 10 ^ 4 * 3.456789 ) ^ 12 has 72 - 48 = 24 digits after the decimal point . the answer is c ."
Answer: c
Problem: convert 150 inches into centimeter ?
Options: a ) 312 cm , b ) 381 cm , c ) 350 cm , d ) 310 cm , e ) 354 cm
Rationale: "1 inch = 2.54 cm 150 inches = 110 * 2.54 = 381 cm answer is b"
Answer: b
Problem: one day eesha started 30 min late from home and reached her office 50 min late while driving 25 % slower than her usual speed . how much time in min does eesha usually take to reach her office from home ?
Options: a ) 22 , b ) 60 , c ) 88 , d ) 26 , e ) 18
Rationale: we know that speed is inversely proportional to time while she drives 25 % slower means she drove at 3434 ( s ) we know that d = s x t when speed became 3434 ( s ) then time taken should be 4343 ( t ) i . e , she has taken 4343 ( t ) - t extra to cover the distance . extra time = t 3 t 3 = 20 min ( as 20 min late due to slow driving ) actual time t = 60 minutes answer : b
Answer: b
Problem: the sum of three consecutive even numbers is 24 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 34
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 24 6 p = 24 = > p = 4 . the middle number is : 4 p = 16 . answer : b"
Answer: b
Problem: two trains of equal length , running with the speeds of 50 and 40 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 5.55 sec , b ) 4.55 sec , c ) 5.95 sec , d ) 6.55 sec , e ) 9.55 sec
Rationale: "rs = 50 - 40 = 10 * 5 / 18 = 50 / 18 t = 50 d = 50 * 50 / 18 = 1250 / 9 rs = 50 + 40 = 90 * 5 / 18 = 25 t = 1250 / 9 * 1 / 25 = 5.55 sec answer : a"
Answer: a
Problem: daniel went to a shop and bought things worth rs . 40 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) a ) 34.7 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.5 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 40 given that out of this rs . 40 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 40 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 40 − 0.3 − x ) = 30 ⇒ ( 40 − 0.3 − x ) = 5 ⇒ x = 40 − 0.3 − 5 = 34.7 ans - a"
Answer: a
Problem: if 6 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in
Options: a ) 1 day , b ) 2.1 days , c ) 3 days , d ) 4.5 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 6 × 2 = 4 m no . of days required to paint 36 m cloth by 6 men = 36 / 4 × 2 = 4.5 day . d"
Answer: d
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts five hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 10 , e ) e ) 5
Rationale: the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 5 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 5 + t ) = 40 * t t = 15 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 15 / 60 = 10 hrs time taken by a = 5 + t = 5 + 15 = 20 hrs time taken by k = 10 hrs so k starts 20 - 10 = 10 hrs after a . ( answer d )
Answer: d
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.001 ) ^ 4 ?
Options: a ) 10 ^ 8 , b ) 10 ^ 9 , c ) 10 ^ 10 , d ) 10 ^ 11 , e ) 10 ^ 12
Rationale: "0.1 = 10 ^ - 1 ( 0.001 ) ^ 4 = ( 10 ^ - 3 ) ^ 4 = 10 ^ - 12 10 ^ 11 * 10 ^ - 12 = 10 ^ - 1 the answer is d ."
Answer: d
Problem: in what time will a train 400 meters long cross an electric pole , if its speed is 144 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 10 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 400 / 40 = 10 seconds answer : c"
Answer: c
Problem: p software has coding line 5 % more than n , n software has coding line 5 / 2 more than m . m software has 108 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 397 , d ) 109 , e ) 110
Rationale: "m s / w has 108 line of code n s / w has = 108 + 108 * 5 / 2 = 378 line of code p s / w 5 % more n ' code 378 + 18.9 = 396.9 or 397 line of code answer : c"
Answer: c
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 2 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 11 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 2 * x hence , a 1 + a 2 + . . + a 20 + n = 22 x so , the fraction asked = 2 x / 22 x = 1 / 11 answer c"
Answer: c
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 20,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 116000 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 20,000 is made = 96,000 + 20,000 = rs . 1 , 16,000 answer : d"
Answer: d
Problem: mary works in a restaurant a maximum of 60 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 560 , d ) 320 , e ) 400
Rationale: mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 40 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 40 ) = $ 400 . the total amount is $ 160 + $ 400 = $ 560 answer c 560 .
