Question:
If \(n\) is an integer, is \(n\) even?
(1) 2n is an even integer.
(2) n − 1 is an odd integer.
If \(n\) is an integer, is \(n\) even?
(1) 2n is an even integer.
(2) n − 1 is an odd integer.
Show Hint
Check whether given conditions actually restrict the integer’s parity — multiplication by 2 always produces even, so it’s not restrictive.
Updated On: Aug 28, 2025
- 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.
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The Correct Option is B
Solution and Explanation
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 ⇒ \(\boxed{B}\).
From (2): \(n - 1\) odd ⇒ \(n\) must be even (odd + 1 = even) ⇒ sufficient. Thus ⇒ \(\boxed{B}\).
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