A jar contains exactly 100 marbles; each marble contains

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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue May 07, 2019 4:04 pm

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A jar contains exactly 100 marbles; each marble contains exactly 2 colors. Forty-three of the marbles are part-green and 21 of the marbles are part-red. If 3 marbles are to be selected at random, what is the probability that at least 2 of them contain no blue?

1) 61 of the marbles are part-orange.
2) 74 of the marbles are part-yellow.

The OA is C

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Tue May 07, 2019 4:04 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon May 13, 2019 4:54 am

If we have 100 marbles, and each marble is made up of 2 colours, we have 200 colours in total. Using either Statement alone, we haven't accounted for very many of the colours, so we could have quite a few half-blue marbles or we could have none, and our probability of picking half-blue marbles could be nonzero or zero. But using both Statements, we have accounted for 43+21+61+74 = 199 of the 200 colours. So we have either 0 half-blue marbles or 1 half-blue marble. In either case, if we pick two or more marbles, we'll never pick two half-blue marbles, and the probability the question is asking for must be zero.

So the answer is C.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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