Hi anant03,
This DS question is ultimately a test of your 'thoroughness'; you can TEST VALUES to answer it, but you have to make sure that you consider that the first example that you come up with might not be the only answer to the question...
We're told that X and Y are INTEGERS. We're asked for the number of ODD integers that are greater than X and less than Y.
1) There are 12 EVEN integers greater than X and less than Y
IF....
X = 0
Then the 12 EVEN integers would be...
2,4,6,8,10
12,14,16,18,20
22,24
Y could actually be 2 DIFFERENT values though: 25 OR 26
IF....
Y = 25
Then the ODD integers between 0 and 25 are....
1,3,5,7,9
11,13,15,17,19
21,23
For a total of 12 odd integers
IIF....
Y = 26
Then the ODD integers between 0 and 26 include 1 EXTRA INTEGER....
1,3,5,7,9
11,13,15,17,19
21,23,25
For a total of 13 odd integers
Fact 1 is INSUFFICIENT
2) There are 24 INTEGERS greater than X and less than Y.
Without the restriction of 'odd' or 'even', the work becomes a lot easier (it's ultimately a Number Property). With 24 CONSECUTIVE integers, half will be odd (12 terms) and half will be even (12 terms) - that will never change. For example....
IF....
X = 0
Then the 24 values would be 1-24 (inclusive) and Y could only be one value...
Y = 25
From our prior work, we know that that answer to the question is 12.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
