BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

probability or combinatrics not sure

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
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
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
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]
Image
Top
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.
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
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]
Image
Top
Master | Next Rank: 500 Posts
Posts: 468
Joined: Mon Jul 25, 2011 10:20 pm
Thanked: 29 times
Followed by:4 members

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
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
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]
Image
Top
Post new topic Post Reply
• Page 1 of 1