Answer: c
Problem: how many seconds will a 600 m long train take to cross a man walking with a speed of 4 km / hr in the direction of the moving train if the speed of the train is 64 km / hr ?
Options: a ) 30 , b ) 36 , c ) 50 , d ) 44 , e ) 60
Rationale: "speed of train relative to man = 64 - 4 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 600 * 3 / 50 = 36 sec . answer : b"
Answer: b
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 40 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 4 : 5 , b ) 9 : 25 , c ) 5 : 4 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 20 / speed b since the times are same , 50 pi / speed a = 40 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 4 correct option : c"
Answer: c
Problem: if ( 2 ^ 13 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 13 , c ) 15 , d ) 16 , e ) 23
Rationale: "given 2 ^ 13 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 13 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans b on comparing the power of 2 = > m = 13"
Answer: b
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36,000 , what will be the amount a receives ?
Options: a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 36000 × 21 / 50 = 15,120 answer is a .
Answer: a
Problem: a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution . if 500 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 10.00 , b ) 15.00 , c ) 11.50 , d ) 10.50 , e ) 9.75
Rationale: "we are given that a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 500 cubic centimeters of solution , we can set up a proportion . we can say : “ 20 grams of glucose is to 1000 cubic centimeters of solution as x grams of glucose is to 500 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 20 / 1000 = x / 500 when we cross multiply we obtain : ( 20 ) ( 500 ) = 1000 x 10000 = 1000 x 10 = x there are 10.00 grams of glucose in the solution in the container . the answer is a ."
Answer: a
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 6 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 6 ( 9 horizontal dots and 6 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 6 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 5 c 1 , ( 6 - 1 = 5 as 1 vertical dot is already occupied by a ) . 9 c 1 * 6 c * 8 c 1 * 5 c 1 = 2160 . answer : c ."
Answer: c
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 6000 , brokerage being 1 / 4 % , is :
Options: a ) 83.08 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: face value = rs . 6000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 6000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 83.33 . = market value of rs . 100 stock = rs . 83.33 - re . 0.25 . = market value of rs . 100 stock = rs . 83.08 answer : a
Answer: a
Problem: the curved surface of a sphere is 64 pi cm 2 . find its radius ?
Options: a ) 1 cm , b ) 4 cm , c ) 2 cm , d ) 3 cm , e ) 5 cm
Rationale: "4 ï € r 2 = 64 = > r = 4 answer b"
Answer: b
Problem: a hollow iron pipe is 42 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 3 g / cm 3 , then the weight of the pipe is :
Options: a ) 2.172 kg , b ) 2.272 kg , c ) 2.282 kg , d ) 2.992 kg , e ) 2.772 kg
Rationale: "external radius = 4 cm , internal radius = 3 cm . volume of iron = 22 / 7 x ( ( 4 square ) - ( 3 square ) ) x 42 = ( 22 / 7 ) x 7 x 1 x 42 cm 3 . = 924 cm 3 . weight of iron = ( 924 x 3 ) gm = 2772 gm = 2.772 kg answer : e"
Answer: e
Problem: a shopping cart contains only apples , oranges , and pears . if there are 3 times as many oranges as apples , and 4 times as many pears as oranges , then the apples are equivalent to what fraction of the pears ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 4 , e ) 3 / 4
Rationale: o = 3 a p = 4 o = 12 a a = p / 12 the answer is c .
