Cheukting/mathqa huggingface dataset:
Question (probability): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (geometry): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (geometry): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): ' 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
Question (geometry): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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