Question

if x and y are consecutive non-zero integers, then it must be true that (a)xy is odd (b) x^2+y is even (c) x+xy is odd (d) x+y is odd

Answer 1

(d) x+y is odd

Explanation:

x and y are consecutive nonzero integers.

Then either

(1) x is even and y is odd

or

(2) x is odd and y is even.

(a) odd times even is even, so (a) is false

(b) According to (1), x^2 + y is odd, and according to (2) x^2 + y is also odd. (b) is false.

(c) Just xy is even according to (1) and (2). According to (1) x + xy is even, and according to (2) x + xy is odd, so (c) is false.

(d) x + y is "odd plus even" or "even plus odd" and is always odd. (d) is true.

Answer: (d) x+y is odd