Answer: c
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 6 % p . a . was rs . 370.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 3360.80 , b ) rs . 3370.80 , c ) rs . 3320.70 , d ) rs . 3230.80 , e ) rs . 3130.80
Rationale: let the sum be rs . p p { [ 1 + 6 / 100 ] 2 - 1 } = 370.80 p ( 6 / 100 ) ( 2 + 6 / 100 ) = 370.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 246 / ( 0.05 ) ( 2.05 ) = 3000 . amount = rs . 3370.80 . answer : b
Answer: b
Problem: q ' = 3 q - 3 , what is the value of ( 3 ' ) ' ?
Options: a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 40
Rationale: "( 3 ' ) ' = ( 3 * 3 - 3 ) ' = 6 ' = 6 * 6 - 6 = 30 answer d"
Answer: d
Problem: five equal cubes , each of side 5 cm , are placed adjacent to each other . the volume of the new solid formed will be
Options: a ) 125 cm 3
b ) 625 cm 3
c ) 15525 cm 3
d ) 1225 cm 3
e ) none
Rationale: solution the new solid formed is a cuboid of length 25 cm , breadth 5 cm and height 5 cm ∴ volume = ( 25 x 5 x 5 ) cm 3 ‹ = › 625 cm 3 answer b
Answer: b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 180 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) rs . 1200 , b ) rs . 1100 , c ) rs . 1300 , d ) rs . 1400 , e ) rs . 1000
Rationale: "90 % 105 % - - - - - - - - 15 % - - - - 180 100 % - - - - ? = > rs . 1200 answer : a"
Answer: a
Problem: a train 80 m in length crosses a telegraph post in 6 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 48 kmph , e ) 19 kmph
Rationale: "s = 80 / 6 * 18 / 5 = 48 kmph answer : d"
Answer: d
Problem: a man can row upstream at 7 kmph and downstream at 33 kmph , and then find the speed of the man in still water ?
Options: a ) 11 , b ) 77 , c ) 30 , d ) 20 , e ) 34
Rationale: "us = 7 ds = 33 m = ( 33 + 7 ) / 2 = 20 answer : d"
Answer: d
Problem: in a class of 150 students 55 speak english ; 85 speak telugu and 30 speak neither english nor telugu how many speak both english and telugu ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: total = 150 english = 55 telugu = 85 none / neither english nor telugu = 30 no . of students who speak only one or both = 150 - 30 = 120 so , 120 stud ' s can speak english or telugu or both . then , no . of stud ' s speak only english = 120 - 85 ( telugu ) = 35 ` ` ` ` ` ` ` ` ` ` telugu = 120 - 55 = 65 remaining 120 - ( 65 + 35 ) = 20 stud ' s can speak both . b )
Answer: b
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 110 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 550 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 110 geese survived the first year : 1 / 5 * ( total ) = 110 - - > ( total ) = 550 . answer : d ."
Answer: d
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) 295
Rationale: "explanation : since the month begins with a sunday , to there will be five sundays in the month . required average = ( 510 × 5 + 240 × 25 / 30 ) = 8550 / 30 = 285 answer : d"
Answer: d
Problem: the price of a t . v . set worth rs . 15000 is to be paid in 20 installments of rs . 1500 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 28088 , c ) 13500 , d ) 19000 , e ) 2799
Rationale: "money paid in cash = rs . 1500 balance payment = ( 15000 - 1500 ) = rs . 13500 . answer : c"
Answer: c
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has three times the width , twice the depth , and half the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 10 , b ) 30 , c ) 15 , d ) 20 , e ) 25
Rationale: "volume of cube = lbh = 5 new cube l , b , h are increases of 3 b , 2 h and a decrease of . 5 l new volume of cube = . 5 l * 3 b * 2 h = 3 * lbh = 3 * 5 = 15 answer : c"
Answer: c
Problem: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 240 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 240 + 120 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 360 / 0.6 = 600 billion gallons therefore percentage of reservoir that was full before the storm = ( 240 / 600 ) * 100 = 40 % option c"
Answer: c
Problem: the average of first six prime numbers greater than 65 is ?
