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# M07-09

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Math Expert
Joined: 02 Sep 2009
Posts: 43894

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15 Sep 2014, 23:34
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Difficulty:

15% (low)

Question Stats:

80% (01:26) correct 20% (01:27) wrong based on 97 sessions

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A conference room is equipped with a total of 45 leather and upholstered chairs. If there are a total of 14 reclining chairs and 20% of the leather chairs are reclining, but 10 of the reclining chairs are upholstered, how many upholstered chairs are non-reclining?

A. 31
B. 25
C. 15
D. 14
E. 10
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43894

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15 Sep 2014, 23:34
Expert's post
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Official Solution:

A conference room is equipped with a total of 45 leather and upholstered chairs. If there are a total of 14 reclining chairs and 20% of the leather chairs are reclining, but 10 of the reclining chairs are upholstered, how many upholstered chairs are non-reclining?

A. 31
B. 25
C. 15
D. 14
E. 10

Solution 1: Table:
CHAIRS Leather Upholstered Total Reclining 0.2X 10 14 Non-reclining ? Total X 45
Now try to fill in the missing areas in the table: we can determine that $$0.2X = 4$$, and $$X = 20$$.

Total non-reclining chairs = $$45 - 14 = 31$$. Leather non-reclining chairs = $$20 - 4 = 16$$. Therefore non-reclining upholstered chairs = $$31 - 16 = 15$$.

Solution 2: Equations

We know that there are 45 chairs total. The number of reclining chairs is 14 including both leather and upholstered chairs. Let $$L$$ denote the number of the leather chairs. Given that 10 of the reclining chairs are upholstered, and 20% of the leather chairs are reclining, we can form an equation: $$10 + 0.2*L = 14$$, $$L = 20$$. Thus, the number of upholstered chairs is $$45 - 20 = 25$$. Out of these 25 upholstered chairs, 10 chairs are reclining. Therefore, $$25 - 10 = 15$$ are non-reclining.

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Joined: 23 Nov 2016
Posts: 76
Location: United States (MN)
GMAT 1: 760 Q50 V42
GPA: 3.51

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09 Mar 2017, 15:20
2
KUDOS
Not a fan of this question. Leather and upholstery are not exclusive; you can have chairs that are upholstered with leather, fabric, or many other materials. For this reason I used a Venn diagram with three circles, in which case you can't find the answer.

Please clarify that the upholstery is not leather in this question.

https://www.merriam-webster.com/diction ... %20leather
https://en.wikipedia.org/wiki/Upholstery
Intern
Joined: 19 Jun 2017
Posts: 11

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08 Sep 2017, 12:23
I think this is a poor-quality question and I agree with explanation. Note that "upholstered" is not the logical opposite of "leather," thus, the answer depends on making this assumption, which should never be the case.
Re M07-09   [#permalink] 08 Sep 2017, 12:23
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# M07-09

Moderators: chetan2u, Bunuel

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