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Agela has 15 pairs of matched socks. If she loses 7...

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by AAPL » Sun Feb 25, 2018 10:39 am
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

The OA is E.

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.

Can any experts help me, please? Thank in advance!
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by DavidG@VeritasPrep » Sun Feb 25, 2018 11:07 am
AAPL wrote: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

The OA is E.

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.

Can any experts help me, please? Thank in advance!
You could also think about it like this:
She starts with 15 pairs, or 15*2 = 30 socks.
She loses 7 leaving her with 23 socks.
In order to have 12 pairs, she'd have to have 12*2 = 24 socks. But she's only got 23!. So the answer is E
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by Brent@GMATPrepNow » Sun Feb 25, 2018 4:25 pm
AAPL wrote: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
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
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by GMATGuruNY » Mon Feb 26, 2018 3:15 am
AAPL wrote: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
15 matched pairs = 30 socks.

E: 12
If Angela has 12 matched pairs left -- for a total of 24 socks -- then the number of socks lost = 30-24 = 6.
Not viable, since Angela must lose 7 socks.

The correct answer is E.
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by GMATGuruNY » Mon Feb 26, 2018 3:16 am
GMATGuruNY wrote:
AAPL wrote: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
When the prompt includes the phrase which of the following, the correct answer is likely to be D or E.
15 matched pairs = 30 socks.

E: 12
If Angela has 12 matched pairs left -- for a total of 24 socks -- then the number of socks lost = 30-24 = 6.
Not viable, since Angela must lose 7 socks.

The correct answer is E.
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