Options: a ) 55 , b ) 77 , c ) 56 , d ) 67 , e ) 98
Rationale: "67 + 71 + 73 + 79 + 83 + 89 = 462 / 6 = 77 answer : b"
Answer: b
Problem: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 25 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 75 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100
Rationale: "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 25 % , so the manufacturing must have been $ 75 . answer = ( a ) ."
Answer: a
Problem: ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition of the maximum and minimum possible values of ' a + b ' ?
Options: a ) 28 , b ) 30 , c ) 22 , d ) 20 , e ) 32
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 21 + 9 = 30 . ans b ."
Answer: b
Problem: what is the area of an equilateral triangle whose one side length is 70 ?
Options: a ) 825 √ 3 , b ) 925 √ 3 , c ) 1025 √ 3 , d ) 1125 √ 3 , e ) 1225 √ 3
Rationale: - > the area of an equilateral triangle with one side length of a is √ 3 a 2 / 4 . thus , √ 3 ( 70 ^ 2 ) / 4 = 1225 √ 3 and the answer is e .
Answer: e
Problem: speed of a boat in standing water is 9 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 10 hours , e ) 15 hours
Rationale: "speed upstream = 7.5 kmph speed downstream = 10.5 kmph total time taken = 105 / 7.5 + 105 / 10.5 = 24 hours answer is b"
Answer: b
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 30 metres ?
Options: a ) 6 , b ) 8 , c ) 12 , d ) 4 , e ) 13
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 30 / 5 = 6 seconds . answer : a"
Answer: a
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 62.50 , his capital is ?
Options: a ) 24,602 , b ) 25,000 , c ) 24,600 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 62.50 32 x - 31 x = 6250 * 4 x = 25,000 . answer : b"
Answer: b
Problem: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1055 , b ) b ) 1075 , c ) c ) 1145 , d ) d ) 1070 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 65 × 9 = 585 . total cost he has to pay = 560 + 585 = 1145 . c )"
Answer: c
Problem: it was calculated that 75 men could complete a piece of work in 20 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 40
Rationale: "before : one day work = 1 / 20 one man ’ s one day work = 1 / ( 20 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 20 * 75 ) the total no . of days required to complete the work = ( 75 * 20 ) / 50 = 30 answer : b"
Answer: b
Problem: the number of diagonals of a polygon of n sides is given by the formula z = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "z = n ( n - 3 ) z = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Problem: divide rs . 32000 in the ratio 3 : 9 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 8000 , 24000
Rationale: "3 / 12 * 32000 = 8000 9 / 12 * 32000 = 24000 answer : e"
Answer: e
Problem: what will be the remainder if 2 ^ 300 is divided by 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: d 4 now if you go on calculating 2 ^ 300 , you will lose so much time and it might not even be feasible to carry out so long of calculations . thus we will make use of a trick here . we will calculate the remainder of each power of 2 till we come across a pattern . 2 ^ 1 divided by 4 leaves the remainder 2 . 2 ^ 2 divided by 4 leaves the remainder 0 . 2 ^ 3 divided by 4 leaves the remainder 0 . 2 ^ 4 divided by 4 leaves the remainder 0 . you can see that all the following powers of two will be divisible by 4 . therefore the remainder when 2 ^ 300 is divided by 4 will be 0 only .
Answer: d
Problem: a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 5 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 351
Rationale: if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 13 / 4 solving it 28 x = 26 x + 78 x = 39 which means m ( d ) = 273 and b ( d ) = 78 so total initially is m ( d ) + b ( d ) = 351 e
Answer: e
Problem: three numbers are in the ratio 1.5 : 2 : 3.5 and their h . c . f is 18 . the numbers are :
Options: a ) 22,36 , 63 , b ) 27,45 , 63 , c ) 27,54 , 63 , d ) 54 , 45 , 36 , e ) 27,36 , 63
Rationale: "let the required numbers be 1.5 x , 2 x and 3.5 x . then , their h . c . f = x . so , x = 18 . the numbers are 27,36 , 63 . answer : e"
Answer: e
Problem: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4500 , how much was it in the beginning ?
