# GMAT OFFICIAL GUIDE DS – Each of the letters in the table above represents…

## Solution:

Let’s start by sketching the given diagram:

We are given that each letter represents one of the numbers 1, 2, or 3, and that each of those numbers only occurs once in each row and in each column. We need to determine the value of r.

Statement One Alone:

v + z = 6

Because v + z = 6, we know that both v and z must be 3.  Let’s fill the information into our table.

Since each row cannot repeat a particular number, we see that neither s nor t can be 3.

Thus, our options for the first row are s = 1, t = 2, and r = 3 or s = 2, t, = 1, and r = 3.  Either way we see that r must equal 3. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

s + t + u + x = 6

Before determining possible values for s, t, u, and x, let’s first see which letters fall in similar rows or columns.

We see that s and t fall in the same row, and u and x fall in the same column. Thus, s ≠ t and u ≠ x. We also see that since these 4 values sum to 6, none of these 4 values can be 3. Let’s put the following possible options in our table.

Option #1

We see that r must equal 3.

Option #2

We see that r must equal 3.

Option #3

We see that r must equal 3.

Option #4

We see that r must equal 3.

We can see that in any of these options, r = 3. Statement two alone is sufficient to answer the question.