2016 · Q27
Consider the following statements in respect of positive odd integers x and y :
- 1x²+y² is even integer.
- 2x²+y² is divisible by 4.
Which of the above statements is/are correct ?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Odd squares are odd, so x²+y² is the sum of two odd numbers — even (statement 1 true). But every odd square is ≡ 1 (mod 8), so x²+y² ≡ 2 (mod 8), which is never divisible by 4 (statement 2 false). Hence statement 1 only (option A).