Options: a ) 5999 , b ) 6788 , c ) 6250 , d ) 4559 , e ) 6989
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4500 x = 6250 answer : c"
Answer: c
Problem: the tax on a commodity is diminished by 25 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 17.5 %
Rationale: "explanation : 100 * 100 = 10000 75 * 110 = 8250 10000 - - - - - - - 1750 100 - - - - - - - ? = 17.5 % e )"
Answer: e
Problem: a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 8 , b ) b 22 , c ) c 27 , d ) d 40 , e ) e 51
Rationale: "l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8"
Answer: a
Problem: the sum of the first 60 positive even integers is 3,750 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 4,700 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 60 positive even integers = 3750 sum of 1 st 100 odd numbers = 5050 - 3750 = 1300 so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 6000 + 1300 = 4700 a is the answer ."
Answer: a
Problem: a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 54.9 %
b ) 58.7 %
c ) 62.5 %
d ) 66.3 %
e ) 70.4 %
Rationale: there are a total of 6 * 6 * 6 = 216 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 4 * 4 * 4 = 64 cubes . the number of cubes with at least one side painted red is 216 - 64 = 152 cubes the probability that a cube has at least one side painted red is 152 / 216 which is about 70.4 % the answer is e .
Answer: e
Problem: ages of two persons differ by 18 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 ) 15,33 , c ) 16,32 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 18 ) = > 3 ( x - 6 ) = ( x + 18 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 12 = > x = 15 . so other person age is x + 18 = 33 answer : option b"
Answer: b
Problem: the h . c . f . of two numbers is 28 and the other two factors of their l . c . m . are 12 and 15 . the larger of the two numbers is
Options: a ) 420 , b ) 430 , c ) 312 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 28 x 12 ) and ( 28 x 15 ) . larger number = ( 28 x 15 ) = 420 . answer a"
Answer: a
Problem: in the first 8 overs of a cricket game , the run rate was only 2.3 what should be the rate in the remaining 20 overs to reach the target of 260 runs ?
Options: a ) 12.08 , b ) 12.18 , c ) 12.0 , d ) 6.19 , e ) 6.21
Rationale: "required run rate = [ 260 - ( 2.3 * 8 ) ] / 20 = 241.60 / 20 = 12.08 answer : a"
Answer: a
Problem: in the first 20 overs of a cricket game , the run rate was only 4.3 . what should be the run rate in the remaining 30 overs to reach the target of 264 runs ?
Options: a ) 5.93 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) 8
Rationale: "explanation : required run rate = ( 264 - ( 4.3 x 20 ) ) / 30 = 178 / 30 = 5.93 answer : a"
Answer: a
Problem: at what price must an article costing rs . 150 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 30 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 216.67 , e ) 62.2
Rationale: "cp = 150 sp = 150 * ( 130 / 100 ) = 195 mp * ( 90 / 100 ) = 195 mp = 216.67 answer : d"
Answer: d
Problem: a man can row 8 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 5.7 , c ) 7.5 , d ) 5.74 , e ) 5.71
Rationale: "m = 8 s = 2 ds = 10 us = 6 x / 10 + x / 6 = 1 x = 3.75 d = 3.75 * 2 = 7.5 answer : c"
Answer: c
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ?
Options: a ) 4
b ) 8
c ) 16
d ) 24
e ) 2
Rationale: there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having three faces coloured = no . of corners = 8 answer : b
Answer: b
Problem: an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1260 ) * 100 = 25 % answer e"
Answer: e
Problem: if the sides of a square are doubled in length , the area of the original square is now how many times as large as the area of the resultant square ?
