Cheukting/mathqa huggingface dataset:
Question (general): what is the least value of x . so that 43 x 87 is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 2 , d ) 6 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 3 + x + 8 + 7 = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . c"
Answer: c
Question (general): 675.987 - ? + 56.84 = 289.654
Options: a ) a ) 443.173 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 629.906 , e ) of these
Rationale: "explanation : 443.173 answer : option a"
Answer: a
Question (other): if shares of two persons in profits are rs . 800 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 800 / 600 = 4 : 3 answer : c"
Answer: c
Question (general): if 7 / 10 of a pencil is green , 4 / 5 of the remaining is gold and the remaining 1 / 2 is white , what is the total length of the pencil ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 4 , e ) 2
Rationale: green is 7 / 10 gold is 4 / 5 which can also be written as 8 / 10 white is 1 / 2 which can also be written as 5 / 10 7 / 10 + 8 / 10 + 5 / 10 = 2 answer is e ) 2
Answer: e
Question (general): what is the smallest no . that should be added to 41381 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 4 + 1 + 3 + 8 + 1 = 17 , the next multiple of 9 is 18 . 1 must be added to 41381 to make it divisible by 9 a"
Answer: a
Question (physics): a takes twice as much time as b & c takes thrice as much time as b to finish a piece of work . working together they can finish the work in 18 days . the no . of days need for b to do the work alone is ?
Options: a ) 30 days , b ) 31 days , c ) 33 days , d ) 41 days , e ) 52 days
Rationale: let a takes x days to complete the work , then b takes x / 2 days and c takes 3 x / 2 days to complete the work . a , b and c together complete the work in 18 days in 1 day , all they together can do = > 1 / x + 2 / x + 2 / 3 x = 1 / 18 3 + 6 + 2 / 3 x = 1 / 18 3 x 23 x 2 = 18 x = 66 days the number of days b alone takes to finish the work = x / 2 = 33 days c
Answer: c
Question (gain): a man can row his boat with the stream at 20 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 6 kmph , d ) 5 kmph , e ) 4 kmph
Rationale: "ds = 20 us = 8 s = ? s = ( 20 - 8 ) / 2 = 6 kmph answer : c"
Answer: c
Question (gain): what will be the compound interest on rs . 25000 after 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 25000 × ( 1 + 12 / 100 ) 3 ) = > 25000 × 28 / 25 × 28 / 25 × 28 / 25 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 option a"
Answer: a
Question (gain): a certain airline ' s fleet consisted of 70 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x be the number of years . 4 x > 70 - 3 x 7 x > 70 x > 10 the answer is e ."
Answer: e
Question (geometry): the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2898 sq m
b ) 1788 sq m
c ) 4312 sq m
d ) 7656 sq m
e ) 1786 sq m
Rationale: let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 352 s = 264 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1762 / ∏ 2 - 1322 / ∏ 2 } = 1762 / ∏ - 1322 / ∏ = ( 176 - 132 ) ( 176 + 132 ) / ∏ = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c
Answer: c
Question (gain): a man buys rs . 60 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 45
Rationale: "dividend on rs . 60 = rs . 9 / 100 x 60 = rs . 5.4 . rs . 12 is an income on rs . 100 . rs . 5.4 is an income on rs . 100 / 12 x 5.4 = rs . 45 . answer : option e"
Answer: e
Question (general): a number of 53 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 16 * 3 + 1 * 5 = 53 - - > 16 + 1 = 17 . answer : e ."
Answer: e
Question (geometry): the rhombus ( afce ) is inscribed in rectangle ( abcd ) . the length of bf = de . if the rectangle has a width of 20 yards and a length of 25 yards , what would be the total length ( the perimeter ) of a fence along the sides defined by afce ?
Options: a ) 80 yards , b ) 82 yards , c ) 84 yards , d ) 85 yards , e ) 90 yards
Rationale: the definition of a rhombus states that every side is of equal length . this definition is the key to solving this question . 1 ) we state that the hypotenuse of either side triangle is x . for this solution , i will be working with the left triangle . 2 ) we state that the bottom and top sides of the rhombus are also x , due to the definition of a rhombus . 3 ) we will define the bottom of the left triangle as y . that is , for the rectangle bottom itself , we can define it as 25 = y + x , where x is a side for the rhombus and y is the bottom part of the left triangle . 4 ) from ( 1 ) , we know that x = 202 + y 2 − − − − − − − √ 202 + y 2 . 5 ) from ( 3 ) , we know x = 25 - y . 6 ) from ( 4 ) and ( 5 ) , we have the equation 202 + y 2 − − − − − − − √ = 25 − y 202 + y 2 = 25 − y 7 ) solving for y , we get 4.5 . 8 ) 25 - 4.5 = 20.5 = x 9 ) since all sides of the rhombus are the same , 20.5 * 4 = 41 * 2 = 82 . the answer is b , 82
Answer: b
Question (gain): on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.4 * 4 = 9.6 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 9.6 % , answer : e"
Answer: e
Question (physics): a can do a piece of work 60 days . b can do work in 20 days . in how many days they will complete the work together ?
