2024 · Q63
Consider the following for the next ten (10) items that follow: Each item contains a Question followed by two Statements. Answer each item using the following instructions: Question : If p is a positive integer, then what is the remainder when pn is divided by p + 1?
Statement In is even.
Statement IIp is even.
Elementary MathematicsNumber System
- AIf the Question can be answered by one of the Statements alone, but not by the other.
- BIf the Question can be answered by either Statement alone.
- CIf the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- DIf the Question cannot be answered even by using both Statements together.
Explanation
Statement I: n even gives pⁿ = (p²)^{n/2} ≡ 1 (mod p+1) since p ≡ −1 — remainder 1, answered alone. Statement II (p even) says nothing about n. One statement alone suffices: option (a).