Options: a ) 25 % , b ) 50 % , c ) 100 % , d ) 200 % , e ) 400 %
Rationale: let the original square have sides of length l and the new square have sides of length 2 l . the resulting areas are l ^ 2 for the original square and 4 l ^ 2 for the new square ( as the length of the side is square to get the area ) . the original square ' s area is l ^ 2 / 4 l ^ 2 or 25 % of the new square ' s area . choice a
Answer: a
Problem: there are 16 bees in the hive , then 10 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 26
Rationale: 16 + 10 = 26 . answer is e .
Answer: e
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 612 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1462 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 612 × 100 ) / ( 6 × 12 ) = rs . 850 bg = bd – td = > 612 = bd - 850 = > bd = 612 + 850 = 1462 answer : option d"
Answer: d
Problem: if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ?
Options: a ) 8 , b ) 18 , c ) 10 , d ) 12 , e ) 14
Rationale: "we know dividend = divisor * quotient + remainder = = = > 507 = divisor * 61 + 19 = = = = = > 488 / 61 = divisor = = = > divisor = 8 ans - a"
Answer: a
Problem: the average salary of raj and roshan is rs . 4000 but the average salary of raj , roshan and thomas is rs . 5000 . what is the salary of thomas ?
Options: a ) 4000 , b ) 5000 , c ) 6000 , d ) 7000 , e ) 8000
Rationale: total salary of raj and roshan = 2 x 4000 = 8000 total salary of raj roshan and thomas = 3 x 5000 = 15000 salary of thomas = 15000 - 8000 = rs . 7000 answer : d
Answer: d
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 45 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 90 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 45 . thus , 3434 ( 90 + x ) = 45 + x or 270 + 3 x = 180 + 4 x or x = 90 answer : d"
Answer: d
Problem: the radius of a semi circle is 35 cm then its perimeter is ?
Options: a ) 32.8 , b ) 180 , c ) 32.1 , d ) 32.2 , e ) 32.9
Rationale: "diameter 70 cm 1 / 2 * 22 / 7 * 70 + 70 = 180 answer : b"
Answer: b
Problem: an inspector rejects 0.06 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3333
Rationale: "let the number of meters to be examined be x then , 0.06 % of x = 2 ( 6 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 3333 answer is e"
Answer: e
Problem: the present worth of rs . 1404 due in two equal half - yearly installments at 8 % per annum simple interest is :
Options: a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) rs . 1600
Rationale: "time = 1 / 2 yr r = 8 % let pw = x si = 1404 - x x * 1 / 2 * 8 / 100 = 1404 - x . ( ref problm 10 of si , rs aggarwal ) x = 1404 * 25 / 26 hence x = 1350 answer : c"
Answer: c
Problem: a train moves with a speed of 72 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 20 , e ) none
Rationale: "solution speed = 72 kmph = ( 72 x 5 / 18 ) m / sec = 20 m / sec . answer d"
Answer: d
Problem: 40 % of 2 is equal to
Options: a ) 0.2 , b ) 0.8 , c ) 0.6 , d ) 0.7 , e ) 0.9
Rationale: 40 % of 2 = ( 40 / 100 ) * 2 = 0.8 answer : option b
Answer: b
Problem: how many positive integers less than 243 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 40 , e ) 64
Rationale: "240 / 4 = 60 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 60 - 20 = 40 answer : d"
Answer: d
Problem: a can finish a piece of work in 5 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 days , b ) 6 days , c ) 7 days , d ) 1 days , e ) 3 days
Rationale: "a 4 days 2 / 5 + ( 2 + x ) / 10 = 1 = > x = 4 days"
Answer: a
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6936 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 2400
Rationale: let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6936 = x = 6936 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2400 . answer : e
Answer: e
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 59.4 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 20 + 20 + 10 + 5 + 2.5 + 1.25 + 0.6 ans b"
Answer: b
Problem: a rectangular tiled patio is composed of 80 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 80 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 12 , e ) 28
Rationale: "r * c = 80 and ( 12 + 4 ) ( c - 2 ) = 80 - - > r = 12 and c = 7 . answer : d ."
