If x and y are integers, is the product xy odd?
(1) x = -5
(2) x and y are consecutive integers
Is xy odd
For a product to be odd, it must NOT be divisible by 2.
Statement 1: We know the value of x but have no idea what y is. It's possible that y is also odd, in which case xy will be odd. For example:
x = -5, y = 1xy = -5 × 1 = -5, odd
However, y could just as easily be even, in which case it would be divisible by 2. Therefore, xy would be even. For example:
x = -5, y = 2xy = -5 × 2 = -10, even
This statement is insufficient.
Statement 2: Given two consecutive integers, one of them must always be even and the other odd. Multiplying the two together will thus result in an even product. For example:
x = 1, y = 2xy = 1 × 2 = 2, even
x = -1, y = 0xy = -1 × 0 = 0, even
x = 8, y = 9xy = 8 × 9 = 72, even
Since xy will always be even in this case, we can definitively answer "no" to the question "Is the product xy odd?" Therefore, Statement 2 alone is sufficient.
Watch the lessons below for more detailed explanations of the concepts tested in this question.
And don't worry, you'll be able to return to this answer from the lesson page.