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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,  [#permalink]

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New post 17 Feb 2016, 03:46
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

88% (01:17) correct 12% (00:54) wrong based on 74 sessions

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Manager
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Joined: 18 Aug 2013
Posts: 124
Location: India
Concentration: Operations, Entrepreneurship
GMAT 1: 640 Q48 V28
GPA: 3.92
WE: Operations (Transportation)
Re: Angela has 15 pairs of matched socks. If she loses 7 individual socks,  [#permalink]

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New post 20 Feb 2016, 05:07
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)
Senior Manager
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Angela has 15 pairs of matched socks. If she loses 7 individual socks,  [#permalink]

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New post 23 Feb 2016, 03:07
Bunuel 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


Kudos for correct solution.

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
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Re: Angela has 15 pairs of matched socks. If she loses 7 individual socks,  [#permalink]

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New post 25 Feb 2018, 17:26
Top Contributor
Bunuel 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

Kudos for correct solution.


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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Re: Angela has 15 pairs of matched socks. If she loses 7 individual socks,   [#permalink] 25 Feb 2018, 17:26
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