If n is a positive integer, what is the value of n?

Statement 1

(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.

35 = 7 * 5

Hence, if we take any set of 7 consecutive integers, the product will be divisible by 35.

Therefore, the minimum value of 'n' is 6. Any value of n greater than or equal to 6 satisfies statement 1.

Hence, the statement alone is not sufficient to find a unique value of n. We can eliminate A and D.

Statement 2

(2) \(n^2 - 8n + 7 < 0\).

\(n^2 - 8n + 7 < 0\)

\((n-1)(n-7) < 0\)

------------ 1 ------------------------ 7 -------------

Any integer value between 1 and 7 satisfies the inequality. The statement alone is not sufficient to find a unique value of n. We can eliminate B.

Combined

From statement 1: \(n\geq6\)
From statement 2: \(1 < n < 7\)

The only common value = 6.

The statements combined help us identify a unique value of n.

Option C