probability or combinatrics not sure

Expert replies

pritam.ryders: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sun Dec 04, 2011 9:51 pm; Location: bangalore

by pritam.ryders » Tue Aug 06, 2013 12:44 am

24 each grey and white colour hand gloves are mixed up in a drawer.
What's the minimum number of gloves you need to take out (blindly) to be sure of having a matching pair

Like this post

Source: Beat The GMAT — Problem Solving | Tue Aug 06, 2013 12:44 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 06, 2013 5:46 am

pritam.ryders wrote:24 each grey and white colour hand gloves are mixed up in a drawer.
What's the minimum number of gloves you need to take out (blindly) to be sure of having a matching pair

To begin, if you take out 2 socks, there's a chance that you will have 1 white sock and 1 gray sock.
However, once you take out the 3rd sock, it will be either white or gray, so you can be certain that you will have a matching pair.

Answer: 3

Note: This is neither a counting question nor a probability question. It uses something called the Pigeonhole Principle.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Aug 06, 2013 11:03 am

Hi pritam.ryders,

There's a detail worth noting in this question. Since the question is NOT a probability/permutation/combination question, the starting number of grey gloves and white gloves is IRRELEVANT (as long as there are at least 2 of each color). There are only 2 colors, so you would have to grab 3 gloves to GUARANTEE a matching pair.

With that same idea in mind, if there were 3 different colors, how many gloves would you need to pull to GUARANTEE a matching pair?

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

mikepamlyla: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Jul 01, 2013 4:42 pm

by mikepamlyla » Tue Aug 06, 2013 4:29 pm

Rich,

If there were 3 colors, then here is the logic:

It would take at least 3 attempts to make sure a matching pair was picked with 2 colors. For 3 colors, it would take a min of 4 attempts to get a matching pair. The question did not ask for a specific color, but just a match of ay color.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Aug 06, 2013 4:32 pm

Hi mikepamlyla,

That is absolutely CORRECT. Nicely reasoned.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Wed Sep 11, 2013 1:49 am

in my opinion Max is 25(if it would have asked), but not sure about min explanation

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Sep 11, 2013 1:27 pm

Hi vipulgoyal,

This is more of a logic question than a math question:

Think of it like this: the goal is to have a matching pair of socks.

1st sock: either gray or white (it doesn't matter)
2nd sock: If it's the same color as the first, then you have a matching pair, but there's no guarantee that it will match (it might be the other color)

Now, if you have 1 gray and 1 white, then then the 3rd sock is GUARANTEED to match one or the other.

This is the MINIMUM number of socks that must be pulled to guarantee a matching pair.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review