If a and b are integers, is a/b an even number?

Statement 1 is sufficient no matter which numbers you pick.
The question is: Is a/b an even integer?

For a/b to be an even integer, 'a' must be even (since a and b are given to be integers) and 'b' must be a factor of 'a' such that the quotient is still even.

Statement 1: If 'a' and 'b' are odd, 'a' is not even and hence we can say that a/b is not an even integer. Now whether it is not an integer itself or whether it is not even, doesn't matter to us. What we know is that it is not an 'even integer'.

Official Solution:


If \(a\) and \(b\) are nonzero integers, is \(\frac{a}{b}\) an even number?

(1) \(ab\) is an odd number.

This statement implies that both \(a\) and \(b\) must be odd. Therefore, \(\frac{a}{b}\) is an odd number divided by an odd number, which cannot be even. Thus, the answer to the question is NO. Sufficient.

(2) \(a + b\) is an even number.

This statement implies that either both \(a\) and \(b\) are odd or both of them are even. If both \(a\) and \(b\) are odd, then \(\frac{a}{b}\) is not even. However, if both \(a\) and \(b\) are even, then \(\frac{a}{b}\) can be even, for example consider \(a=4\) and \(b=2\). It is important to note that if both \(a\) and \(b\) are even, then \(\frac{a}{b}\) can also be odd (consider \(a=b=2\)) as well as non-integer (consider \(a=2\) and \(b=4\)). This statement is not sufficient to answer the question.


Answer: A