Bunuel wrote:

If a, b and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?

A. abc

B. a + b + c

C. a + bc

D. a(b + c)

E. (a + b)(b + c)

Since a, b, and c are consecutive integers, we see that a and c could both be even while b is odd, OR a and c could both be odd while b is even.

Since even + odd = odd, we see that a + b will always be odd, and b + c will always be odd; and, since odd x odd = odd we see that , (a + b)(b + c) will always be odd.

Answer: E

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