Question

If \(n\) is an integer, is \(n\) even?
(1) 2n is an even integer.
(2) n − 1 is an odd integer.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
• D. EACH statement ALONE is sufficient.

Hint:

Check whether given conditions actually restrict the integer’s parity — multiplication by 2 always produces even, so it’s not restrictive.

Answer 1

The Correct Option is B

From (1): \(2n\) even ⇒ true for all integers \(n\) (even or odd), so no conclusion about \(n\) ⇒ not sufficient.
From (2): \(n - 1\) odd ⇒ \(n\) must be even (odd + 1 = even) ⇒ sufficient. Thus ⇒ \(\boxed{B}\).