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OG13- D.S- Q114

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OG13- D.S- Q114

by mehrasa » Fri May 08, 2015 12:21 am
Adepartment 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. Howmany 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.

1) insufficient
2) it can be 3 person with ratio 6:9:12
or for 9 person with ration 2:3:4 ====> insufficient

together it comes to 9 person

to me the answer is C
what do you think?
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Source: — Data Sufficiency |
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by GMATGuruNY » Fri May 08, 2015 1:32 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.
All of these 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, iINSUFFICIENT.

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, the two cases that satisfy statement 2 also satisfy statement 1:
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.
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