Data Sufficiency

jjjinapinch wrote:Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that the marble will be blue?

(1) There are a total of 24 marbles in the jar, 8 of which are red.
(2) The probability that the marble selected will be white is 1/2.

Official Guide question
Answer: C

If we know how many red, white and blue marbles are there in the jar, we can get the probability that the marble will be blue upon drawing a marble.

OR

If we know how many blue marbles and the total number of marbles are there in the jar, we can get the probability that the marble will be blue upon drawing a marble.

OR

If we know how many red and white marbles and the total number of marbles are there in the jar, we can get the probability that the marble will be blue upon drawing a marble.

Statement 1: There are a total of 24 marbles in the jar, 8 of which are red.

This means that there are 24 - 8 = 16 white and blue marbles; however, we do not know the number of blue marbles. Insufficient.

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

Certainly not sufficient as we do not know the number of blue marbles.

Statement 1 & 2:

Say there are b numbers of blue marbles, thus the number of white marbles = 16 - b

=> The probability that the marble selected will be white = (16 - b) / 24 = 1/2

16 - b = 12

b = 4

The probability that the marble selected will be blue = 4/14 = 1/6. Sufficient.

The correct answer: C

Hope this helps!

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Hi All,

We're told that each of the marbles in a jar is either red or white or blue and that one marble is to be selected at random from the jar. We're asked for the probability that the marble will be blue. To answer this question, we either need the exact number of total marbles and blue marbles OR a ratio that defines the number of blue marbles to the total.

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

With the information in Fact 1, we know that 24 - 8 = 16 of the 24 marbles are blue OR white, but we don't know exactly how many blue marbles there are - so the answer to the question could be different probabilities.
Fact 1 is INSUFFICIENT

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

With the information in Fact 2, we know that 1/2 of the total marbles are blue OR red, but we don't know what fraction the blue marbles represent - so the answer to the question could be different probabilities.
Fact 2 is INSUFFICIENT

Combined, we know:
-There are 24 total marbles
-8 marbles are red
-Half of the marbles are white --> (1/2)(24) = 12 white marbles
Thus, we CAN determine the number of blue marbles (24 - 8 - 12 = 4 blue marbles) and we can answer the question (4/24 = 1/6).
Combined, SUFFICIENT

Final Answer: C

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

jjjinapinch wrote: ↑

Mon Jul 24, 2017 9:24 am

Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that the marble will be blue?

(1) There are a total of 24 marbles in the jar, 8 of which are red.
(2) The probability that the marble selected will be white is 1/2.

Official Guide question
Answer: C

Solution:

Question Stem Analysis:

We need to determine the probability of selecting a blue marble at random, given that the jar has red, white, and blue marbles.

Statement One Alone:

From statement one, we see that 24 - 8 = 16 marbles are either blue or white. However, since we can’t determine the number of blue marbles, we can’t determine the probability of selecting a blue marble. Statement one alone is not sufficient.

Statement Two Alone:

From statement two, we see that the probability of selecting a white marble is 1/2. However, since we can’t determine the number of blue marbles, we can’t determine the probability of selecting a blue marble. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that, of the total 24 marbles, 8 of them are red and ½ x 24 = 12 of them are white. Therefore, there must be 24 - 8 - 12 = 4 blue marbles. Hence, the probability of selecting a blue marble at random is 4/24 = 1/6. Both statements together are sufficient.

Answer: C