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Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]
11 Sep 2012, 03:42

Expert's post

1

This post was BOOKMARKED

SOLUTION

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]
11 Sep 2012, 08:28

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]
12 Sep 2012, 11:32

5

This post received KUDOS

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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Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]
14 Sep 2012, 04:50

1

This post received KUDOS

Expert's post

SOLUTION

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]
26 Nov 2012, 13:01

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]
30 Jun 2015, 11:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: John has 10 pairs of matched socks. If he loses 7 individual [#permalink]
30 Jun 2015, 21:22

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
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30 Jun 2015, 21:22

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