Andy has 20 pairs of matched gloves. If he loses 11 individual gloves, which of the following is NOT a possible number o

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:19 am

Andy has 20 pairs of matched gloves. If he loses 11 individual gloves, which of the following is NOT a possible number of matched pairs he has left?

A. 9
B. 11
C. 13
D. 14
E. 15

Answer: e
Source: Veritas Prep

We're starting with a total of 40 gloves.
After losing 11 individual gloves, there are 29 gloves remaining

Since 15 PAIRS of gloves would require 30 individual gloves, we can see that it's impossible to have 15 PAIRS of gloves among the remaining 29 gloves.

Answer: E

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:19 am

Andy has 20 pairs of matched gloves. If he loses 11 individual gloves, which of the following is NOT a possible number of matched pairs he has left?

A. 9
B. 11
C. 13
D. 14
E. 15

Answer: e

Solution:

If all the 11 gloves he loses are from different matching pairs, then he has 20 - 11 = 9 pairs of matched gloves left. In other words, 9 is the minimum number of matched pairs he could have.

If 10 of the 11 gloves he loses are from 5 different matching pairs and the last glove is from the 6th pair of gloves, then he has 20 - 6 = 14 pairs of matched gloves left. In other words, 14 is the maximum number of matched pairs he could have.

Therefore, he could not have 15 matched pairs of gloves left.

Alternate Solution:

If Andy loses 11 gloves from his original 20 x 2 = 40 gloves, then he has 29 gloves remaining. We see that he could not have 15 pairs of gloves left (matching or not) because 15 pairs would require 30 gloves, and he has only 29 gloves.

Answer: E