3. If R is an integer between 1 & 9, P - R = 2370, what is the value of R?
I. P is divisible by 4.
II. P is divisible by 9.
4. A man distributed 43 chocolates to his children. How many of his children are more than five years old?
I. A child older than five years gets 5 chocolates.
II. A child 5 years or younger in age gets 6 chocolates.
5. Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speeds for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum?
I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras.
II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.
6. x, y, and z are three positive odd integers, Is x+z divisible by 4?
I. y - x = 2
II. z - y = 2
7. The unit price of product P1 is non-increasing and that of product P2 is decreasing. Which product will be costlier 5 years hence?
I. Current unit price of P1 is twice that of P2.
II. 5 years ago, unit price of P2 was twice that of P1.
8. X is older than Y, Z is younger than W and V is as old as Y. Is Z younger than X?
I. W may not be older than V
II. W is not older than V
9. How long did Mr. X take to cover 5000 km. journey with 10 stopovers?
I. The $$i^{th}$$ stopover lasted $$i^2$$ minutes.
II. The average speed between any two stopovers was 66 kmph.
10. Is $$[(x^{-1} - y^{-1} )/(x^{-2} -y^{-2}]>1$$?
I. x + y > 0
II. x and y are positive integers and each is greater than 2.
11.
In a game played by two people there were initially N match sticks kept on the table. A move in the game consists of a player removing either one or two matchsticks from the table. The one who takes the last matchstick loses. Players make moves alternately. The player who will make the first move is A. The other player is B.The smallest value of N (greater than 5) that ensures a win for B is
12. The largest of N (less than 50) that ensures a win for B is
13. There were 'x' pigeons and 'y' mynahs in a cage. One fine morning, 'p' birds escaped to freedom. The bird-keeper, knowing only that p = 7, was able to figure out without looking into the cage that at least one pigeon had escaped. Which of the following does not represent a possible (x,y) pair?
14. The remainder when $$2^{60}$$ is divided by 5 equals
15. Mr.X enters a positive integer Y(>1) in an electronic calculator and then goes on pressing the square . root key repeatedly. Then
16. What is the sum of the following series: $$ \frac{1}{1 \times 2} + \frac{1}{2 \times 3}+\frac {1}{3 \times 4}$$ ....... $$+ \frac{1}{100 \times 101}$$?
17. The value of $$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}$$
18. Let a, b be any positive integers and x = 0 or 1, then
19. There are six boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a white ball or a black ball in such a manner that at least one box contains a black ball and all the boxes containing black balls are consecutively numbered. The total number of ways in which this can be done equals.
20. Consider the following steps :
1. Put x = 1, y = 2
2. Replace x by xy
3. Replace y by y +1
4. If y = 5 then go to step 6 otherwise go to step 5.
5. Go to step 2
6. Stop Then the final value of x equals
21. In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
22. From any two numbers $$x$$ and $$y$$, we define $$x* y = x + 0.5y - xy$$ . Suppose that both $$x$$ and $$y$$ are greater than 0.5. Then
$$x* x < y* y$$ if
23. Consider a function $$f(k)$$ defined for positive integers $$k = 1,2, ..$$ ; the function satisfies the condition $$f(1) + f(2) + .. = \frac{p}{p-1}$$. Where $$p$$ is fraction i.e. $$0 < p < 1$$. Then $$f(k)$$ is given by
24. 116 people participated in a singles tennis tournament of knock out format. The players are paired up in the first round, the winners of the first round are paired up in second round, and so on till the final is played between two players. If after any round, there is odd number of players, one player is given a bye, i.e. he skips that round and plays the next round with the winners. Find the total number of matches played in the tournament.
25. If n is any positive integer, then $$n^{3} - n$$ is divisible
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