Options: a ) 12 days , b ) 16 days , c ) 15 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 60 , ratio = 60 : 20 = 3 : 1 no of days = 60 / ( 3 + 1 ) = 90 / 4 = 15 days answer : c"
Answer: c
Question (other): if there are 10 apples and 20 oranges , what is the ratio of apples to oranges ?
Options: a ) 10 : 20 , b ) 2 : 4 , c ) 1 : 2 , d ) 4 : 8 , e ) it can not be determined from the information given
Rationale: a ratio should be reduced to the lowest common denominator . 10 : 20 means 10 x : 20 x which can be written as 1 ( 10 ) : 2 ( 10 ) . . . answer : c
Answer: c
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 9500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 700 , d ) rs . 1500 , e ) rs . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 9500 = 38000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 6000 salary of may is rs . 6500 salary of january = rs . 500 answer : a"
Answer: a
Question (general): what two - digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5 ?
Options: a ) 94 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 10 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 10 x ^ 2 + y ^ 2 - 2 xy = 15 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 94 thus the answer is a"
Answer: a
Question (general): last week david spent 20 percent of his wages on recreation . this week , his wages are 30 percent less than last week ʼ s wages and he spent 20 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options: a ) 75 % , b ) 72 % , c ) 70 % , d ) 73 % , e ) 74 %
Rationale: "say david ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.70 * 100 = $ 70 , so he spends 0.2 * 70 = $ 14 on recreation ; 14 / 20 = 0.70 , hence the amount he spends on recreation this week is 70 % of the amount he spent on recreation last week : 20 * 0.7 = 14 answer : c"
Answer: c
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 180 votes . find the total number of valid votes ?
Options: a ) 450 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 180 = > 4 x / 10 = 180 = > 4 x = 1800 = > x = 450 . answer : a"
Answer: a
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 10 liters of milk , the can would be full and the ratio of milk and water would become 5 : 2 . find the capacity of the can ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: let c be the capacity of the can . ( 4 / 7 ) * ( c - 10 ) + 10 = ( 5 / 7 ) * c 4 c - 40 + 70 = 5 c c = 30 the answer is d .
Answer: d
Question (physics): a car runs at the speed of 55 km per hour when not serviced and runs at 90 kmph when serviced . after servicing the car covers a certain distance in 3 hours . how much time will the car take to cover the same distance when not serviced ?
Options: a ) 8 hours , b ) 6 hours , c ) 9 hours , d ) 7 hours 12 minutes , e ) none
Rationale: explanation : time = 90 * 3 / 45 = 6 hours answer â € “ b
Answer: b
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 24 kmph , find the speed of the stream ?
Options: a ) 18 kmph , b ) 6 kmph , c ) 8 kmph , d ) 10 kmph , e ) 12 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 24 / 3 = 8 kmph . answer : c"
Answer: c
Question (other): a began business with rs . 27000 and was joined afterwards by b with rs . 36000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1.5 , b ) 6.5 , c ) 7.5 , d ) 8 , e ) 2
Rationale: "27 * 12 : 36 * x = 2 : 1 x = 4.5 12 - 4.5 = 7.5 answer : c"
Answer: c
Question (general): a certain kind of fuel is 1515 high octane and 4545 regular octane . if high octane costs 3 times as much as regular octane , what fraction of the cost of the fuel is due to the high octane ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 3 / 7 , d ) 3 / 5 , e ) 4 / 5
Rationale: let x be the amount of fuel high octane = x / 5 regular = 4 x / 5 price of regular = y price of high octante = 3 y cost of high octane in the fuel = 3 y * x / 5 total cost = 3 y * x / 5 + 4 x / 5 * y % = cost of high octante / total cost = 3 / 7 answer is c
Answer: c
Question (probability): 8 coins are tossed . whats is the probability that one and only one turns up head ?
