If n is an integer, is n even?
(1) n² − 1 is an odd integer.
(2) 3n + 4 is an even integer.

Target question: Is n even?

Statement 1: n² − 1 is an odd integer.
If n² −1 is an odd integer, then n² must be an even integer.
If n² is an even integer, then n must be even.
Rationale: (odd)² = odd, but (even)² = even
As such, statement 1 is SUFFICIENT

Statement 2: 3n + 4 is an even integer.
If 3n + 4 is an even integer, then 3n must be an even integer (since Even + Even = Even).
If 3n must be an even integer, then n must be even.
Rationale: (odd)(even) = even and
As such, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

pareekbharat86 wrote: 0, an integer, satisfies both statements. Yet, we know 0 is neither positive nor negative. Why D?

You're right, 0 is neither positive nor negative
However, the question isn't asking whether n is positive or negative. It's asking whether n is even.
0 is even

Cheers,
Brent