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Choose the correct statement.

If x and y are integers, is the product xy odd?

(1) x = -5

(2) x and y are consecutive integers

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. Each statement ALONE is sufficient to answer the question. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

Title

Is xy odd

Your Result

Correct

Difficulty

Easy

Your Pace

0:01

Others' Pace

0:51

Video Explanation

Text Explanation

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 = 1
xy = -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 = 2
xy = -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 = 2
xy = 1 × 2 = 2, even

x = -1, y = 0
xy = -1 × 0 = 0, even

x = 8, y = 9
xy = 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.

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