Last visit was: 23 Apr 2024, 20:15 It is currently 23 Apr 2024, 20:15

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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 27 Sep 2010
Posts: 66
Own Kudos [?]: 314 [310]
Given Kudos: 20
Location: Kolkata, India
Schools:ISB, Terry MBA, University of Miami, HULT MBA, York University
Send PM
Most Helpful Reply
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64883 [92]
Given Kudos: 426
Location: Pune, India
Send PM
avatar
Senior Manager
Senior Manager
Joined: 26 Jul 2010
Posts: 294
Own Kudos [?]: 153 [35]
Given Kudos: 41
Location: European union
Send PM
General Discussion
avatar
Intern
Intern
Joined: 14 Nov 2010
Posts: 1
Own Kudos [?]: 4 [4]
Given Kudos: 0
Send PM
Re: Need Help to Understand [#permalink]
3
Kudos
1
Bookmarks
6:9:12 relate to each other just like 2:3:4 and you get 3 member of staff. That is why you cannot find out exactly how many members tehre are 9 or 3
avatar
Intern
Intern
Joined: 08 Nov 2012
Posts: 2
Own Kudos [?]: 4 [2]
Given Kudos: 1
Send PM
Re: A department manager distributed a number of pens, pencils, [#permalink]
2
Kudos
Answer to this question is E:

Start considering (2) ---> if the manager distributes a total of 18 pens, 27 pencils and 36 pads with each person receiving x pens, y pencils and z pads, means that the number of the staff has to be a factor of both 18,27 and 36. That value could be 3 or 9 --> Not sufficient

Now move to (1) ---> Clearly not sufficient as we do not have any information about the total number of persons or pens,pencils and pads distributed. We have just three ratios.

Considering Together ---> We know form (1) that the number of person should be 3 or 9. If people are 3 we have to distribute 18,27 and 36 --> 6pens, 9pencils, 12 pads for each person. If people are 9 we distribute 2 pens, 3 pencils, 4 pads. In both cases the ratio is the same 2:3:4. Hence not Sufficient.

Hope it's clear.

By the way AMAZING FORUM!
User avatar
Senior Manager
Senior Manager
Joined: 22 Jul 2012
Status:Gonna rock this time!!!
Posts: 356
Own Kudos [?]: 166 [0]
Given Kudos: 562
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE:Information Technology (Computer Software)
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
Karishma,

Thanks for your reply. I have the following doubt..

How do I learn to recognize that there can be multiple instances of sets who have the same ratio..

2:3:4 is the ratio of distribution.

18, 27 and 36 are the actuals distributed..

9 was the first no that came to my mind..

I then multiplied 2 to the ratio to get 4:6:8 and the actuals cannot be distributed in this ratio and I picked the answer to be sufficient...

had I multiplied the ratio by 3, I would have got 6:9:12 and I would have known that the answer is insufficient..

Please help me understand and learn thought process..
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64883 [7]
Given Kudos: 426
Location: Pune, India
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
6
Kudos
1
Bookmarks
Expert Reply
Sachin9 wrote:
Karishma,

Thanks for your reply. I have the following doubt..

How do I learn to recognize that there can be multiple instances of sets who have the same ratio..

2:3:4 is the ratio of distribution.

18, 27 and 36 are the actuals distributed..

9 was the first no that came to my mind..

I then multiplied 2 to the ratio to get 4:6:8 and the actuals cannot be distributed in this ratio and I picked the answer to be sufficient...

had I multiplied the ratio by 3, I would have got 6:9:12 and I would have known that the answer is insufficient..

Please help me understand and learn thought process..


