nupurgupt wrote:

How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than y and less than y

(2) There are 24 integers greater than x and less than y

The way I thought about this is:

(1) Take the interval from 2 to 10 -->

even integers in b/w = 4, 6, 8

odd integers in b/w = 3, 5, 7, 9

Take the interval from 3 to 11 -->

even integers in b/w = 4, 6, 8

odd integers in b/w = 5, 7, 9

Therefore, INSUFFICIENT

(2) Take the interval from 2 to 9 -->

6 integers in b/w = 3, 4, 5, 6, 7, 8

odd integers in b/w = 3, 5, 7

Take the interval from 3 to 10 -->

6 integers in b/w = 4, 5, 6, 7, 8, 9

odd integers in b/w = 5, 7, 9

Therefore, SUFFICIENT

Is there a better explanation for the question (not using brute force).

Any inputs would be appreciated =)

For statement 2 it would be faster without considering numbers.

We know there are 24 integers between x and y. If we have a set of even number of integers exactly half would be odd and the other half even. So statement 2 is sufficient.

If you have copied down statement 1 correctly (12 greater than y and also less than y), then it is clearly insufficient since we have no knowledge of x!!