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# A department manager distributed a number of pens, pencils

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A department manager distributed a number of pens, pencils [#permalink]

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15 Nov 2010, 00:54
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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.

[Reveal] Spoiler:
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.

[Reveal] Spoiler: OA

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Re: Need Help to Understand [#permalink]

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15 Nov 2010, 08:00
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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.

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.

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.

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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 26 Jul 2010 Posts: 358 Location: European union Followers: 2 Kudos [?]: 47 [5] , given: 41 Re: A department manager distributed a number of pens, pencils, [#permalink] ### Show Tags 13 Dec 2012, 18:11 5 This post received KUDOS 1 This post was BOOKMARKED I got it only by using common sense. Its not tricky if you think about it . (1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively. This shows you how many more pads [b]one person[b] gets compared to the number of pencils or pens he gets. (2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads. This can give you an idea how many gadgets are there in total to distribute, but we cannot know how many people will take them. There can be just one person taking all the 18 pens, 27 pencils, 36 pads (in the proportion of 2:3:4 as stated in (1) ) There can be three people, each taking 6 pens, 9 pencils, 12 pads (2:3:4) There can be 9 people, each taking 2 pens, 3 pencils, 4 pads (2:3:4) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6667 Location: Pune, India Followers: 1828 Kudos [?]: 11110 [5] , given: 218 Re: A department manager distributed a number of pens, pencils [#permalink] ### Show Tags 04 Jan 2013, 07:15 5 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Need Help to Understand [#permalink]

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15 Nov 2010, 04:53
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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
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Re: A department manager distributed a number of pens, pencils, [#permalink]

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13 Dec 2012, 18:00
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jogorhu wrote:
Economist 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.

Can someone clarify how the answer is E.

"Tricky question. ans E

1. 9 employees - each employee get 2 pens, 3 pencils, 4 pads
2. 3 employees - each employee get 6 pens, 9 pencils, 12 pads

in both cases the ratio is 2:3:4"

I found this response from Spider. Answer is E
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Re: A department manager distributed a number of pens, pencils, [#permalink]

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14 Dec 2012, 01:51
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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!
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Re: A department manager distributed a number of pens, pencils [#permalink]

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08 Sep 2013, 23:17
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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

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?
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Re: A department manager distributed a number of pens, pencils [#permalink]

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18 May 2014, 11:06
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Statement (1) tells us the ratio of pens, pencils, and pads that each staff member received, but there is no way to tell how many staff members there actually are.

Statement (2) tells us that 18 pens, 27 pencils, and 36 pads were distribued. Note that the overall total is in the ratio of 2 pens:3 pencils:4pads mentioned in Statement (1). However, there is still no way to know how many staff members there are just by knowing the total number of pens/pencils/pads distributed.

Combining (1) & (2) we know the ratio of pens:pencils:pads for each staff member and the total distributed among all staff, but we still cannot say for sure how many staff members there are. We do not know how many pens/pencils/pads were given to each staff member...only the ratio in which they were distributed. There are several possibilities that would satisfy (1) and (2)...for example,

2 pens/3 pencils/4 pads for each staff member, 9 staff members total = 18 pens, 27 pencils, 36 pads

OR

6 pens/9 pencils/12 pads for each staff member, 3 staff members total = 18 pens, 27 pencils, 36 pads

and other examples would work as well. There could even be only 1 staff member who gets all 18 pens, 27 pencils, and 36 pads.

Hence E
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A department manager distributed a number of pens, pencils, [#permalink]

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27 Nov 2012, 19:08
rashminet84 wrote:

To know the number of people, simply knowing the ratio of division is not enough. Both the statements only provide the ratio of distribution.

Hi Bunuel,
What other information would have made the problem sufficient?

Regards,
Sachin
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Re: A department manager distributed a number of pens, pencils, [#permalink]

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13 Dec 2012, 17:48
Economist 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.

Bump!

Why not B?

If we know that the quantity of goods disbursed was 18/27/36, can we assume that 9 employees received the goods in the ratio 2/3/4?
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Re: A department manager distributed a number of pens, pencils, [#permalink]

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13 Dec 2012, 18:46
Ivan91 wrote:
I got it only by using common sense. Its not tricky if you think about it .
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
This shows you how many more pads [b]one person[b] gets compared to the number of pencils or pens he gets.

(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
This can give you an idea how many gadgets are there in total to distribute, but we cannot know how many people will take them.

There can be just one person taking all the 18 pens, 27 pencils, 36 pads (in the proportion of 2:3:4 as stated in (1) )
There can be three people, each taking 6 pens, 9 pencils, 12 pads (2:3:4)
There can be 9 people, each taking 2 pens, 3 pencils, 4 pads (2:3:4)

So, 1 person could get 6/9/12, another could get 6/9/12 and another could get 6/9/12

18/27/36 total, spread among 3 people.

But we could also have 9 people, each of which receive the supplies 2/3/4.

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Re: A department manager distributed a number of pens, pencils [#permalink]

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03 Jan 2013, 21:53
Karishma,

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..

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Re: A department manager distributed a number of pens, pencils [#permalink]

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04 Jan 2013, 08:09
VeritasPrepKarishma wrote:
Sachin9 wrote:
Karishma,

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..

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.

This was amazing, thanks a lot..
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Re: A department manager distributed a number of pens, pencils [#permalink]

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27 Apr 2013, 15:31
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.

[Reveal] Spoiler:
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.

In both options essentially the same information is provided. When you realize that statement 1 is insufficient and that 1 and 2 are effectively same info. immediately mark E.
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Re: A department manager distributed a number of pens, pencils [#permalink]

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08 Sep 2013, 17:47
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
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Re: A department manager distributed a number of pens, pencils [#permalink]

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21 May 2014, 03:58
Why not C?

Statement 1 is saying pens: pencils: pads 2:3:4 to each office staff.

Statement 2 is saying total number of pens 18 pencils 27 pads 36

1+2

Staff 1 2:3:4

Staff 2 4: 6: 8

Staff 3 6: 9: 12

Staff 4 8: 12: 16

Staff 5 10: 15: 20

Staff 6 12: 18: 24

Staff 7 14: 21: 28

Staff 9 16: 24: 32

Staff 9 18: 27: 36

So total no of staff is 9.

Bunuel wrote:
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

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?

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Re: A department manager distributed a number of pens, pencils [#permalink]

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21 May 2014, 07:09
Expert's post
arindamsur wrote:
Why not C?

Statement 1 is saying pens: pencils: pads 2:3:4 to each office staff.

Statement 2 is saying total number of pens 18 pencils 27 pads 36

1+2

Staff 1 2:3:4

Staff 2 4: 6: 8

Staff 3 6: 9: 12

Staff 4 8: 12: 16

Staff 5 10: 15: 20

Staff 6 12: 18: 24

Staff 7 14: 21: 28

Staff 9 16: 24: 32

Staff 9 18: 27: 36

So total no of staff is 9.

Bunuel wrote:
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

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?

Post you quote shows two different cases...

There can also be 3 members each receiving 6 pens, 9 pencils and 12 pads.
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Re: A department manager distributed a number of pens, pencils [#permalink]

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03 Nov 2014, 03:00
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.

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.

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.

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.
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Re: A department manager distributed a number of pens, pencils [#permalink]

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04 Nov 2014, 21:25
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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.

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.

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.
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