GMAT Math

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

[email protected] wrote:Hi Arun6765,

In these types of situations, it can sometimes be helpful to try 'locking in' certain variables, so that you can "play around" with other variables (and see what happens).

This question tells us that X and Y are integers. It essentially asks us for the number of ODD integers between X and Y (but not counting X or Y).

1) There are 12 EVEN integers greater than X and less than Y

Let's try 'locking in' 12 consecutive even integers....
2 4 6 8 10
12 14 16 18 20
22 24

With this list of 12 even integers...
X COULD be 0 or 1
Y COULD be 25 or 26

How do those options effect the question that is asked?
IF... X=0, Y=26, then the answer to the question is 13
IF... X=1, Y=25, then the answer to the question is 11
Fact 1 is INSUFFICIENT

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

This Fact doesn't describe the integers as 'odd' or 'even', so we're just dealing with 24 consecutive integers. Since we know that X and Y are integers, by definition - half of those 24 integers will be odd and half will be even.

As an example, let's "lock in" the integers 1 through 24... In this scenario
X MUST be 0
Y MUST be 25
The answer to the question is 12.

If we increase or decrease X, then we have to also increase or decrease Y by the same value - but this won't change the number of odd or even integers. Thus, the answer to the question will ALWAYS be 12.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[email protected] wrote:Hi aalobaidy,

Each of the two statements are essentially 'Facts' that you have to incorporate into how you solve the prompt - and you MUST follow that information. Here, Fact 2 tells us that there are 24 integers between X and Y - no more, no less (and you should not overthink that information). When including that Fact, X=1 and Y=1,000,000 is NOT a possibility, since there are 999,998 integers between those two values - and that result does NOT match what you were told.

No GMAT questions are ever trying to 'trick' you. Data Sufficiency questions ARE designed to test you in a variety of ways though, including the 'thoroughness' of your thinking (as you probably noticed in Fact 1).

GMAT assassins aren't born, they're made,
Rich

aalobaidy wrote: Let me explain my problem;
X=1 and y=1000000 truly has 24 integers larger than x and smaller than y.
My wife says i am confused cuz am over complicating things.
Please advise.

[email protected] wrote:Fact 2 tells us that there are 24 integers between X and Y - no more, no less (and you should not overthink that information).