Answer: d
Problem: the maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 91 , b ) 81 , c ) 1001 , d ) 1911 , e ) none
Rationale: olution required number of students . = h . c . f of 891 and 810 . â € ¹ = â € º 81 . answer b
Answer: b
Problem: what is the slope of a line on a standard xy - plane that passes through the point ( 1 , 3 ) and ( 4 , – 3 ) ?
Options: a ) - 1 , b ) 2 , c ) - 2 , d ) 1 / 2 , e ) - 1 / 2
Rationale: plug the values for the coordinates into the formula for the slope of a line : slope = y 2 - y 1 / x 2 - x 1 = - 3 - 3 / 4 - 1 = - 6 / 3 = - 2 correct answer c ) - 2
Answer: c
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 124 signs ?
Options: a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256
Rationale: "ok let ' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c"
Answer: c
Problem: pipe a can fill a tank in 5 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 67 , b ) 10 , c ) 18 , d ) 26 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 5 - 1 / x = 1 / 10 = > 1 / x = 1 / 5 - 1 / 10 = 1 / 10 = > x = 10 . answer : b"
Answer: b
Problem: a large box contains 20 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 500 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 20 * 25 = 500 correct answer b"
Answer: b
Problem: find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 .
Options: a ) 240 / 1587 , b ) 240 / 1545 , c ) 240 / 1547 , d ) 240 / 1542 , e ) 240 / 1512
Rationale: "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c"
Answer: c
Problem: if 40 % of a number is greater than 80 % of 5 by 2 , what is the number ?
Options: a ) 3 , b ) 15 , c ) 20 , d ) 2 , e ) 5
Rationale: "explanation : 40 / 100 * x - 80 / 100 * 5 = 2 40 / 100 * x - 4 = 2 40 / 100 * x = 6 x = 6 * 100 / 40 x = 15 answer : option b"
Answer: b
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 1.5 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35.75 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 1.5 x = 41.5 x dollars ; we know that harry also earned the same 41.5 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 11.5 x additional dollars . since for each additional hour he gets 3 x dollars then he worked for 11.5 x / 2 x = 5.75 additional hours , so harry worked for total of 30 + 5.75 = 35.75 hours . answer : a ."
Answer: a
Problem: in a group of 80 people , 45 have visited iceland and 33 have visited norway . if 41 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 80 = 45 + 33 - 41 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Problem: seven 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 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways . hence the probability is 6 / 279936 = 1 / 46656 answer : b"
Answer: b
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 8000 , brokerage being 1 / 4 % , is :
Options: a ) 110.86 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 8000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 8000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 111.11 = market value of rs . 100 stock = rs . 111.11 - re . 0.25 . = market value of rs . 100 stock = rs . 110.86 . answer : a"
Answer: a
Problem: p starts a business with rs . 4000 . after 4 months , q joins with p as his partner . after a year , the profit is divided in the ratio 2 : 3 . q ' s contribution in the capital is ?
Options: a ) rs . 7000 , b ) rs . 11000 , c ) rs . 8000 , d ) rs . 10000 , e ) rs . 9000
Rationale: solution : let ' s q ' s capital is x . p : q = ( 4000 * 12 ) : ( x : 8 ) = 2 : 3 . so q ' s share = ( 4000 * 12 / 8 x ) = 2 / 3 = > x = ( 4000 * 12 * 3 ) / ( 2 * 8 ) = rs . 9000 answer : option e
Answer: e
Problem: what is the probability of getting exactly 1 head in a single throw of five fair coins ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32
Rationale: "one possible case is htttt . p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 1 = 5 possible cases . p ( 1 head ) = 5 * 1 / 32 = 5 / 32 the answer is d ."
Answer: d
Problem: - 64 * 29 + 468 = ?
Options: a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these
Rationale: = > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d
Answer: d
Problem: there are 70 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64
Rationale: "x + ( x - 14 ) = 70 - - > x = 42 . answer : c ."
