Dear crazypriya,
I'm happy to help.

I don't know that there's a good way to do this other than plugging in one at at time. Let
N = total number of marbles.
If N = 7, then there's a 100% chance of picking two red marbles. That doesn't work.

If N = 10, then there's a 7/10 chance of getting red on the first pick, and 6/9 = 1/3 of getting red on the second pick. That's a (7/10)*(1/3) = 7/30 chance, which is approx. 23.33%. That doesn't work.

If N = 20, then there's a 7/20 chance of getting red on the first pick, and 6/19 of getting red on the second pick. That's a (7/20)*(6/19) = 21/190 chance, which is slightly more than 10 percent. That doesn't work.

If N = 21, then there's a 7/21 = 1/3 chance of getting red on the first pick, and 6/20 = 3/10 of getting red on the second pick. That's a (1/3)*(3/10) = 1/10, or 10% chance. This works.

I disagree with the order of answers given in the spoiler. The total number of marbles is 21, and the % probability that Jennifer wins is 10.

Does all this make sense?
Mike
_________________

Thanks Mike....
Yes u r correct. The total number of marbles is 21, and the % probability that Jennifer wins is 10.

Actually this plugging method was given in OE....so I was wondering if there is any better method to do this....

Dear crazypriya,
No, I don't think there's a better way. You see, there are two variables, and only one equation relating them. If we set it up with algebra, we would get a complicated equation that we couldn't solve anyway. The format itself demands plug-in approach.
Does this make sense?
Mike
_________________

is this question missing the other answer choices? # of marbles and % probability that Jennifer will win?

Dear se7en14,
This is a Two-Part Analysis question (2PA), one of the four question types on the GMAT's IR section. In 2PA questions, the same list of possible answers applies to both questions. Here, crazypriya posted the question in plaintext format, but on the GMAT it would be part of a chart, which would make the selection process slightly clearer.
See this for an explanation of the basis of 2PA:
http://magoosh.com/gmat/2012/integrated ... -analysis/
See this for 2PA practice questions:
http://magoosh.com/gmat/2013/gmat-integ ... questions/

Please let me know if you have any further questions.
Mike
_________________