John Has 10 Pairs of Matched Socks. If He Loses 7 Individual Socks GMAT Problem Solving

Question: John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of the matched socks he can have left?

1. 7
2. 6
3. 5
4. 4
5. 3

“John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of the matched socks he can have left?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:
Approach Solution (1):

General rule for such kind of problems:
To maximize one quantity, minimize the other;
To minimize one quantity, maximize the other
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.

Correct option: B

Approach Solution (2):

Because we have to maximize the pair of matched socks, we will remove 3 pairs (6 socks) out of 10 pairs and 1 sock from the 4th pair.
Thus the no of matching socks pair remaining = 10 – 4 = 6

Correct option: B
If we were asked for the minimum no. of pairs of matched socks, we would have removed all the 7 socks from 7 different pairs out of the 10 pairs.
Thus the no. of matching socks pairs remaining = 10 – 7 = 3

Correct option: E

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