How many odd integers are greater than the integer x and les

[gmat blows]

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

This is from the GMATPrep 1. I thought this was a Ctrap and chose A - I honstly, have no clue how to approach this problem. any insight will be appreciated. thanks.
OA: B

[Maverick]

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

.......x........................y.............

(1) If x and y are both odd: x.(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e).y. 11 odds.

But if x is odd and y is even: x.(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).y. Look at the last odd. 12 odds.. Insufficient.

(2) There are even number of integers between x & y. It is possible only when there are 12 even & 12 odd integers between x & y.[/b]

[RonPurewal]

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

.......x........................y.............

(1) If x and y are both odd: x.(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e).y. 11 odds.

But if x is odd and y is even: x.(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).(e.o).y. Look at the last odd. 12 odds.. Insufficient.

(2) There are even number of integers between x & y. It is possible only when there are 12 even & 12 odd integers between x & y.[/b]

well played.

[Sam]

Hi Guys,
I have a question...The given statement (2) never says that the 24 integers between x and y are consecutive integers right? So all the 24 integers can be even or all can be odd. In this case it can be 24 odds or 24 evens. And yes if the statement said that the 24 integers are consecutive then your answer is correct...
Any thoughts??

[RonPurewal]

The given statement (2) never says that the 24 integers between x and y are consecutive integers right?

it doesn't have to. since the statement is counting all integers between x and y, they must be consecutive.

if you can find 24 integers between x and y, with "holes" between some of them (i.e., they're not all consecutive), then the "holes" also represent integers between x and y. therefore, there would actually be more than 24 integers between x and y.

remember: if a statement says "there are N of these things", then that means all of these things.

[ToThePromiseLand]

Is there a more formulaic or conceptual approach to this?
When I saw this question I thought to list out the possible scenarios as shown above, but looked at the clock, thought that there MUST be some approach I was missing, guessed and moved on.

Ron?

[tim]

Nope. This IS the conceptual case. If you are looking at a solution that explores only two cases and conclude that there isn't enough time for that, you'll probably want to focus more on speed and time management than trying to simplify this problem further.

[Everything OR Nothing]

To reduce time in this kind of problems, you can take a smaller range eg: 12345 here 2 even integers are there and in 123456 there are 2 even integers ( in between first and last terms,but total number of integers between first and last term is odd in one case and even in one case)

This kind of generalization helps to solve in reduced time in real exam scenario.

[tim]

Thanks!