Data Sufficiency

BTGmoderatorDC 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.

OA E

Source: Official Guide

We have to find out the number of staff members in the department.

Let's take each statement one by one.

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2 : 3 : 4, respectively.

Say the common ratio is m, thus each staff member received 2m pens, 3m pencils and 4m pads. Or, x = 2m, y = 3m and z = 4m.

Can't get the number of staff members in the department. Insufficient.

(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

Number of staff = 18/x = 27/y = 36/z.

Can't get the number of staff members in the department. Insufficient.

(1) and (2) together

Number of staff = 18/x = 18/2m = 9/m; 27/y = 27/3m = 9/m; 36/z = 36/4m = 9/m.

Obviously, from each computation, we get the number of staff = 9/m.

Since m and the number of staff are positive numbers, the possible values of m are 1, 3, and 9; thus, the possible values of the number of staff are 9, 3 and 9.

No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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Jay's solution is great.
I just wanted to mention that this question hinges largely on the fact that the number of pens, pencils, and pads that each staff member receives MUST HAVE INTEGER VALUES.

So, for example, if statement 1 were different and statement 2 read "The manager distributed a total of 11 pens, 2 pencils, and 13 pads," then we could be certain that there must be only 1 staff member, since there's no other way for each staff member to receive the same number of items. So, in this case, statement 2 would be sufficient on its own.

Conversely, if statement 1 were different and statement 2 read "The manager distributed a total of 10 pens, 12 pencils, and 14 pads," then we could NOT be certain of the number of staff members. In this instance, there could be 1 staff member or 2 staff members, so statement 2 would be insufficient on its own.

Cheers,
Brent