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CAT-2008-Previous Years Paper

Question
12 out of 25
 

Suppose, the seed of any positive integer i is defined as follows: seed(n) = n, if n < 10 = seed(s(n)), otherwise where s(n) indicates the sum of digits of n.

For example, seed (7) = 7, seed (248) = seed (2 + 4 + 8) = seed (14)= (1 + 4) = seed = 5 etc. How many positive integers n, such that n < 500, will have seed(n) = 9?



A 39
B 72

C 81
D 108

E 55

Ans. E

Our answer would be the number of integers between 1 and 500, which are divisible by 9.

The smallest is 9 and the largest is 495.

In the first 499 natural numbers, we have 495 as the last multiple of 9, and this is 55th multiple of 9.

Hence, (e).

CAT-2008-Previous Years Paper Flashcard List

25 flashcards
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In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:   A. If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.   B. If the number of players, say it, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n-1) players are grouped into (n-l)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.   Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+l)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament. What is the number of matches played by the champion? A: The entry list for the tournament consists of 83 players. B: The champion received one bye. A If Question can be answered 1mm A alone but not from B alone. B If Question can be answered from B alone but not from A alone. C If Question can be answered from either of A or B alone. D If Question can be answered from A and B together but not from any of them alone. E If Question cannot be answered even from A and B together.
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In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:   A. If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.   B. If the number of players, say it, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n-1) players are grouped into (n-l)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.   Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+l)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament. If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n? A: Exactly one player received a bye in the entire tournament. B: One player received a bye while moving on to the fourth round from the third round A If Question can be answered 1mm A alone but not from B alone. B If Question can be answered from B alone but not from A alone. C If Question can be answered from either of A or B alone. D If Question can be answered from A and B together but not from any of them alone. E If Question cannot be answered even from A and B together.
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