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There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks

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There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks [#permalink]

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New post 09 Mar 2011, 08:15
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There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks in sock drawer. What is the least number of socks that you have to pull out to make sure that you will have a matching pair? (Assume that all the socks are identical except for the color)

(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
[Reveal] Spoiler: OA
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Re: There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks [#permalink]

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New post 09 Mar 2011, 08:37
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banksy wrote:
253. There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks in sock drawer. What is the least number of socks that you have to pull out to make sure that you will have a matching pair? (Assume that all the socks are identical except for the color)
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11




2 Blue socks, 4 white socks, 6 black socks and 8 red socks.

Question is asking what is the worst case scenario to get matching socks?

Since there are 4 colors, if you draw 4 socks, worst case scenario is you could still have 1 sock per color and not have a match.

Therefore, upon drawing the 5th sock, you will definitely have a match since the 5th sock will form a least a pair with the 1st 4

So 4+1 = 5

Ans: B
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Re: There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks [#permalink]

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Re: There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks [#permalink]

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New post 02 Jun 2017, 03:50
This type of question does not involve any calculation.
Just logic is required.
We ahve 4 different types of socks (Blue, White, Black, Red). In the worse case, you will draw each of 4 different colors in the 4 first drawals.
Then, the next drawal will definitely be one of those for color.

Answer is B
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Re: There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks [#permalink]

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New post 05 Jun 2017, 15:49
banksy wrote:
There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks in sock drawer. What is the least number of socks that you have to pull out to make sure that you will have a matching pair? (Assume that all the socks are identical except for the color)

(A) 3
(B) 5
(C) 7
(D) 9
(E) 11


We need to determine the fewest number of socks that we must pull to get a matching pair.

Pull one: blue

Pull two: white

Pull three: red

Pull four: black

We see that on the 5th pull, no matter what color sock is pulled, we’d have a matching pair.

Answer: B
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Re: There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks   [#permalink] 05 Jun 2017, 15:49
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