Each of the marbles in a jar is either red or white or blue. If one…

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Last Updated on May 10, 2023

GMAT OFFICIAL GUIDE DS

Solution:

We are given that there are red, white, and blue marbles in a jar. Thus, we can create the following probability equation:

P(red) + P(white) + P(blue) = 1

We must determine the probability of selecting a blue marble. Isolating P(blue) in the above equation, we have:

P(blue) = 1 – [P(red) + P(white)]

Thus, if we can determine the probability of selecting a red marble and the probability of selecting a white marble, we can determine the probability of selecting a blue marble.

Statement One Alone: 

There are a total of 24 marbles in the jar, 8 of which are red.

Using the information in statement one, we can determine that P(red) = 8/24 = 1/3.  However, we cannot determine the probability of selecting a blue marble since we still don’t know the probability of selecting a white marble. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone: 

The probability that the marble selected will be white is 1/2.

Statement two alone provides no information about the probability of selecting a red marble. We can eliminate answer choice B.

Statements One and Two Together: 

Using the information from our two statements, we know that:

P(red) = 1/3 and P(white) = 1/2. Thus, we can determine the probability of selecting a red marble. Although we know the answer will be C, we can complete the problem as follows:

P(blue) = 1 – [P(red) + P(white)]

P(blue) = 1 – [1/3 + 1/2]

P(blue) = 1 – 5/6

P(blue) = 1/6

Answer: C 

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