A number is to be written in each of the small squares in the figure above so that the sum of the numbers in any row is

[M7MBA]

A number is to be written in each of the small squares in the figure above so that the sum of the numbers in any row is the same as the sum of the numbers in any column: What number does \(x\) represent?

(1) \(z\) represents \(5.\)
(2) \(y\) represents \(8.\)

Answer: A

Source: GMAT Prep

[swerve]

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A number is to be written in each of the small squares in the figure above so that the sum of the numbers in any row is the same as the sum of the numbers in any column: What number does \(x\) represent?

(1) \(z\) represents \(5.\)
(2) \(y\) represents \(8.\)

Answer: A

Source: GMAT Prep

Given: \(9+ x + y = 4 + y + z\)

Statement 1: \(z\) represents \(5\).
\begin{align*}
9+ x + y &= 4 + y + z \\
9+ x + y &= 4 + y + 5 \\
9 + x + y &= 9 + y \\
x + y - y &= 9 -9 \\
x &= 0 \qquad \text{Sufficient} \Large{\color{green}\checkmark}
\end{align*}

Statement 2: \(y\) represents \(8\).

\(9 + x + 8 = 4 + 8 + z\)
\(1\) equation, \(2\) unknowns, therefore Insufficient. \(\Large{\color{red}\chi}\)

Therefore, A