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题库 / GMATLA-DS-37
If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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- if n is not divisible by 2, then n is odd, so both (n - 1) and (n + 1) are even. so the product (n - 1)(n + 1) contains one multiple of 2 and one multiple of 4, so it contains at least 2 x 2 x 2 = three 2's in its prime factorization.
- if n is not divisible by 3, then exactly one of (n - 1) and (n + 1) is divisible by 3contains a 3 in its prime factorization.
- thus, the overall prime factorization of (n - 1)(n + 1) contains three 2's and a 3.
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