Apr 20 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Apr 20 10:00 PM PDT  11:00 PM PDT The Easter Bunny brings … the first day of school?? Yes! Now is the time to start studying for the GMAT if you’re planning to apply to Round 1 of fall MBA programs. Get a special discount with the Easter sale! Apr 21 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Apr 21 10:00 PM PDT  11:00 PM PDT $84 + an extra $10 off for the first month of EMPOWERgmat access. Train to be ready for Round 3 Deadlines with EMPOWERgmat's Score Booster. Ends April 21st Code: GCENHANCED Apr 22 08:00 AM PDT  09:00 AM PDT What people who reach the high 700's do differently? We're going to share insights, tips, and strategies from data we collected on over 50,000 students who used examPAL. Save your spot today! Apr 23 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, April 23rd at 8 pm ET Apr 24 08:00 PM EDT  09:00 PM EDT Maximize Your Potential: 5 Steps to Getting Your Dream MBA Part 3 of 5: Key TestTaking Strategies for GMAT. Wednesday, April 24th at 8 pm ET Apr 27 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54372

A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
Show Tags
14 Mar 2019, 23:57
Question Stats:
41% (02:30) correct 59% (02:33) wrong based on 29 sessions
HideShow timer Statistics
TOUGH QUESTION: A drawer in a darkened room contains 100 red socks, 80 green socks, 60 blue socks and 40 black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at least 10 pairs? (A pair of socks is two socks of the same color. No sock may be counted in more than one pair). (A) 21 (B) 23 (C) 24 (D) 30 (E) 50
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Intern
Joined: 17 Sep 2018
Posts: 23

Re: A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
Show Tags
15 Mar 2019, 01:46
My logic may be wrong. Luckily the question asks for 10 pairs (and not 10 pairs of the same colour). We just need the one combination which might disprove an answer. We can consider each answer in turn applying pretty much the same logic (each letter represents the colour of the sock and Bl. represents black socks):
A. He can pick out 19Bl., 1R and 1G. That's 9.5 pairs and short of the 10 pairs. At this point the youngster may consider turning the lights on, looking at the socks he is picking out or asking for help. B. Same logic applies as above: 19Bl., 1R, 1G, 1B and the final one has to be any of Bl, B, R or G, making 10 pairs. It is necessary to think of mathematical counterarguments: he could've equally have picked out 5G, 5B, 5R, 8Bl giving 10 pairs! Other combos? 6G, 6B, 6R and 2Bl giving 10 pairs. What if the first few socks were all of different colours then 1G, 1R, 1B, 20 Bl. 10 Pairs. I think it help picking out the extremes. C. Again, same logic so as to test out the B. 1G, 1R, 1B and 21Bl works and at this point we probably would have exhausted most of our time on the question.



CEO
Joined: 18 Aug 2017
Posts: 3001
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
Show Tags
16 Mar 2019, 01:53
Bunuel wrote: TOUGH QUESTION: A drawer in a darkened room contains 100 red socks, 80 green socks, 60 blue socks and 40 black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at least 10 pairs? (A pair of socks is two socks of the same color. No sock may be counted in more than one pair). (A) 21 (B) 23 (C) 24 (D) 30 (E) 50 so as to get 1 pair of socks we would require to pick atleast 5 socks ;similarly to get 2 pairs of socks 7 socks are required to be removed for 3 pairs of socks 9 socks are required to be removed... if we observe there is a pattern of 2p+3 ; p is no of desired pairs ; so here p = 10 we get 23 IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Intern
Joined: 10 May 2018
Posts: 7

Re: A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
Show Tags
23 Mar 2019, 00:24
Can someone please provide a more detailed explanation to this one?



Intern
Joined: 11 May 2018
Posts: 18
Location: India

Re: A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
Show Tags
23 Mar 2019, 14:31
question asks for 10 pair of socks, 10 pairs irrespective of color (Red, Green, Black, and Blue).
trick here is to know for getting 1 pair we need 5 socks.
To get 1st pair we need atleast 5 socks > 2 of same color and 3 of different To get 2nd pair we need additional 2 socks > 3 (left out from previous selection) + 2 new socks To get 3rd pair we need additional 2 socks and so on.
For each pair we need additional 2 socks. After 1st pair we need 9 more pairs so total socks to be drawn = 5 + 2*9 = 23
Answer : B



Manager
Joined: 17 Jul 2016
Posts: 56

A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
Show Tags
23 Mar 2019, 20:08
These problems are about considering the worst case scenario.
How can I not get pairs?
The first four socks can be red, green, black, blue
They are also of the form ODD, ODD, ODD, ODD (1 of each)
The fifth sock has to form a pair. Let's assume we get a blue pair.
So now we have red, green, black, blue, blue,
and are of the form ODD, ODD, ODD, EVEN
How can I not get a pair on the 6th selection? I have to get a blue (there was an even number so adding one won't form a pair)
So now we have red, green, black, blue, blue, blue. We are back to ODD, ODD, ODD, ODD
No matter what I get on the 7 selection it will form a pair and the form will be
ODD, ODD, ODD, EVEN
To maintain this "worst case scenario" the 8th selection must be of the same color as the 7th (be the even one).
The 9th must necessarily form another pair.
So (x,y) represent (pairs, selections).
(1,5) (2,7) (3,9)....(10,y)
We can great an equation y=2x+3. Substituting 10 for x we obtain 23.




A drawer in a darkened room contains 100 red socks, 80 green socks, 60
[#permalink]
23 Mar 2019, 20:08






