r s t
u v w
x y z
Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?
1) v + z = 6
2) s + t + u + x = 6
Statement 1: v+z = 6
Since v and z each must be 1, 2 , or 3, the equation above implies that v=3 and z=3, yielding the following grid:
r...s...t
u...
3...w
x...y...
3
3 must appear in column 1 but cannot be repeated in rows 2 or 3.
Thus, the grid must look like this:
3...s...t
u...3...w
x...y...3
Thus, r=3.
SUFFICIENT.
Statement 2: s + t + u + x = 6
The grid in statement 1 implies two cases:
Case 1:
3...
1...2
2...3...
1
1...2...3
Case 2:
3...
2...1
1...3...
2
2...1...3
In each case, s+t+u+x = 6 and r=3.
If the value of r DECREASES, then the value of s+t+u+x will have to INCREASE.
Thus, for it to be true that s+t+u+x=6, r=3.
SUFFICIENT.
The correct answer is
D.
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