When you saw 18, 27 and 36, what came to your mind was that the number of people could have been 9 which would mean that he gave 2 pens, 3 pencils and 4 pads. You know that 9 is divisible by 3. That should make you realize that the number of people could have been 3 too which would mean that the manager distributed 6 pens, 9 pencils and 12 pads. 9 does not have 2 as a factor so it will not work.
avatar
Intern
Intern
Joined: 25 Jun 2013
Posts: 4
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
I think answer is B. the explanation from the people considering the answer as E is missing the point that option b also tells the total. Hence don't just conclude that b provide the same information as a ( ratio), why are you not considering the total provided in b and the fact that each employee receives the pen, pencils,.. In same ratio.

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618614 [8]
Given Kudos: 81563
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
5
Kudos
3
Bookmarks
Expert Reply
sanjaykvbsingh wrote:
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

I think answer is B. the explanation from the people considering the answer as E is missing the point that option b also tells the total. Hence don't just conclude that b provide the same information as a ( ratio), why are you not considering the total provided in b and the fact that each employee receives the pen, pencils,.. In same ratio.

Posted from GMAT ToolKit


The correct answer is E.

There can be two cases:
There can be 9 managers each receiving 2 pens, 3 pencils and 4 pads.
There can be 3 managers each receiving 6 pens, 9 pencils and 12 pads.

Does this make sense?
User avatar
Senior Manager
Senior Manager
Joined: 17 Apr 2013
Status:Verbal Forum Moderator
Posts: 361
Own Kudos [?]: 2197 [0]
Given Kudos: 298
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
VeritasPrepKarishma wrote:
subhabrata1986 wrote:
I am facing problem to understand answer of a OG12 DS question.

Question:
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

ANSWER I DID:
BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:
(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]
(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?


Ok, look the question tells us the following:
Staff Member 1 - x pens, y pencils, z pads
Staff Member 2 - x pens, y pencils, z pads
.
.
.
Staff Member n - x pens, y pencils, z pads
Total no of pens - nx, total no of pencils - ny and total no of pads - nz
Question: What is n?

Stmnt 1: x:y:z = 2:3:4. So values of x, y and z can be 2, 3 and 4 or 4, 6 and 8 or 6, 9 and 12 or any other values in the ratio 2:3:4. They needn't necessarily be 2, 3 and 4. Just the ratio required is 2:3:4.
Of course n can be anything here. Not sufficient.

Stmnt 2: nx = 18, ny = 27 and nz = 36.
Note here that nx:ny:nz = 18:27:36 = 2:3:4 (They had 9 as a common factor)
Since n is a common factor on left side, x:y:z = 2:3:4 (Ratios are best expressed in the lowest form.)

This is a case of what we call "We already knew that." Information given in stmnt 1 is already part of stmnt 2 so it is not possible that stmnt 2 alone is not sufficient but together stmnt 1 and 2 are.

Now to your question:
Why can't we say that the number of staff members must be 9?
Because ratio of 2:3:4 is same as ratio of 6:9:12 which is same as 18:27:36 (When you multiply each number of a ratio by the same number, the ratio remains unchanged).
If 18, 27 and 36 pens, pencils and pads are distributed in the ratio 2:3:4, I could give them all to one person (18:27:36 is the same ratio as 2:3:4), to 3 people (giving them 6 pens, 9 pencils and 12 pads each. 6:9:12 is the same ratio as 2:3:4) or to 9 people (giving them 2 pens, 3 pencils and 4 pads). Hence I don't know how many staff members are there.


Karishma I have a doubt here:

NX:NY:NZ = 18:27:36

N[X:Y:Z] = 9 [2:3:4]

Karishma I agree that N is unknown, but on Right hand side when we reduced to the lowest ration, 9 is the only viable possibility. Hence N=9, May be I am missing something will need your insight.
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64883 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
1
Kudos
2
Bookmarks
Expert Reply
honchos wrote:

Karishma I have a doubt here:

NX:NY:NZ = 18:27:36

N[X:Y:Z] = 9 [2:3:4]

Karishma I agree that N is unknown, but on Right hand side when we reduced to the lowest ration, 9 is the only viable possibility. Hence N=9, May be I am missing something will need your insight.


