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# A company has ordered 84 sofas, 180 tables,

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Intern
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A company has ordered 84 sofas, 180 tables,  [#permalink]

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18 Nov 2015, 01:04
2
9
00:00

Difficulty:

95% (hard)

Question Stats:

43% (03:15) correct 57% (02:30) wrong based on 149 sessions

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A company has ordered 84 sofas, 180 tables, and 264 chairs. It has departments in four cities. Each department received the same set of furniture. How many departments does the company have?

(1) One department refused the tables, and those tables were evenly distributed among the rest.

(2) One department refused the chairs, and those chairs were evenly distributed among the rest
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Re: A company has ordered 84 sofas, 180 tables,  [#permalink]

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18 Nov 2015, 14:48
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Hi vmahi77,

This is a "layered" DS question and far more involved than most DS questions that you'll see on Test Day. The 'key' to solving it is to figure out how many departments COULD exist and consider the resulting 'math' for each possibility.

We're told that a company has departments in 4 cities, so we know that there are AT LEAST 4 departments (although a city could have MORE than 1 department within it, so we have to consider that). We're told that each department received the SAME set of furniture, so we can use those furniture numbers to figure out the possible number of departments.

The fastest way to do that is to use prime factorization on the number of sofas, tables and chairs:

84 sofas = (2)(2)(3)(7)

180 tables = (2)(2)(3)(3)(5)

264 chairs = (2)(2)(2)(3)(11)

To figure out the number of departments that COULD exist, we have to pull out the common prime factors. Among the 3 sets, those are....

(2)(2)(3)

We know that there are at least 4 departments (2x2), but there could also be 6 departments (2x3) or 12 departments (2x2x3). The question asks how many departments there are, so the answer will be one of those 3 numbers. The issue is whether more than one possibility exists with each of the given Facts....

Fact 1: One department refused the tables, and those tables were evenly distributed among the rest.

With 4 departments, there would be 45 tables each. If 1 refused its 45 tables, then they would be evenly distributed among the other 3 departments. Thus, 4 is a possible answer.

With 6 departments, there would be 30 tables each. If 1 refused its 30 tables, then they would be evenly distributed among the other 5 departments. Thus, 6 is a possible answer.

With 12 departments, there would be 15 tables each. If 1 refused its 15 tables, then they would NOT be evenly distributed among the other 11 departments. Thus, 12 is NOT possible answer.
Fact 1 has 2 potential answers; Fact 1 is INSUFFICIENT

Fact 2: One department refused the chairs, and those chairs were evenly distributed among the rest.

With 4 departments, there would be 66 chairs each. If 1 refused its 66 chairs, then they would be evenly distributed among the other 3 departments. Thus, 4 is a possible answer.

With 6 departments, there would be 44 chairs each. If 1 refused its 44 chairs, then they would NOT be evenly distributed among the other 5 departments. Thus, 6 is NOT a possible answer.

With 12 departments, there would be 22 chairs each. If 1 refused its 22 chairs, then they would be evenly distributed among the other 11 departments. Thus, 12 is a possible answer.
Fact 2 has 2 potential answers; Fact 2 is INSUFFICIENT

Combined, we know...
There are 4 or 6 possible departments.
There are 4 or 12 possible departments.

Thus, there MUST be 4 departments.
Combined, SUFFICIENT

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##### General Discussion
Manager
Joined: 08 Aug 2015
Posts: 52
Re: A company has ordered 84 sofas, 180 tables,  [#permalink]

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18 Nov 2015, 03:00
I solved it this way. I'm sure it's not the perfect approach.

Look the two statements that are given - there's no way we can answer the question using only one of these statements. Hence, A, B and D cannot be the answer.

Now, consider both the statements together. What we can say is that if there's one less department that the number actually present, the chairs (264) and tables (180) can be equally divided. Now, if you look at numbers which divide both 264 and 180, there are a lot; I assumed 6 and 12 as a small sample set.

Hence, 7 and 13 can be the number of departments across the four cities. Now these can be distributed in any manner (We're not really concerned with that). Because more than one value can fit the situation, we cannot zone in on one absolute value. Hence, I marked 'E' as the answer.

Is my approach right? Anyone?
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Re: A company has ordered 84 sofas, 180 tables,  [#permalink]

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03 Oct 2016, 21:31
How is it okay to assume that the minimum number of departments is 4?

I could have the same department spread across multiple cities. Say, my sales team is across City A and city B and that I actually split the furniture across the two divisions of the same department in ways not mentioned in this question premise.
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Re: A company has ordered 84 sofas, 180 tables,  [#permalink]

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08 Oct 2016, 10:05
Hi rajarams,

You bring up an interesting point. To that end, if this question appeared on the Official GMAT, then the writers probably would have stated "there is at least one department in each of 4 cities" as a means to clarify the issue.

That having been said, your way of interpreting the question actually ignores a vital piece of information that you're given to work with. If a department could have been spread across two (or more) cities, then the number of cities would not matter. The result of that idea should have prompted you to rethink the way that you were interpreting the question.

GMAT assassins aren't born, they're made,
Rich
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A company has ordered 84 sofas, 180 tables,  [#permalink]

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08 Oct 2016, 10:27
EMPOWERgmatRichC wrote:
Hi rajarams,

You bring up an interesting point. To that end, if this question appeared on the Official GMAT, then the writers probably would have stated "there is at least one department in each of 4 cities" as a means to clarify the issue.

That having been said, your way of interpreting the question actually ignores a vital piece of information that you're given to work with. If a department could have been spread across two (or more) cities, then the number of cities would not matter. The result of that idea should have prompted you to rethink the way that you were interpreting the question.

GMAT assassins aren't born, they're made,
Rich

Yes. To be frank, I missed the minimum number of departments point when I marked E as the answer. But then when I looked up the solution, I was not sold on this. For the question, in its original form, I still think E is the right answer. I guess the question premise did not place a lot of emphasis on the cities connection so that it gets ignored by most test takers. If it were made clearer as you had suggested, it is no more as much of a trap question as the original one is.
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Re: A company has ordered 84 sofas, 180 tables,  [#permalink]

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08 Oct 2016, 23:28
This question has a flaw in itself in not mentioning the minimum number of departments each city can have.
Answer would be E since there's no information about the min no of departments. If this is the case, it can be 2,3,4,6,12( HCF). Answer would be C if the information has been given about the min no of departments in each city. In this case it will be 4.

Although the question might miss a few information, this is a very good one testing the concept of HCF.
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Re: A company has ordered 84 sofas, 180 tables,  [#permalink]

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08 Dec 2017, 02:15
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Re: A company has ordered 84 sofas, 180 tables, &nbs [#permalink] 08 Dec 2017, 02:15
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