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M07-09

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M07-09 [#permalink]

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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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Re M07-09 [#permalink]

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New post 15 Sep 2014, 23:34
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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.


Answer: C
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M07-09 [#permalink]

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New post 09 Mar 2017, 15:20
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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
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Re M07-09 [#permalink]

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New post 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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