Please submit your concern

Explanation:

From statement (A) alone:

Exactly 1 player received a bye in the entire tournament. We get many values of n between 65 and 128 that satisfy this condition.

For example, n can have the value 124 in round 1, to follow the pattern, [124-62-31-16-8-4-2-1].

Also, n can have the value 127 in round 1, to follow the pattern, [127-64-32-16-8-4-2-1].

∴ We cannot answer the question on the basis of statement (A) alone.

From statement (B) alone:

One player received a bye while moving on to the fourth round from the third round.

Here also, we get multiple values of n.

For example, n can have the value 124 in round 1, where 1 player received a bye while moving from round 3 to round 4 following the pattern, [124-62-31-16-8-4-2-1].

Also, n can have the value 122 in round 1, where 1 player received a bye while moving from round 3 to round 4 following the pattern, [122-61-31-16-8-4-2-1].

∴ We cannot answer the question on the basis of statement (B) alone.

From statements (A) and (B) together:

n can only have the value 124 in round 1, where exactly 1 player received a bye while moving from round 3 to round 4 following the pattern [124-62-31-16-8-4-2-1].

∴ We can answer the question using both the statements (A) and (B) together.

Hence, option (d).

Note: An analysis of how 124 was arrived at when using both conditions together:

Let the number of players in the first round be n. Since only one player gets a bye, and that too when moving from the third to the fourth round, hence we have the following conditions:

1. There will be n players in the first round, where n is even.

2. There will be n/2 players in the second round, where n/2 is even.

3. There will be n/4 players in the third round, where n/4 is odd.

4. There will be n4+12=n+48 players in the fourth round, where n+48 should be even.

5. All numbers of players in the subsequent rounds should also be even.

From condition 3, we can conclude that:

n+48=2k, where k is an integer

Hence, n = 16k – 4; so, within the given range, n could be 76 or 92 or 108 or 124.

Writing the pattern for each of the above possible values of n, we have:

76: [76-38-19-10-5-3-2-1]

92: [92-46-23-12-6-3-2-1]

108: [108-54-27-14-7-4-2-1]

124: [124-62-31-16-8-4-2-1]

We see that only 124 satisfies condition 5.

Hence, option (d).

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