The Parity Detective

The question involves integers and asks what 'must be even/odd' — or has answer choices that vary in their parity. Sometimes the trap is hidden inside an exponent or a sign question.

Trying to solve for the actual values of x and y. You usually don't need them — just their parities. Also: forgetting that 2 is the only even prime, so it sneaks in to break parity-based shortcuts.

1. Memorize the parity rules: odd + odd = even, odd + even = odd, even + even = even.
2. For multiplication: anything × even = even. odd × odd = odd.
3. For exponents: even^n is always even, odd^n is always odd (sign matters separately).
4. Determine the forced parities from the constraints in the question.
5. Test each answer choice for whether it MUST, COULD, or CANNOT match the required parity.
6. When stuck, plug in one specific odd value and one specific even value and observe what happens.

Parity questions are pure pattern recognition — no calculation needed if you spot it. They appear in 1-2 questions per real GRE Quant section, and they're huge time-savers when recognized instantly.