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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Jeffery Miller

Head of GMAT Instruction

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