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18 Nov 2015, 02:04
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
42% (02:50) correct
58%
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wrong
based on 267
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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
(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
18 Nov 2015, 15:48
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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
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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
Final Answer:
GMAT assassins aren't born, they're made,
Rich
General Discussion
18 Nov 2015, 04:00
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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?
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?
