Statement 1: As v and z can have values either 1 or 2 or 3, for (v + z) to be equal to 6, v and z both must be equal to 3.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
Now, as v is present second row and second column, no other member of second row and second column can have the value of 3. This means s and u cannot be equal to 3. Similarly, t and x cannot be equal to 3.
Since there are three numbers and each number occurs in a row exactly once, r must be equal to 3 as no other member of first row or first column can have the value of 3.
Sufficient
Statement 2: Sum of the numbers in first row and first column = (r + s + t) + (r + u + x) = 2r + (s + t + u + x) = 2r + 6
Now, each number occurs exactly once in each row and each column.
Hence, sum of all the numbers in first row = (1 + 2 + 3) = 6 and sum of all the numbers in first column = (1 + 2 + 3) = 6
hence, (2r + 6) = 12 ---> 2r = 6 ---> r = 3
Sufficient
The correct answer is D.
