## A department manager distributed a number…

## Solution:

We are given that a department manager distributed pens, pencils, and pads. Each member received x pens, y pencils, and z pads. We must determine how many staff members were in the department.

**Statement One Alone: **

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

We are given a ratio of the number of pens, pencils, and pads that each staff member received. However, only knowing the ratio is not enough information to determine the number of staff members in the department. Statement one alone does not provide enough information to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

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

Although we know that the manager distributed a total of 18 pens, 27 pencils and 36 pads to all staff members, we still cannot determine how many staff members were in the department. For example, if each staff member received 6 pens, 9 pencils and 12 pads, then there were 3 staff members. On the other hand, if each staff member received 2 pens, 3 pencils and 4 pads, then there were 9 staff members. Thus, we do not know how many staff members were in the department. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

From statements one and two we know that number of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively, and that the manager distributed a total of 18 pens, 27 pencils, and 36 pads. However, without knowing how many pens, pencils, and pads each staff member actually received, we still cannot determine how many staff members were in the department.

You might have been tempted to say that there were 9 staff members, which is based on the assumption that each of them received the same number of pens (x=2), pencils (y=3), and pads (z=4). However, there are additional solutions that agree with the criteria given in the problem. For example, there could also be 3 staff members who each receive 6 pens, 9 pencils, and 12 pads, or there could be 1 staff member who receives all of the 18 pens, 27 pencils, and 36 pads.

**Answer:** E