Angela has 15 pairs of matched socks. If she loses 7 individual socks,

Question

Angela has 15 pairs of matched socks. If she loses 7 individual socks, which of the following is NOT a possible number of matched pairs she has left?

A. 8
B. 9
C. 10
D. 11
E. 12

Kudos for correct  solution .

ynk · Answer

I think if Angela loses 7 individual socks,then she is bound to have lost minimum of 3 pairs and 1 individual sock,in this way she is left with only 11 pairs of socks (15-(3+1)).

Hence,12 cannot be the answer as maximum is 11.

Hence, option (E)

TeamGMATIFY · Answer

We need to make different cases and then check for each option.
Case 1: All 7 socks lost are from different pair
Therefore number of pairs left = 8

Case 2: 1 pair lost and 5 from individual socks
Therefore number of pairs left = 9

Case 3: 2 pairs lost and 3 individual socks
Therefore number of pairs left = 10

Case 4: 3 pairs lost and 1 individual socks
Therefore number of pairs left = 11

Hence the number of pairs that is not possible is 12 Option E

BrentGMATPrepNow · Answer

We can also systematically eliminate 4 of the 5 answer choices.

Let's say the 15 PAIRS of socks are as follows:  AA, BB, CC, DD, EE, FF, GG, HH, II, JJ, KK, LL, MM, NN, OO

Let's first see what happens if we "lose"  7 unmatched socks . Say, we lose, A, B, C, D, E, F, G
We get: A, B, C, D, E, F, G,   HH, II, JJ, KK, LL, MM, NN, OO  
We have  8  pairs remaining. 
So, we can ELIMINATE A

Now let's see what happens if we "lose"  1 pair of matched socks and 5 unmatched socks . Say, we lose, AA, B, C, D, E, F
We get: B, C, D, E, F,   GG, HH, II, JJ, KK, LL, MM, NN, OO  
We have  9  pairs remaining. 
So, we can ELIMINATE B

Let's see what happens if we "lose"  2 pairs of matched socks and 3 unmatched socks . Say, we lose, AA, BB, C, D, E
We get: C, D, E,   FF, GG, HH, II, JJ, KK, LL, MM, NN, OO  
We have  10  pairs remaining. 
So, we can ELIMINATE C

Let's see what happens if we "lose"  3 pairs of matched socks and 1 unmatched sock . Say, we lose, AA, BB, CC, D
We get: D,   EE, FF, GG, HH, II, JJ, KK, LL, MM, NN, OO  
We have  11  pairs remaining. 
So, we can ELIMINATE D

By the process of elimination, the correct answer is E

Cheers,
Brent

TheNightKing · Answer

If they are all of different color then she will have 7 pairs left. That's the min.

If they are all of the same color then she will have 11 pairs left. That's the max.

So 12 is not possible.

Option E.

Adarsh_24 · Answer

30-2*12=6
We need at least 7. So 12 is the answer.

Angela has 15 pairs of matched socks. If she loses 7 individual socks,

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Angela has 15 pairs of matched socks. If she loses 7 individual socks,

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