The posted problem has been transcribed incorrectly.
In the version above, the two statements contradict each other:
If there are a total of 12 integers between x and y (statement 1 above), then there cannot be a total of 24 even integers between x and y (statement 2 above).
On the GMAT, the two statements will never contradict each other.
The original problem is from GMATPrep.
In the GMATPrep version, the two statements read as follows:
How many odd integers are greater than integer X and less than the integer y?
1. There are 12 even integers greater than x and less than y
2. There are 24 integers greater than X and less than Y
jain2106, please edit your post accordingly.
Statement 1: There are 12 even integers greater than x and less than y.
Let the 12 consecutive even integers greater than x and less than y be the following:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
Here, x<0 and y>22.
If x=-1 and y=23, then every odd integer between 1 and 21, inclusive, will be greater than x and less than y, for a total of 11 odd integers.
If x=-1 and y=24, then every odd integer between 1 and 23, inclusive, will be greater than x and less than y, for a total of 12 odd integers.
INSUFFICIENT.
Statement 2: There are 24 integers greater than x and less than y.
EXACTLY HALF of these 24 consecutive integers must be odd.
Thus, the number of odd integers greater than x and less than y = 12.
SUFFICIENT.
The correct answer is
B.
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