If N is 9,
X = 2, Y = 3 and Z = 4
There were 9 staff members and each got 2 pens, 3 pencils and 4 pads.
Ratio of pens:pencils:pads = 2:3:4

But if N is 3,
X = 6, Y = 9 and Z = 12
There were 3 staff members and each got 6 pens, 9 pencils and 12 pads.
Ratio of pens:pencils:pads = 2:3:4

N could even take the unlikely value of 1
X = 18, Y = 27 and Z = 36
There was only 1 staff member and he/she got 18 pens, 27 pencils and 36 pads.
Ratio of pens:pencils:pads = 2:3:4
User avatar
Intern
Intern
Joined: 15 Mar 2015
Posts: 16
Own Kudos [?]: 6 [0]
Given Kudos: 26
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
Could we also consider the case of 1 employee getting all the 18 pens, 27 pencils and 36 pads ?
Intern
Intern
Joined: 22 Nov 2017
Posts: 8
Own Kudos [?]: 2 [0]
Given Kudos: 5
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
Hi,

Do you know where I can find more DS questions of Ratio type. Exactly or close to this? Thanks for your help.
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618614 [0]
Given Kudos: 81563
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
Expert Reply
Re: A department manager distributed a number of pens, pencils [#permalink]
1
Bookmarks
VeritasKarishma wrote:
subhabrata1986 wrote:
I am facing problem to understand answer of a OG12 DS question.

Question:
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

ANSWER I DID:
BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:
(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]
(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?


Ok, look the question tells us the following:
Staff Member 1 - x pens, y pencils, z pads
Staff Member 2 - x pens, y pencils, z pads
.
.
.
Staff Member n - x pens, y pencils, z pads
Total no of pens - nx, total no of pencils - ny and total no of pads - nz
Question: What is n?

Stmnt 1: x:y:z = 2:3:4. So values of x, y and z can be 2, 3 and 4 or 4, 6 and 8 or 6, 9 and 12 or any other values in the ratio 2:3:4. They needn't necessarily be 2, 3 and 4. Just the ratio required is 2:3:4.
Of course n can be anything here. Not sufficient.

Stmnt 2: nx = 18, ny = 27 and nz = 36.
Note here that nx:ny:nz = 18:27:36 = 2:3:4 (They had 9 as a common factor)
Since n is a common factor on left side, x:y:z = 2:3:4 (Ratios are best expressed in the lowest form.)

This is a case of what we call "We already knew that." Information given in stmnt 1 is already part of stmnt 2 so it is not possible that stmnt 2 alone is not sufficient but together stmnt 1 and 2 are.

Now to your question:
Why can't we say that the number of staff members must be 9?
Because ratio of 2:3:4 is same as ratio of 6:9:12 which is same as 18:27:36 (When you multiply each number of a ratio by the same number, the ratio remains unchanged).
If 18, 27 and 36 pens, pencils and pads are distributed in the ratio 2:3:4, I could give them all to one person (18:27:36 is the same ratio as 2:3:4), to 3 people (giving them 6 pens, 9 pencils and 12 pads each. 6:9:12 is the same ratio as 2:3:4) or to 9 people (giving them 2 pens, 3 pencils and 4 pads). Hence I don't know how many staff members are there.

VeritasKarishma
Thanks for the nice explanation with kudos.
In the highlighted part, the question ask about member(S). So, can we limit the possibility of one person? I mean: Is it possible to distribute to one member as the question stem used the plural sign (memberS)?
Thanks__
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64883 [2]
Given Kudos: 426
Location: Pune, India
Send PM
A department manager distributed a number of pens, pencils [#permalink]
2
Kudos
Expert Reply
Asad wrote:
VeritasKarishma wrote:
subhabrata1986 wrote:
I am facing problem to understand answer of a OG12 DS question.

Question:
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

ANSWER I DID:
BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:
(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]
(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?


