Problem Solving

BTGmoderatorDC 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

OA E

Source: Veritas Prep

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

BTGmoderatorDC 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

If Angela loses 7 socks such that each is from a distinct pair of matched socks, then the other 7 socks that are left from these pairs of matched socks would not form a pair. So, the number of pairs of matched socks left would be 8, which is the minimum number of pairs of matched socks left.

However, Angela could lose 7 socks such that 6 of those socks form 3 pairs of matched socks. Furthermore, the final lost sock would come from another pair of matched socks, and thus she would have lost 4 total pairs of matched socks. Therefore, 11 is the maximum number of pairs of matched socks that could be left, so 12 pairs of matched socks IS NOT possible.

Answer: E