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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## OG2015 PS John has 10 pairs ##### This topic has 3 expert replies and 0 member replies ## OG2015 PS John has 10 pairs 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 OA: B Could someone please explain what is the right approach to this problem? Thanks! ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 lionsshare 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 OA: B Could someone please explain what is the right approach to this problem? Thanks! Make a little visual to help conceptualize what's going on here. We have ten pairs of socks, Let's designate them with letters: AA, BB, CC ...JJ I we lose 7 socks and we want to have the greatest number of pairs remaining, we'd rather lose paired socks, right? (If we lost A, B, C, D, E, F, and G, we'd only have three pairs remaining.) If we lost AA, BB, CC, and D, We'd still have six pairs left. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

GMAT Instructor
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lionsshare 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

OA: B

Could someone please explain what is the right approach to this problem? Thanks!
If John is lucky, he would wish that he lost the greatest number of paired socks out of 7 pairs. Out of these, we can have at the max. 3 pairs (3*2 = 6) and the 7th individual sock is left. It is obvious that the 4th pair is also useless for John.

So, the maximum number of paired sock John has is 6.

Hope this helps!

-Jay
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### GMAT/MBA Expert

GMAT Instructor
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lionsshare 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
Letâ€™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.

Alternate solution:

Since we want to determine the greatest number of pairs of matched socks John can have left, we can assume he loses the least number of pairs of matched socks. Since he loses 7 socks, we can assume that he loses 3 pairs of matched socks plus 1 sock from a 4th pair. Thus he can have a maximum of 6 pairs of matched socks remaining.

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jeff@targettestprep.com

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