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# M07-09

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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15 Sep 2014, 23:34
2
2
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:29) correct 20% (01:25) wrong based on 108 sessions

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

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

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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15 Sep 2014, 23:34
Official Solution:

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

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

Solution 1: Table:
CHAIRS metal wooden 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 = $$45 - 14 = 31$$. metal non-reclining chairs = $$20 - 4 = 16$$. Therefore non-reclining wooden chairs = $$31 - 16 = 15$$.

Solution 2: Equations

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

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Joined: 23 Nov 2016
Posts: 75
Location: United States (MN)
GMAT 1: 760 Q50 V42
GPA: 3.51

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09 Mar 2017, 15:20
2
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.
Intern
Joined: 02 Jan 2018
Posts: 26
Location: United Kingdom
GMAT 1: 740 Q50 V41
GPA: 3.7

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07 Jul 2018, 02:35
1
I think this is a poor-quality question and I agree with explanation. For a 500 level question, it's non obvious (without knowledge of chairs) that leather and uphostered are mutually exclusive.

Language could read "leather OR uphostered" which might help with clarity.
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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07 Jul 2018, 08:18
londonconsultant wrote:
I think this is a poor-quality question and I agree with explanation. For a 500 level question, it's non obvious (without knowledge of chairs) that leather and uphostered are mutually exclusive.

Language could read "leather OR uphostered" which might help with clarity.

Thank you. Edited the question. Hope now it's clear.
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Re: M07-09 &nbs [#permalink] 07 Jul 2018, 08:18
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# M07-09

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