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Problem #63 · September 28, 2026

Even and odd numbers

If aa is an even number, which of the following numbers must be even?
  1. Aa2+15a^{2} + 15
  2. B3(a+5)3(a + 5)
  3. Ca+7a + 7
  4. Da2+34a^{2} + 34

WORKED EXAMPLE

Solution

If aa is even, then a2a^{2} is also even. If an even number is added to an even number, the result is even: a2+34a^{2}+34 is necessarily even. In the other options, the odd number (1515 or 77) is added to an even number, or the odd number (a+5a+5) is multiplied by an odd number — the result is odd.
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