Georgia, who lives in a cold area, has 13 pairs of matched g

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alanforde800Maximus: Master | Next Rank: 500 Posts; Posts: 187; Joined: Tue Sep 13, 2016 12:46 am

by alanforde800Maximus » Sun Oct 16, 2016 12:58 am

Georgia, who lives in a cold area, has 13 pairs of matched gloves in different patterns. If she loses 9 individual gloves, what is the greatest number of pairs of matched gloves she can have left?

a) 9
b) 8
c) 7
d) 6
e) 5

Please assist with above problem.

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Source: Beat The GMAT — Problem Solving | Sun Oct 16, 2016 12:58 am

melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sun Oct 16, 2016 3:22 am

Its easier to just draw two arrows as pairs and count manually.

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Sun Oct 16, 2016 5:46 am

total pair of gloves : 13
total gloves individual = 13*2 = 26
if 9 are removed then left with = 26-9 = 17
let there are max n pairs
we can have 2*n<17
n<8.5
n=8

Fiza Gupta

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Dec 15, 2016 4:11 am

alanforde800Maximus wrote:Georgia, who lives in a cold area, has 13 pairs of matched gloves in different patterns. If she loses 9 individual gloves, what is the greatest number of pairs of matched gloves she can have left?

a) 9
b) 8
c) 7
d) 6
e) 5

Please assist with above problem.

We want to get the maximum number of paired gloves with Georgia, so she needs to be lucky. She should wish that the gloves she lost were paired ones. Out of 9 individuals gloves, one can have only 4 paired set. The 9th individual glove's counterpart is also useless for Georgia, so for her 4 + 1 = 5 pairs are useless.

=> She can max have 13 - 5 = 8 paired gloves

OA: B

What is the question had been:

Georgia, who lives in a cold area, has 13 pairs of matched gloves in different patterns. If she loses 9 individual gloves, what is the least number of pairs of matched gloves she can have left?

Well, in that case, we assume that the none of the 9 individual gloves had a pair.

=> 9 pairs are useless => least number of pairs of matched gloves she can have left = 13 - 9 = 4

Hope this helps!

-Jay

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