In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue Jun 30, 2020 8:04 am

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In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Source: Magoosh

Source: Beat The GMAT — Problem Solving | Tue Jun 30, 2020 8:04 am

shekki: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Jun 30, 2020 11:41 am

Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If so

by shekki » Tue Jun 30, 2020 12:18 pm

it's an easy one. consider the worst case scenario, that everytime we pick a sock, it's a unique colour. so, it will happen for only the first 3 times. the first 3 socks picked can be of any random individual colour. however the 4th sock has to belong to one of the 3 colours as we dont have any other colour option. hence OA 4

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If so

by Brent@GMATPrepNow » Tue Jun 30, 2020 12:54 pm

VJesus12 wrote: ↑
Tue Jun 30, 2020 8:04 am
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Source: Magoosh

If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don't have a matching sock. So, we can select 3 socks WITHOUT having a matching pair.
However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected.

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If so

by Scott@TargetTestPrep » Thu Apr 22, 2021 10:23 am

VJesus12 wrote: ↑
Tue Jun 30, 2020 8:04 am
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Solution:

We can remove 1 black, 1 gray, and 1 orange sock first. The next sock selection of any color would ensure that at least one pair of socks of the same color has been removed.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If so

by Scott@TargetTestPrep » Thu Apr 22, 2021 10:29 am

VJesus12 wrote: ↑
Tue Jun 30, 2020 8:04 am
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

A. 4
B. 7
C. 9
D. 10
E. 11

[spoiler]OA=A[/spoiler]

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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