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
Answer: E
Source: Veritas Prep
Angela has 15 pairs of matched socks. If she loses 7 individual socks, which of the following is NOT a possible number
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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