Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2017
Hard
If a and b are integers and a-b is even, which of the following must always be even?
- Aab
- Ba^2+b^2+1
- Ca^2+b+1
- ab-b
Explanation
a-b even means a and b share the same parity (both even or both odd). Check ab-b = b(a-1) in both cases: if both are even, b is even, so b(a-1) is even. If both are odd, then a-1 is even, so b(a-1) is even. Either way, ab-b is always even. The other options fail in at least one parity case (e.g. ab is odd when both a,b are odd).
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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