2023 · Q76
Item contains a Question followed by two Statements. Answer each item using the following instructions : Question : Is p² + q² + q odd, where p, q are positive integers?
Statement I2p + q is odd.
Statement IIq - 2p is odd.
Elementary MathematicsNumber System
- AChoose this option if the Question can be answered by one of the Statements alone but not by the other.
- BChoose this option if the Question can be answered by either Statement alone.
- CChoose this option if the Question can be answered by using both Statements together, but cannot be answered by using either Statement alone.
- DChoose this option if the Question cannot be answered even by using both Statements together.
Explanation
Statement I (2p + q odd) only implies q is odd, since 2p is even; then q² + q = q(q + 1) is even, but p²'s parity is unknown, so p² + q² + q is undecided. Statement II (q − 2p odd) likewise only forces q odd, leaving p² unknown. Even together, p is unconstrained, so the parity cannot be determined (D).