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by GMATGuruNY » Thu Mar 10, 2011 7:34 am
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.
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the total number of pens + pencils + pads must be a multiple of 9.
No way to determine the exact number of staff members.
Insufficient.

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The given values are divisible both by 3 and by 9. Thus:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

Statements 1 and 2 combined:
In statement 2, pens:pencils:pads = 18:27:36 = 2:3:4, the same ratio given in statement 1. Thus, statement 1 offers no information beyond what is given in statement 2:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

The correct answer is E.
Last edited by GMATGuruNY on Thu Mar 10, 2011 8:04 am, edited 2 times in total.
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by mundasingh123 » Thu Mar 10, 2011 7:56 am
GMATGuruNY 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.
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the number of staff members must be a multiple of 9.
No way to determine the exact number of staff members.
Insufficient.

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The given values are divisible both by 3 and by 9. Thus:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

Statements 1 and 2 combined:
In statement 2, pens:pencils:pads = 18:27:36 = 2:3:4, the same ratio given in statement 1. Thus, statement 1 offers no information beyond what is given in statement 2:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

The correct answer is E.
Hi GmatGuruNY , thanks for Helping .
I am surely missing something .
U stated while discussing Sttmnt A
the number of staff members must be a multiple of 9
Then u Stated while discussing Sttmnt B
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
So when u combine Sttmnt A and Sttmnt B, Should nt we be able to tell that the number of staff members is 9 as it is the figure that is common to both Sttmnt A and Sttmnt B
What am i missing ? :9
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by GMATGuruNY » Thu Mar 10, 2011 8:01 am
mundasingh123 wrote:
GMATGuruNY 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.
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the number of staff members must be a multiple of 9.
No way to determine the exact number of staff members.
Insufficient.

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The given values are divisible both by 3 and by 9. Thus:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

Statements 1 and 2 combined:
In statement 2, pens:pencils:pads = 18:27:36 = 2:3:4, the same ratio given in statement 1. Thus, statement 1 offers no information beyond what is given in statement 2:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

The correct answer is E.
Hi GmatGuruNY , thanks for Helping .
I am surely missing something .
U stated while discussing Sttmnt A
the number of staff members must be a multiple of 9
Then u Stated while discussing Sttmnt B
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
So when u combine Sttmnt A and Sttmnt B, Should nt we be able to tell that the number of staff members is 9 as it is the figure that is common to both Sttmnt A and Sttmnt B
What am i missing ? :9
I've amended my post above: Statement 1 tells us that the sum of pens + pencils + pads (not the number of staff members) must be a multiple of 9.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by mundasingh123 » Thu Mar 10, 2011 8:41 am
GMATGuruNY wrote:
mundasingh123 wrote:
GMATGuruNY 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.
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the number of staff members must be a multiple of 9.
No way to determine the exact number of staff members.
Insufficient.

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The given values are divisible both by 3 and by 9. Thus:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

Statements 1 and 2 combined:
In statement 2, pens:pencils:pads = 18:27:36 = 2:3:4, the same ratio given in statement 1. Thus, statement 1 offers no information beyond what is given in statement 2:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

The correct answer is E.
Hi GmatGuruNY , thanks for Helping .
I am surely missing something .
U stated while discussing Sttmnt A
the number of staff members must be a multiple of 9
Then u Stated while discussing Sttmnt B
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
So when u combine Sttmnt A and Sttmnt B, Should nt we be able to tell that the number of staff members is 9 as it is the figure that is common to both Sttmnt A and Sttmnt B
What am i missing ? :9
I've amended my post above: Statement 1 tells us that the sum of pens + pencils + pads (not the number of staff members) must be a multiple of 9.
Hi GmatGuruNY,Even then the problem remains ,
U stated while discussing Sttmnt A
the number of staff members must be a multiple of 9
That is 9,18,27
Then u Stated while discussing Sttmnt B
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
The only figure that is common is 9
If we take 18 which is also a multople of 9 and if we use Sttmnt A
which says the ratio is 2:3:4 , then we get 18 *2 :18 * 3 : 18 *4 = 36: 54:72 which doesnt match with the ratio given in Sttmnt B
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by GMATGuruNY » Thu Mar 10, 2011 8:53 am
mundasingh123 wrote:
GMATGuruNY wrote:
mundasingh123 wrote:
GMATGuruNY 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.
Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
Since 2+3+4 = 9, the number of staff members must be a multiple of 9.
No way to determine the exact number of staff members.
Insufficient.

Statement 2: The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
The given values are divisible both by 3 and by 9. Thus:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

Statements 1 and 2 combined:
In statement 2, pens:pencils:pads = 18:27:36 = 2:3:4, the same ratio given in statement 1. Thus, statement 1 offers no information beyond what is given in statement 2:
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.

The correct answer is E.
Hi GmatGuruNY , thanks for Helping .
I am surely missing something .
U stated while discussing Sttmnt A
the number of staff members must be a multiple of 9
Then u Stated while discussing Sttmnt B
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
So when u combine Sttmnt A and Sttmnt B, Should nt we be able to tell that the number of staff members is 9 as it is the figure that is common to both Sttmnt A and Sttmnt B
What am i missing ? :9
I've amended my post above: Statement 1 tells us that the sum of pens + pencils + pads (not the number of staff members) must be a multiple of 9.
Hi GmatGuruNY,Even then the problem remains ,
U stated while discussing Sttmnt A
the number of staff members must be a multiple of 9
That is 9,18,27
Then u Stated while discussing Sttmnt B
There could be 3 staff members, each receiving 6 pens, 9 pencils, and 12 pads.
There could be 9 staff members, each receiving 2 pens, 3 pencils, and 4 pads.
Since the number of staff members could be 3 or 9, insufficient.
The only figure that is common is 9
If we take 18 which is also a multople of 9 and if we use Sttmnt A
which says the ratio is 2:3:4 , then we get 18 *2 :18 * 3 : 18 *4 = 36: 54:72 which doesnt match with the ratio given in Sttmnt B
As I noted in my second post, my original post was incorrect: the total number of staff members does NOT have to be a multiple of 9. Statement 1 tells us only that the sum of pens + pencils + pads must be a multiple of 9:
We could have 2 pens, 3 pencils and 4 pads. 2+3+4 = 9.
We could have 4 pens, 6 pencils, and 8 pads. 4+6+8 = 18.
We could have 18 pens, 27 pencils, and 36 pads. 18+27+36 = 81.
We could have 200 pens, 300 pencils, and 400 pads. 200+300+400 = 900.
All of the sums above are multiples of 9.
The number of staff members, however, could be different values.
Given the scenarios listed above, we could have 3 staff members, 9 staff members, or 100 staff members.

Clear?
Last edited by GMATGuruNY on Fri May 08, 2015 1:24 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by mundasingh123 » Thu Mar 10, 2011 9:59 am
Thanks Mitch for clarifying this question . I was making a very fundamental mistake and was in the process forgetting that Sttmnt A was just providing redundant info when u are considering both the sttmnts together
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by singhr10 » Sat Jun 11, 2011 3:13 pm
In case the statement 2 is changed to below will the ans be B
2: The manager distributed a total of 6 pens,9 pencils and 12 pads.

I am basically taking a GCF of 6, 9 and 12 and it comes out as 3. Hence we get a unique number of staff members as 3.
Am i correct or missing something here.

Thanks,
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