## Worst case Scenario Problem

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### Worst case Scenario Problem

by Sak32 » Wed Nov 06, 2013 2:26 am
You have 10 pairs of socks, 5 black pairs and 5 blue pairs, but they are not paired up. Instead, they are all mixed up in a drawer. Its early in the morning and you don't want to turn on the lights in your dark room.
1) How many socks must you pull out to garantee that you have a pair of one color?
2) How many must you pull out to have two good pairs (Each pair is the same color)?

The answer for 1) is 3 and for 2) its 5.

Why isn't 2 for 1) and 4 for 2) instead?

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by ganeshrkamath » Wed Nov 06, 2013 2:47 am
Sak32 wrote:You have 10 pairs of socks, 5 black pairs and 5 blue pairs, but they are not paired up. Instead, they are all mixed up in a drawer. Its early in the morning and you don't want to turn on the lights in your dark room.
1) How many socks must you pull out to garantee that you have a pair of one color?
2) How many must you pull out to have two good pairs (Each pair is the same color)?

The answer for 1) is 3 and for 2) its 5.

Why isn't 2 for 1) and 4 for 2) instead?
1) You pick one color, say black, first and another, say blue, in the second try. Now the third sock you pull out has two be either black or blue. Hence, to guarantee that you have a pair of one color, you have to pull out at least 3 socks.

2) First, you pull out black.
Second, you pull out blue.
Thrid, you pull out black. (one pair complete)
Fourth, you pull out black.
Fifth, you pull out either. (two pairs complete)
So, to guarantee two pairs of the same color, you have to pull out at least 5 socks.

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by Patrick_GMATFix » Wed Nov 06, 2013 7:44 am
Doesn't sound like it could be an official GMAT Q because
1) question doesn't specify whether a sock can go on either foot. If LEFT and RIGHT feet's socks are different, then I could pull out 10 socks (say all left footed socks) without completing a pair)

2) second question is ambiguous as well. Does it mean "what is the least # you must pull to have two good pairs?" or "what # must you pull to guarantee that you have two good pairs (similar to Q.1)?

Anyway, problem is best solved with brute-force because the items, the selections, and the possible outcomes of each pick are few in number.