Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

(A) 7 (B) 6 (C) 5 (D) 4 (E) 3

General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.

The lowest number of pairs we can make from 7 individual socks is 3 pairs and one sock from a fourth pair. Hence, the greatest number of pairs of matched socks John can have left is 10 - 4 = 6.

Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]

Show Tags

11 Sep 2012, 09:28

2

This post received KUDOS

Since question is asking the Greatest number of pairs left after John loses 7 socks, it is better to count the socks in pairs.

In total 7 socks are lost, which can be counted as 3 pairs of socks (3x2) + 1 single socks. So in total 4 pairs are lost as 1 single sock can not be counted in a pair.

Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]

Show Tags

12 Sep 2012, 12:32

7

This post received KUDOS

2

This post was BOOKMARKED

John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left? (A) 7 (B) 6 (C) 5 (D) 4 (E) 3

Because we have to maximize the pair of matched socks, we will remove 3 pairs(6 socks) out of 10 pairs & 1 sock from the 4th pair. Thus the no of matching socks pair remaining = 10 -4 = 6 Answer B

If we were asked minimum no of pairs of matched socks, we would have removed all the 7 socks from 7 different pairs out of 10 pairs. Thus the no of matching socks pair remaining = 10 -7 = 3 Answer E

Hope it helps
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

(A) 7 (B) 6 (C) 5 (D) 4 (E) 3

General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.

The lowest number of pairs we can make from 7 individual socks is 3 pairs and one sock from a fourth pair. Hence, the greatest number of pairs of matched socks John can have left is 10 - 4 = 6.

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]

Show Tags

26 Nov 2012, 14:01

Hi there This might sound silly but when I read this question I initially drew out aa bb cc etc as his socks and crossed out one letter of each 7 pairs which left me with 3 pairs left, could someone explain how clearly this is a wrong approach? How do I know that his socks are all the same. Thank u

Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]

Show Tags

30 Jun 2015, 22:22

If he loses 7 socks, to maximise the number of pairs of matching socks we should assume that he lost 3 pairs of socks and 1 sock from a different pair, so that rules out 4 pairs. maximum possible pairs he is left with is 6.
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

(A) 7 (B) 6 (C) 5 (D) 4 (E) 3

Let’s label each pair of socks with letters.

AA = pair 1

BB = pair 2

CC = pair 3

DD = pair 4

EE = pair 5

FF = pair 6

GG = pair 7

HH = pair 8

JJ = pair 9

KK = pair 10

We are given that he loses 7 individual socks and need to find the greatest number of pairs of matched socks he can have left. Strategically, this means that if we lose one sock from a particular pair of socks, we also want to lose the other sock from that same pair. So, for instance, John could lose the following:

A, A, B, B, C, C, D

The pairs of socks John has left are as follows:

EE, FF, GG, HH, JJ, and KK.

Thus, the greatest number of pairs of matched socks John could have left is 6 pairs.

The answer is B.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]

Show Tags

28 Jul 2017, 07:57

I used the answer choices to help me get to the answer

A. 7 Pairs left. Means initially he has 7*2+7 = 21 Socks. Not possible, since he had total of 10 pairs (20 Socks) B. 6 Pairs left. Means initially he has 6*2+7 = 19 Socks. Possible.

Rest all options will decrease the pair of Socks. Since the MAX pair possible is asked, the right answer has to be B.
_________________