Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the

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Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3.
(2) The probability that the person will select a red card is 1/6.

Answer: E

Source: Official Guide

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Vincen wrote:
Wed Sep 15, 2021 8:38 am
Terry holds 12 cards, each of which is red, white, green, or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than 1/2 that the card selected will be either red or white?

(1) The probability that the person will select a blue card is 1/3.
(2) The probability that the person will select a red card is 1/6.

Answer: E

Source: Official Guide
Given: 12 cards - each card is red, white, green, or blue

Target question: Is the probability less than 1/2 that the card selected will be either red or white?
This is a good candidate for rephrasing the target question.
In order for P(selected card is red or white) < 1/2, it must be the case that there are fewer than 6 cards that are either red or white.
Let R = # of red cards in the deck
Let W = # of white cards in the deck
Let G = # of green cards in the deck
Let B = # of blue cards in the deck
REPHRASED target question: Is R + W < 6?

Statement 1: The probability that the person will select a blue card is 1/3
This tells us that B = 4 (since 4/12 = 1/3)
There are several CONFLICTING scenarios that satisfy statement 1. Here are two:
Case a: R = 2, W = 1, G = 5 and B = 4. In this case, R + W = 2 + 1 = 3. So, R + W < 6
Case b: R = 2, W = 6, G = 0 and B = 4. In this case, R + W = 2 + 6 = 8. So, R + W > 6
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The probability that the person will select a red card is 1/6
This tells us that R = 2 (since 2/12 = 1/6)
There are several CONFLICTING scenarios that satisfy statement 2. Here are two:
Case a: R = 2, W = 1, G = 5 and B = 4. In this case, R + W = 2 + 1 = 3. So, R + W < 6
Case b: R = 2, W = 6, G = 0 and B = 4. In this case, R + W = 2 + 6 = 8. So, R + W > 6
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E
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