Last visit was: 14 May 2025, 22:56 It is currently 14 May 2025, 22:56
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
avatar
vmahi77
Joined: 30 Sep 2014
Last visit: 04 Dec 2017
Posts: 6
Own Kudos:
37
 [36]
Given Kudos: 3
Posts: 6
Kudos: 37
 [36]
5
Kudos
Add Kudos
31
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,791
Own Kudos:
12,365
 [15]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,791
Kudos: 12,365
 [15]
10
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
General Discussion
User avatar
vp101
Joined: 08 Aug 2015
Last visit: 04 May 2024
Posts: 47
Own Kudos:
Given Kudos: 73
Posts: 47
Kudos: 39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
rajarams
Joined: 31 Oct 2011
Last visit: 25 Nov 2020
Posts: 44
Own Kudos:
Given Kudos: 25
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE:Programming (Computer Software)
Products:
GMAT 1: 660 Q48 V32
Posts: 44
Kudos: 103
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,791
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,791
Kudos: 12,365
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
avatar
rajarams
Joined: 31 Oct 2011
Last visit: 25 Nov 2020
Posts: 44
Own Kudos:
Given Kudos: 25
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE:Programming (Computer Software)
Products:
GMAT 1: 660 Q48 V32
Posts: 44
Kudos: 103
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
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.
avatar
SriramK
Joined: 07 Jun 2015
Last visit: 11 Jun 2018
Posts: 5
Own Kudos:
Given Kudos: 24
Posts: 5
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Kritisood
Joined: 21 Feb 2017
Last visit: 19 Jul 2023
Posts: 497
Own Kudos:
Given Kudos: 1,091
Location: India
GMAT 1: 700 Q47 V39
Products:
GMAT 1: 700 Q47 V39
Posts: 497
Kudos: 1,194
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The common multipliers that are not less than 4 are 4,6,12
4 departments: 21, 45, 66
6 departments: 14, 30, 44
12 departments: 7, 15, 22

statement one gets rid of 12 departments option as 15 (refused tables)/ 11(remaining dept) is not an integer
statement two gets rid of 6 departments options as 45(refused sofas)/5(remaining dept) is not an integer

hence 4 departments is the answer ie c
User avatar
minustark
Joined: 14 Jul 2019
Last visit: 01 Apr 2021
Posts: 471
Own Kudos:
384
 [1]
Given Kudos: 52
Status:Student
Location: United States
Concentration: Accounting, Finance
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Products:
GMAT 1: 650 Q45 V35
Posts: 471
Kudos: 384
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vmahi77
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

From the stem, it can be inferred the company has at least 4 departments. Lets find the common multiples of the furniture.
Sofas: 84 = 4 * 21 = 4 * 3 * 7
Tables: 180 = 4 * 45 = 4 * 3* 3 * 5
Chairs: 264 = 4* 66 = 4 * 3 * 2* 11

Common multiples are: 4 and 12, so no of departments has to be either 4 or 12.

1) If the company has 4 departments, it can distribute 45 tables to each department. So, if one department refused the tables, the other 3 department can receive the remaining 45 tables. Again, if the company has 12 departments, the other 11 departments cannot divide the allotted 15 tables per department. So, the company has 4 departments. Sufficient.

2) If the co. has 4 departments, each will get 66 chairs, which can be divisible among the other 3 departments if one department refuses the chairs. If the co has 12 departments, the allotted chairs is 22, which can also be divisible among other 11 departments. Not sufficient.

A is the answer.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,791
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,791
Kudos: 12,365
Kudos
Add Kudos
Bookmarks
Bookmark this Post
minustark
vmahi77
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

From the stem, it can be inferred the company has at least 4 departments. Lets find the common multiples of the furniture.
Sofas: 84 = 4 * 21 = 4 * 3 * 7
Tables: 180 = 4 * 45 = 4 * 3* 3 * 5
Chairs: 264 = 4* 66 = 4 * 3 * 2* 11

Common multiples are: 4 and 12, so no of departments has to be either 4 or 12.

1) If the company has 4 departments, it can distribute 45 tables to each department. So, if one department refused the tables, the other 3 department can receive the remaining 45 tables. Again, if the company has 12 departments, the other 11 departments cannot divide the allotted 15 tables per department. So, the company has 4 departments. Sufficient.

2) If the co. has 4 departments, each will get 66 chairs, which can be divisible among the other 3 departments if one department refuses the chairs. If the co has 12 departments, the allotted chairs is 22, which can also be divisible among other 11 departments. Not sufficient.

A is the answer.

Hi minustark,

Most of your work here is perfect, BUT you missed one option - there could be 6 total departments (not just 4 or 12) and that impacts the answer to the question.

GMAT assassins aren't born, they're made,
Rich
avatar
GameFace
Joined: 22 Jun 2021
Last visit: 03 Mar 2022
Posts: 1
GMAT 1: 710 Q48 V39
GPA: 4
Products:
GMAT 1: 710 Q48 V39
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
Each department received the same set of furniture.
Therefore, the number of departments must be a common factor of 84 180, 264.

84=2*2*3*7
180=2*2*3*3*5
264=2*2*3*2*11

Therefore, the common prime factors are 2, 2 and 3.
Common factors are a combination of these, 2*2*3, 2*3, 2*2.
Hence, the common factors are 12, 6 and 4.

-------------------------

(1)
Quote:
One department refused the tables, and those tables were evenly distributed among the rest.
So the number of tables must be divisible by one of the common factors as well as the (common factor-1).

180 is divisible by 12, but not by 11, so 12 is out.
180 is divisible by 6 as well as by 5.
180 is divisible by 4 as well as by 3.


So the possible number of departments are 6 and 4.

Hence (1) is insufficient.

-------------------------

(2)
Quote:
One department refused the chairs, and those chairs were evenly distributed among the rest.
Following the same procedure as (1),

264 is divisible by 12 as well as by 11.
264 is divisible by 6, but not by 5, so 6 is out.
264 is divisible by 4 as well as by 3.

So the possible number of departments are 12 and 4.

Hence (2) is insufficient.

-------------------------

(1,2)
Based on (1), the possible number of departments are 6 and 4.
From (2), the possible number of departments are 12 and 4.

The common answer is 4.
Hence, the number of departments possible is 4.

Option C
User avatar
thakurarun85
Joined: 10 Jul 2021
Last visit: 21 Sep 2022
Posts: 225
Own Kudos:
51
 [1]
Given Kudos: 29
Posts: 225
Kudos: 51
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
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
the number of department can be 3 and 2 as well in such case S, T, C will be 28,60,88 and 42,90, 132. In such case the answer will be inconclusive which is E. Please correct me if I am wrong.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,791
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,791
Kudos: 12,365
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi thakurarun85,

The prompt tells us that the company has departments in 4 cities, so there cannot be just 2 or 3 departments (there has to be at least 4).

GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,856
Own Kudos:
Posts: 36,856
Kudos: 983
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Math Expert
101414 posts