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OG2015 PS John has 10 pairs

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OG2015 PS John has 10 pairs

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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!

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Post
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

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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.

The correct answer: B

Hope this helps!

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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
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

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