John has 10 pairs of matched socks. If he loses 7 individual

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.

So, 10 - 4 = 6 pairs of socks.

B

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.

I'm thinking that if he has 10 pairs, that is 20 socks. If he loses 7 individual socks, then the greatest number of socks he could have left is:

20-7= 13 -> 6 pairs, since 13/2 is not an integer.

Hence, the answer is B.

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

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.

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.

I used the answer choices to help me get to the answer

A. 7 Pairs left. Means initially he has 7*2+7 = 21 Socks. Not possible, since he had total of 10 pairs (20 Socks)
B. 6 Pairs left. Means initially he has 6*2+7 = 19 Socks. Possible.

Rest all options will decrease the pair of Socks. Since the MAX pair possible is asked, the right answer has to be B.

Bunuel niks18 VeritasPrepKarishma

Is below approach correct:
Total no of socks: 20
No of socks lost: 7
No. of socks remaining: 13

Out of 13 socks, I can make only 6 matched pairs at max.

_____________________
Yes.

Individual socks lost = 7
3 pairs are lost and 1 socks but a pair is not completed with only 1 sock.
Hence, maximum number of pairs of matched socks he can have left = 10 - 4 = 6 pairs
So, Answer choice is (B).

I am just wondering if we can apply combinatorics here?

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