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A box contains 18 red socks, 16 green socks, and 12 blue socks. What i 06 Jul 2022, 02:05
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95% (hard)

Question Stats:

48% (02:33) correct 52% (01:53) wrong based on 135 sessions

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A box contains 18 red socks, 16 green socks, and 12 blue socks. What is the least number of socks that must be selected to guarantee that the selections contain at least 5 pairs of socks? (A pair of socks is two socks of the same color)

(A) 11
(B) 12
(C) 13
(D) 15
(E) 17­
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B
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A box contains 18 red socks, 16 green socks, and 12 blue socks. What i 10 Jul 2022, 06:44
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A box contains 18 red socks, 16 green socks, and 12 blue socks. What is the least number of socks that must be selected to guarantee that the selections contain at least 5 pairs of socks? (A pair of socks is two socks of the same color)

(A) 11

(B) 12

(C) 13

(D) 15

(E) 17
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In order to end up with five pairs, we obviously need to have at least ten socks. But if we pick 10 socks, are we guaranteed to have five pairs? No, we could have four pairs and two mismatched socks.

What about 11? Now we could have four pairs and three mismatched socks.

If we add one more, it must pair with one of the three mismatched socks. That's 12.

Answer choice B.
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A box contains 18 red socks, 16 green socks, and 12 blue socks. What i 26 May 2024, 11:59
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Bunuel KarishmaB ScottTargetTestPrep MartyMurray TestPrepUnlimited

Hello Experts! Can not make sense of the wordings of the question nor the solution presented above. Please provide your solution for this question.

Thanks in advance!­
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A box contains 18 red socks, 16 green socks, and 12 blue socks. What i 26 May 2024, 12:24
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Feb2024
Bunuel KarishmaB ScottTargetTestPrep MartyMurray TestPrepUnlimited

Hello Experts! Can not make sense of the wordings of the question nor the solution presented above. Please provide your solution for this question.

Thanks in advance!­
Show more
­A box contains 18 red socks, 16 green socks, and 12 blue socks. What is the least number of socks that must be selected to guarantee that the selections contain at least 5 pairs of socks? (A pair of socks is two socks of the same color)

(A) 11
(B) 12
(C) 13
(D) 15
(E) 17­

To guarantee that we have at least 5 pairs of socks of the same color, we need to consider the worst-case scenario. What is the maximum number of socks we can have without having 5 pairs of socks?

We could pick 4 pairs of socks, which is a total of 8 socks. Then, since there are three different colors of socks, we can pick 1 sock from each color, making a total of 11 socks. At this point, we still do not have 5 pairs of socks of the same color. However, the next sock, regardless of its color, would complete a pair, giving us 5 pairs of socks.

So, the least number of socks that must be selected to guarantee that the selection contains at least 5 pairs of socks is 12.

For example, we could have 4 pairs of red socks (8 red socks), 1 individual red sock, 1 green sock, and 1 blue sock, making a total of 11 socks. The next sock, regardless of its color, would complete a pair, ensuring we have 5 pairs of socks.

Answer: B.

To understand the concept better, check other Worst Case Scenario Questions from our Special Questions Directory for additional practice.
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