Answer: c
Problem: a is twice as good a work man as b and together they finish the work in 14 days . in how many days a alone can finish the work ?
Options: a ) 12 , b ) 21 , c ) 77 , d ) 99 , e ) 22
Rationale: "wc = 2 : 1 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 a can do the work in 21 days . answer : b"
Answer: b
Problem: find the least number must be subtracted from 165826 so that remaining no . is divisible by 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "on dividing 165826 by 4 we get the remainder 2 , so 2 should be subtracted b"
Answer: b
Problem: hcf and lcm two numbers are 14 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 154 , d ) 264 , e ) 364
Rationale: "14 * 396 = 36 * x x = 154 answer : c"
Answer: c
Problem: a train 240 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 28.8 sec , b ) 20.33 sec , c ) 60 sec , d ) 48 sec , e ) 49 sec
Rationale: "total length = 240 + 240 = 480 speed = 60 km / h = ( 60 * 5 ) / 18 = 50 / 3 m / s time = ( 480 * 3 ) / 50 = 28.8 sec . answer : a"
Answer: a
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 2 x km .
Options: a ) 16 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 35 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 2 x / ( x / 8 ) = 16 kmph answer : a"
Answer: a
Problem: if x and y are positive integers , and y = x ^ 2 + 8 , the greatest common divisor of a and b can not be
Options: a ) 9 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: if x is 1 , 2 , 4 , or 8 , then gcd of x and y is 1 , 2 , 4 , and 8 respectively . so , by poe the answer must be a . still : if x is a multiple of 9 , then y is 8 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : a .
Answer: a
Problem: a light flashes every 12 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 300 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 12 sec for 1 min = 5 flashes so for 1 hour = 5 * 60 = 300 flashes . answer : b"
Answer: b
Problem: some of the 68 % solution of acid was removed and this was replaced with an equal amount of 11 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 7 / 11 , b ) 7 / 17 , c ) 8 / 17 , d ) 8 / 19 , e ) 11 / 19
Rationale: "let x be the fraction of the original solution that was replaced . 0.68 * ( 1 - x ) + 0.11 ( x ) = 0.35 0.57 x = 0.33 x = 33 / 57 = 11 / 19 the answer is e ."
Answer: e
Problem: how many natural numbers between 23 and 137 are divisible by 7 ?
Options: a ) 12 , b ) 17 , c ) 16 , d ) 13 , e ) 15
Rationale: "solution : these numbers are 28 , 35 , 42 , … . , 133 . this is in a . p . in which a = 28 , d = ( 35 - 28 ) = 7 and l = 133 . let the number of there terms be n . then , tn = 133 a + ( n - 1 ) d = 133 by solving this we will get n = 16 . answer c"
Answer: c
Problem: ages of two sisters differ by 9 years . if 5 years ago , the elder one was twice as old the younger one , find their present age
Options: a ) 1228 , b ) 1423 , c ) 1632 , d ) 1834 , e ) 1932
Rationale: explanation : let the age of younger sister be x , then elder sister ' s age is ( x + 9 ) = > 2 ( x - 5 ) = ( x + 9 - 5 ) [ 5 years before ] = > 2 x - 10 = x + 4 = > x = 14 . so older sister ' s age is x + 9 = 23 answer : option b
Answer: b
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 6 , and the ratio of flour to baking soda is 5 to 1 . if there were 30 more pounds of baking soda in the room , the ratio of flour to baking soda would be 4 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 45 , e ) 70
Rationale: "sugar : flour = 3 : 6 = 1 : 2 = 5 : 10 flour : soda = 5 : 1 = 10 : 2 ; thus we have that sugar : flour : soda = 5 x : 10 x : 2 x . also given that 10 x / ( 2 x + 30 ) = 4 / 1 - - > x = 60 - - > sugar = 5 x = 30 . answer : a"
Answer: a