If S is an even integer, then which of the following are true?

1.S + 1 will be odd

2.2S - 1 will be odd

3.S squared + 1 will be odd

4.S squared - 1 will be odd

5.S squared + 2 will be odd

A1 & 2 only

B1, 2 & 3 only

C1, 2, 3 & 4 only ✓ Correct

D3, 4 & 5 only

Correct answer: (C) 1, 2, 3 & 4 only

Explanation

Statements 1, 2, 3 and 4 are true.

S is even, so S + 1 = even + odd = odd (Statement 1 true).

2S is even, so 2S - 1 is odd (Statement 2 true).

S even makes S^2 even, so S^2 + 1 is odd (Statement 3 true).

Likewise S^2 - 1 = even - 1 = odd (Statement 4 true).

But S^2 + 2 = even + even = even, so Statement 5 is not odd.

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