Orange08 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 x and less than y
(2) There are 24 integers greater than x and less than y
why are the integers assumed consecutive over here?
Target question: How many odd integers are greater than the integer x and less than the integer y? Statement 1: There are 12 even integers greater than x and less than y There are many scenarios that satisfy statement 1. Here are two:
Case a: x = 1 and y = 25. In this case, the answer to the target question is
there are 11 odd integers greater than the integer x and less than the integer yCase b: x = 1 and y = 26. In this case, the answer to the target question is
there are 12 odd integers greater than the integer x and less than the integer ySince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: There are 24 integers greater than x and less than yASIDE: Many students will read the statement 2 and conclude that, since we aren't told whether those 24 integers are CONSECUTIVE integers, there's no way to tell how many how many odd integers there are.
However, the integers between x and y will always be consecutive.
For example, the integers between 5 and 11 are 6, 7, 8, 9 and 10 (consecutive)
Similarly, the integers between -2 and 8 are -1, 0, 1, 2, 3, 4, 5, 6 and 7 (consecutive) Since even and odd integers alternate in consecutive integers (e.g., 1 is odd, 2 is even, 3 is odd, 4 is even,... etc.) , we know that 12 of the 24 integers must be even, and the other
12 must be oddSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.