## QBM037

Q1.If A and B together can complete a task in 6 2/3 days, B and C together can complete it in 12 days, and C and A together can complete it in 7 1/2 days, then how many days will it take for A alone to complete half the task?
1) 2( 8/11) days

2) 5 days

3) 7 (8/11) days

4) 5 (8/11) days
Q2.In a race of 200 meters, A beats S by 20 meters and N by 40 metres. If S and N are running a race of 100 metres with exactly the same speed as before, then by how many metres will S beat N?
(1)11.11 metres

(2) 10 metres

(3)12 metres

(4) 25 metres
Q3.A rod of length 1 is broken into four pieces. What is the probability that the four pieces are the sides of a trapezoid?
Q4.Take a deck of 52 playing cards consecutively numbered from 1 to 52. A perfect shuffle occurs when you divide the deck in two, one half in each hand, and riffle them together in an alternating fashion; after the shuffle the cards in the deck will be ordered as follows:
1, 27, 2, 28, 3, 29, ... , 24, 50, 25, 51, 26, 52
Notice that the top card always stays on top and the bottom card always stay on the bottom. Imagine now that you repeatedly shuffle the cards, performing a perfect shuffle every time. How many times will you have to do this before all the cards in the deck are restored to their original position?
Q5. Is the number 2438100000001 prime or composite? No calculators or computers allowed!
Q6. A man has to invite six of his friends on his birthday for dinner. He can send invitations by post, by phone or by his servant. In how many ways can he send invitations to his friends so that each of his friends gets only one invitation?
(1)120

(2)720

(3)729

(4)216
Q7. On 1st January 1969, a person purchases Rs. 10,000, 4% debentures. On 1st Jan. 1970, he sells 3/4 of it at a discount of 6% and invests the proceeds in steel shares at Rs. 470 per share. He sells the remaining debentures at Rs. 105 and purchases bonds at a price of Rs. 75 per bond. Each bond pays Rs. 5. Each share pays Rs. 16. Find the alternation in his annual income in 1970?
(1)Rs. 15 decrease

(2)Rs. 25 increase

(3)Rs. 15 increase

(4) None
Q8. A 3 x 2 grid is placed so that its corners are at (0,0) and (3,2). A legal move is defined as a move either in the positive x or positive y direction. The darkened point has been removed from the grid. Now, how many possible paths are there from (0,0) to (3,1)?
1) 3

2) 6

3) 11

4) 7
Q9. How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?
A.4! - 3!

B.4

C.8

D.6
Q10. The sum of A and B is 12 and their reciprocals add up to 3/8. Then A and B are:
a) 5, 7

b) 3, 9

c) 4, 8

d) 2, 10
Q11. An elastic ball is propped from a height of 20 m. If the height of fall is twice the height of bounce, the total distance travelled by the ball before it comes to rest is
1) 40 m

2)60 m

3)80 m

4) infinite
Q12. The largest value of min (2 + x^{2}, 6 - 3x) when x > 0 is
(1)1

(2)2

(3)3

(4) 4
Q13. When is the product of two consecutive natural numbers a non-trivial integer power; that is, for which natural numbers n, t, k is n(n+1) = tk, for natural numbers t and k > 1?
Q14. An absentminded professor buys two boxes of matches and puts them in his pocket. Every time he needs a match, he selects at random (with equal probability) from one or other of the boxes. One day the professor opens a matchbox and finds that it is empty. (He must have absentmindedly put the empty box back in his pocket when he took the last match from it.) If each box originally contained n matches, what is the probability that the other box currently contains k matches? (Where 0 k n.)
Q15. 2/3rd of the balls in a bag are black, the rest are red. If 5/9th of the black balls and 7/8th of the red balls are defective, find the total number of balls in the bag, if the number of non-defective balls is 146.
(a)216

(b)432

(c)648

(d)578
END

## how to solve

I have seen very few similar questions to Q12 on this site for the first time. But no where i could find any hint or solution. Any guru ot there