Options: a ) 1 / 256 , b ) 1 / 32 , c ) 1 / 64 , d ) 1 / 128 , e ) 1 / 189
Rationale: explanation : possible outcomes ( sample space ) when 8 coins are tossed are : ( h , h , h , h , h , h , h , h ) , ( h , h , h , h , h , h , h , t ) , ( h , h , h , h , h , h , t , h ) , ( h , h , h , h , h , h , t , t ) , . . . . . . . ( t , t , t , t , t , t , t , t ) = 28 required outcomes : ( h , t , t , t , t , t , t , t ) , ( t , h , t , t , t , t , t , t ) , ( t , t , h , t , t , t , t , t ) , ( t , t , t , h , t , t , t , t ) , ( t , t , t , t , h , t , t , t ) , ( t , t , t , t , t , h , t , t ) , ( t , t , t , t , t , t , h , t ) , ( t , t , t , t , t , t , t , h ) = 8 so the required probability = 8 / 28 = 1 / 32 answer : b
Answer: b
Question (geometry): a rectangular lawn of dimensions 110 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 4800 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 110 + 60 – 10 ) 10 = > 1600 m 2 1600 * 3 = rs . 4800 answer : b"
Answer: b
Question (general): if you multiply all the numbers on your mobile phone , what is the answer ?
Options: a ) 2 , b ) 6 , c ) 1 , d ) 0 , e ) 7
Rationale: d 0 their is a zero in your phone .
Answer: d
Question (general): if x is 20 percent greater than 12 , then x =
Options: a ) 10.2 , b ) 12.1 , c ) 8.1 , d ) 15.6 , e ) 14.4
Rationale: "x is 20 % greater than 12 means x is 1.2 times 12 ( in other words 12 + 20 / 100 * 12 = 1.2 * 12 ) therefore , x = 1.2 * 12 = 14.4 answer : e"
Answer: e
Question (general): if 7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ ( 7 ^ 9 ) - 7 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 11 / 2 , c ) 242 , d ) 3 ^ 10 , e ) 7 ^ 11 - 1
Rationale: "7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ 7 ^ 9 - 7 ^ k 7 * ( 7 ^ k ) = 7 ^ ( 49 * 7 ^ 9 ) = 7 ^ ( 7 ^ 2 * 7 ^ 9 ) = 7 ^ ( 7 ^ 11 ) 7 ^ k + 1 = 7 ^ ( 7 ^ 11 ) so k + 1 = 7 ^ 11 so k = 7 ^ 11 - 1 answer is e"
Answer: e
Question (other): find the probability in a group of 10 students sitting in a row , two of them always sit next to each other
Options: a ) 0.5 , b ) 0.4 , c ) 0.3 , d ) 0.2 , e ) 0.1
Rationale: assume that these 2 students are 1 and then u can sit is 9 ! and these 2 students can sit by 2 ways then total ways are 9 ! * 2 and the probability is 9 ! * 2 / 10 ! = 1 / 5 = 0.2 answer : d
Answer: d
Question (general): a student got 74 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 66 % , b ) 67 % , c ) 68 % , d ) 69 % , e ) 70 %
Rationale: "74 + 81 + x = 3 * 75 x = 70 the answer is e ."
Answer: e
Question (physics): a leak in the bottom of a tank can empty the full tank in 3 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 1440 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 3 - 1 / 12 ) = 1 / 4 work done by the inlet in 1 min . = ( 1 / 4 × 1 / 60 ) = 0.004167 volume of 0.004167 part = 6 litres . therefore , volume of whole = 0.004167 x 6 ‹ = › 1440 litres . answer d"
Answer: d
Question (other): the ratio of 2 numbers is 4 : 6 and their h . c . f . is 8 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 52 , d ) 96 , e ) 60
Rationale: "let the numbers be 4 x and 6 x their h . c . f . = 8 so the numbers are 4 * 8 , 6 * 8 = 32,48 l . c . m . = 96 answer is d"
Answer: d
Question (general): when positive integer n is divided by 4 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 35 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 4 , the remainder is 1 i . e . , n = 4 x + 1 values of n can be one of { 1 , 5 , 9 , 13 , 17 , . . . . . . . . . . . 29 , 33 , 37 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , . . . . . . . . } combining both the sets we get n = { 5,33 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 35 or 35 x in case of n = 33 p = 2 so for min value of p , we take min value of n . b is the answer ."
Answer: b
Question (gain): sam invested rs . 12000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 13230.0 , b ) 12300.02 , c ) 16537.5 , d ) 15000.0 , e ) 16537.11
Rationale: "p = rs . 12000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 12000 * ( 1 + 5 / 100 ) 2 ] = ( 12000 * 21 / 20 * 21 / 20 ) = rs . 13230.00 answer : a"
Answer: a
Question (gain): john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 18 , what was the price before the first discount ?
Options: a ) $ 32 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 65.23
Rationale: let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 18 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 18 solve for x x = $ 32 correct answer a
Answer: a
Question (general): the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 16 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 36 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 16 = 36 km apart , they take 1 hour to be 1000 m apart , they take 36 * 1000 / 1000 = 36 min . answer is e"
Answer: e
Question (geometry): a cube of edge 5 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 10 cm * 5 cm , find the rise in water level ?
Options: a ) 2.5 cm , b ) 3.6 cm , c ) 5 cm , d ) 6.43 cm , e ) 7.56 cm
Rationale: "increase in volume = volume of the cube = 5 * 5 * 5 cm ^ 3 rise in water level = volume / area = 5 * 5 * 5 / 10 * 5 = 2.5 cm answer is a"
Answer: a
Question (general): two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 15 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 5 ) = 2 / 15 answer : b ) 2 / 15"
Answer: b
Question (physics): 4 men and 12 boys finish a piece of work in 4 days , 7 men and 6 boys do it in 5 days . the ratio between the efficiencies of a man and boy is ?
Options: a ) 18 : 19 , b ) 17 : 19 , c ) 15 : 19 , d ) 18 : 14 , e ) 18 : 11
Rationale: "4 m + 12 b - - - - - 4 days 7 m + 6 b - - - - - - - 5 days 16 m + 48 b = 35 m + 30 b 18 b = 19 m = > 5 m = 6 b m : b = 18 : 19 answer : a"
Answer: a
Question (physics): a boatman trying to cross the river . the width of the river is 400 m . he is selling boat with 10 m / sec . he takes 50 sec to cross the river due to flow of water . calculate the drift .
Options: a ) 500 , b ) 400 , c ) 300 , d ) 200 , e ) 100
Rationale: the distance boatman travel to cross the river = 50 * 10 = 500 m he sell the boat diagonally . so height = 400 m , base be x and hypotenuse = 500 m so by pythagoras theorem , square of 400 + square of x = square of 500 so , square of x = 250000 - 160000 x = â ˆ š 250000 - 160000 , x = â ˆ š 90000 = 300 drift = 300 m answer c
Answer: c
Question (geometry): the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 60 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 25 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 60 ounces of a substance has a volume of ( 48 / 112 ) * 60 = 25 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 60 will have a volume a little more than 24 , that is 25 c"
Answer: c
Question (physics): the average speed of a train is 87 kmph . the train was scheduled to start at 9 am in bangalore , and as per schedule it has to reach a destination of 348 km away from bangalore at 1 : 45 pm same day and a halt was scheduled onthe way . for how long was the halt scheduled ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 60 minutes , e ) none of these
Rationale: speed of train = 87 kmph and distance it covers is 348 km . time taken to cover the distance = distance / speed = 348 / 87 = 4 hours . but total time taken by train to reach destination is = 1 : 45 pm – 9 a . m = 4 hours 45 minutes . time of halt = total time – take taken without halt = 4 hours 45 minutes – 4 hours = 45 minutes a )
Answer: a
Question (physics): the height of the wall is 4 times its width and length of the wall is 3 times its height . if the volume of the wall be 10368 cu . m . its width is
Options: a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 4 x and length = 12 x 12 x ã — 4 x ã — x = 10368 x = 6 answer : c"
Answer: c
Question (physics): a courtyard is 24 meter long and 14 meter board is to be paved with bricks of dimensions 25 cm by 15 cm . the total number of bricks required is :
Options: a ) 6000 , b ) 8000 , c ) 8960 , d ) 2000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2400 ã — 1400 / 25 ã — 15 ) = 8960 option c"
Answer: c
Question (gain): rajan and rakesh started a business and invested rs . 20,000 and rs . 25,000 respectively . after 4 months rakesh left and mukesh joined by investing rs . 15,000 . at the end of the year there was a profit of rs . 4,600 . what is the share of rajan ?
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: ratio of share of rajan , rakesh nd mukesh = > 20000 : 25000 : 15000 = > 4 : 5 : 3 = > 4 * 12 : 5 * 4 : 3 * 8 [ since rakesh left after 4 months nd mukesh joined after 4 months . . . ] = > 12 : 5 : 6 share of rajan = > 4600 * 12 / 23 = 2400 answer : e
Answer: e
Question (general): when a = x + ( 3 / x ) and b = x - ( 3 / x ) , ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 4096
Rationale: "- - > ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = { ( 2 ) ^ ( a ^ 2 - b ^ 2 ) } = 2 ^ ( a - b ) ( a + b ) . since a - b = 6 / x and a + b = 2 x , 2 ^ ( a - b ) ( a + b ) = 2 ^ ( 6 / x ) ( 2 x ) = 2 ^ 12 = 4096 therefore , the answer is e"
Answer: e