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There are 30 socks in a drawer. Sixty percent of the socks are red, an

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There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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New post 26 Feb 2011, 11:41
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Question Stats:

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There are 30 socks in a drawer. Sixty percent of the socks are red, and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least 2 blue socks have been chosen?

(A) 2
(B) 3
(C) 14
(D) 19
(E) 20
[Reveal] Spoiler: OA
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Re: There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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New post 26 Feb 2011, 13:16
Since the drawer has 18 red and 12 blue socks, taking a minimum of 20 out would ensure that there are at least 2 blue socks. Answer E.
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Re: There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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New post 26 Feb 2011, 15:00
Hello, Madelaine!

This is actually not a probability problem. Instead, it is an optimization problem, a minor type of question on GMAT.

Your first step is to calculate 60% of 30, which yields 18. Now, you must be sure you picked at least 2 blue socks. The only way is to pick all the other socks plus 2 blue socks. In this case, you would have to pick 18 red socks plus the 2 blue ones. Hence, answer is 20. If you had 4 green, 6 yellow and 8 red socks, the answer would be the same. You would have to pick all of those pluse 2 blue ones.

Hope it helps!

If you liked that, please Kudos me! :D
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There are 30 socks in a drawer. 60% of the socks are red and the... [#permalink]

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New post 16 Aug 2016, 06:51
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There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?

A) 2
B) 3
C) 14
D) 16
E) 20

Please explain in detail your answer so that everyone can follow it.
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Re: There are 30 socks in a drawer. 60% of the socks are red and the... [#permalink]

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New post 16 Aug 2016, 07:03
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EBITDA wrote:
There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?

A) 2
B) 3
C) 14
D) 16
E) 20

Please explain in detail your answer so that everyone can follow it.


60% of 30 = 18.
So, there are 18 red socks and there are 12 blue socks.

Check out this possible cases once we have selected TWO socks:
case a: 2 red socks, in which case we have a pair of matching socks. DONE!
case b: 2 blue socks, in which case we have a pair of matching socks. DONE!
case c: 1 red sock and 1 blue sock. No matching socks, so we're not done yet.

Since the first 2 cases result in a pair of matching socks, let's focus on case 3 and what happens when we select a 3rd sock.
If we have 1 red sock and 1 blue sock, then the next sock we select will EITHER match the red sock OR match the blue sock.
In both cases, we are guaranteed to have a pair of matching socks.

So, selecting 3 socks guarantees that we have a pair of matching socks.

Answer:
[Reveal] Spoiler:
B

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There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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Re: There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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New post 31 Oct 2017, 09:55
Bunuel wrote:
There are 30 socks in a drawer. Sixty percent of the socks are red, and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least 2 blue socks have been chosen?

(A) 2
(B) 3
(C) 14
(D) 19
(E) 20


red socks : 18
at least blue required :2
minimum number of socks to be taken from the drawer without looking in order to be certain that at least 2 blue socks have been chosen would be 20

IMO E
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Re: There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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New post 02 Nov 2017, 16:04
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Bunuel wrote:
There are 30 socks in a drawer. Sixty percent of the socks are red, and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least 2 blue socks have been chosen?

(A) 2
(B) 3
(C) 14
(D) 19
(E) 20


Since 60% of the 30 socks are red, there are 0.6 x 30 = 18 red socks. Assume the worst case scenario; that is, we draw all 18 red socks without looking. Then, if we draw two more socks, we are guaranteed to have at least 2 blue socks. So, at least 20 socks must be drawn to ensure that two blue socks have been chosen.

Answer: E
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Re: There are 30 socks in a drawer. 60% of the socks are red and the... [#permalink]

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New post 04 Dec 2017, 09:22
EBITDA wrote:
There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least two socks of the same colour have been chosen?

A) 2
B) 3
C) 14
D) 16
E) 20

Please explain in detail your answer so that everyone can follow it.




Hi...

Here 30 pair of socks, 60% of one colour etc are DATAS which are not required.

You have 2 colour socks.
To be sure that you have picked atleast 2 of same colour, you require to pick three..
Either all 3 will be of same colour OR 2 of one colour and third of second colour..

Ans B
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Re: There are 30 socks in a drawer. Sixty percent of the socks are red, an [#permalink]

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New post 17 Dec 2017, 08:42
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Madelaine88 wrote:
There are 30 socks in a drawer. Sixty percent of the socks are red, and the rest are blue. What`s the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least 2 blue socks have been chosen?

A - 2
B - 3
C - 14
D - 19
E - 20



Lets make it a little tricky.

There are 30 pairs of socks in a drawer. Sixty percent of those are red, and the rest are blue. What`s the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least 1 pair of blue socks have been chosen?
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Re: There are 30 socks in a drawer. Sixty percent of the socks are red, an   [#permalink] 17 Dec 2017, 08:42
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