Ok, look the question tells us the following:
Staff Member 1 - x pens, y pencils, z pads
Staff Member 2 - x pens, y pencils, z pads
.
.
.
Staff Member n - x pens, y pencils, z pads
Total no of pens - nx, total no of pencils - ny and total no of pads - nz
Question: What is n?

Stmnt 1: x:y:z = 2:3:4. So values of x, y and z can be 2, 3 and 4 or 4, 6 and 8 or 6, 9 and 12 or any other values in the ratio 2:3:4. They needn't necessarily be 2, 3 and 4. Just the ratio required is 2:3:4.
Of course n can be anything here. Not sufficient.

Stmnt 2: nx = 18, ny = 27 and nz = 36.
Note here that nx:ny:nz = 18:27:36 = 2:3:4 (They had 9 as a common factor)
Since n is a common factor on left side, x:y:z = 2:3:4 (Ratios are best expressed in the lowest form.)

This is a case of what we call "We already knew that." Information given in stmnt 1 is already part of stmnt 2 so it is not possible that stmnt 2 alone is not sufficient but together stmnt 1 and 2 are.

Now to your question:
Why can't we say that the number of staff members must be 9?
Because ratio of 2:3:4 is same as ratio of 6:9:12 which is same as 18:27:36 (When you multiply each number of a ratio by the same number, the ratio remains unchanged).
If 18, 27 and 36 pens, pencils and pads are distributed in the ratio 2:3:4, I could give them all to one person (18:27:36 is the same ratio as 2:3:4), to 3 people (giving them 6 pens, 9 pencils and 12 pads each. 6:9:12 is the same ratio as 2:3:4) or to 9 people (giving them 2 pens, 3 pencils and 4 pads). Hence I don't know how many staff members are there.

VeritasKarishma
Thanks for the nice explanation with kudos.
In the highlighted part, the question ask about member(S). So, can we limit the possibility of one person? I mean: Is it possible to distribute to one member as the question stem used the plural sign (memberS)?
Thanks__


Yes, number of members can be 1. We will use plural because we don't know the actual number. The only constraint is that since he does distribute it to members, number of members cannot be 0.

It's like - How many people are in the room?
A valid answer is 1 person.
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29894 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
1
Bookmarks
Expert Reply
Top Contributor
subhabrata1986 wrote:
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.


Given: A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads.

Target question: How many staff members were in the department?

Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
2 + 3 + 4 = 9
So, the TOTAL number of pens, pencils, and pads each worker receives is a multiple of 9.
There's no way we can use this information to determine the number of workers
Statement 1 is NOT SUFFICIENT

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
Important: Notice that 18 pens, 27 pencils, and 36 pads is in the same ratio as noted in statement 1. So, statement 2 doesn't seem to be adding a whole lot of new information. So I'm already thinking that statement 2 it's not sufficient. Let's see if we can find two conflicting cases that satisfy statement 2
Case a: It could be the case that there's 1 worker, and that worker receives 18 pens, 27 pencils, and 36 pads. In this case, the answer to the target question is the department has 1 staff member
Case b: It could be the case that there are 3 workers, and each worker receives 6 pens, 9 pencils, and 12 pads. In this case, the answer to the target question is the department has 3 staff members
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that the same counter-examples I used to show that statement 2 is not sufficient also satisfy the conditions stated in statement 1. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: It could be the case that there's 1 worker, and that worker receives 18 pens, 27 pencils, and 36 pads. In this case, the answer to the target question is the department has 1 staff member
Case b: It could be the case that there are 3 workers, and each worker receives 6 pens, 9 pencils, and 12 pads. In this case, the answer to the target question is the department has 3 staff members
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 32633
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: A department manager distributed a number of pens, pencils [#permalink]
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.
GMAT Club Bot
Re: A department manager distributed a number of pens, pencils [#permalink]
Moderator:
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne