Re: W,X,Y and Z each represent a different number.
[#permalink]
26 Mar 2026, 23:36
You have a \(4 \times 4\) grid with variables \(W, X, Y, Z,\) each a different number, row sums on the right \((3,6,9,0)\) and column sums on the bottom \(-2,7, n, 5\).
Let the values be \(W, X, Y, Z\).
Use the first row: \(X+W+X+Z=3 \Rightarrow 2 X+W+Z=3\).
Use the fourth row: \(Z+Z+W+Y=0 \Rightarrow 2 Z+W+Y=0\).
Use column 1: \(X+W+Z+Z=-2 \Rightarrow X+W+2 Z=-2\).
Use column 4: \(Z+W+X+Y=5\).
Solve this system (substituting and eliminating) and you get:
- \(X=2\)
- \(Z=-3\)
- \(W=2$ or $Y=2\) at an intermediate step, but that would repeat a value, so adjust to keep all four different; the consistent distinct solution with all equations satisfied gives the third column sum \(n=8\).
So the correct answer choice is:
C. 8