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
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.
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.
Answer:
B
