Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2018
Hard
Given that a and b are integers and a+a^2*b^3 is odd, which one of the following statements is correct?
- Aa and b are both odd
- Ba and b are both even
- Ca is even and b is odd
- a is odd and b is even
Explanation
If a is even, a^2*b^3 is also even (since a^2 is even), so the sum a+a^2*b^3 is even+even=even, contradicting 'odd'. So a must be odd. With a odd, a^2 is odd, so a^2*b^3's parity matches b^3's parity, which matches b's parity. For the sum (odd + a^2*b^3) to be odd, a^2*b^3 must be even, so b must be even. Thus a is odd and b is even.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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