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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]

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11 Sep 2012, 09:28

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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.

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12 Sep 2012, 12:32

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

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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

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30 Jun 2015, 12:58

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

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

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27 May 2016, 07:19

Bunuel wrote:

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.
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Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

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Re: John has 10 pairs of matched socks. If he loses 7 individual
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27 May 2016, 07:19

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