Question from Score800:

[Jeanette]

1. A jar has 10 marbles, a combination of black and white. 2 marbles are randomly chosen from the jar. If q is the probability that both will be black, is q > 1/3?

(1) Less than 1/2 of the marbles in the jar are white.
(2) The probability that 1 white marble and 1 black marble will be chosen together is 7/15.


(A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(D) Either statement BY ITSELF is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

For condition 1, if there are 6 black and 4 white, then the probability of drawing 2 blacks is exactly 1/3: 6/10*5/9. If there are more than 6 black, then the probability is greater than 1/3. So condition 1 alone is not sufficient to answer if the probability is >1/3.

Now, regarding condition 2, there are 10x9 possible combinations for drawing 2 out of 10 marbles. If there are 5+5, then there are 5x4 possibilities for 2 black and 5x4 combinations for both white, which leaves a 50/90 probability of a black and white. If there is a 4-6 split, then there are 6x5 combos for 2 of one and 4x3 combos for 2 of the other, which leaves 48/90 possibilities for one of each. If there is a 7-3 split, then there are 7x6 possibilities for 2 of one and 3x2 combos for 2 of the other, which leaves 42/90 possibilities for one of each, or 7/15. However, we still don't know if there are 7 white and 3 black, or 3 white and 7 black. For that we need condition 1. So the answer is that both conditions are necessary to determine if the probability of 2 blacks is 1/3.

Okay, I figured this out after a 1/2 hour of work, but obviously there is no such time on the actual test to figure it out. What would you suggest as a shortcut? (Has anyone ever seen such a question on a real GRE?)

[Goldust]

I think that such questions appear on the GMAT, not on the GRE.

[econ_phd_2009]

yep , this type of problems are encounted in GMAT under the DATA sufficiency part.

[Jeanette]

Oh. It was in the GRE section of score800. I find that score800 often has question types mixed in that don't belong on the GRE. It must be a bug in their system.