The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value of x?
1) y = 16
2) The difference between y and z IN THAT ORDER is 4

Excellent opportunity to use the k technique, one of the most powerful tools of our method when dealing with ratios.
\[\left. \begin{gathered}
x = 3k \hfill \\
y = 4k\,\,\, \hfill \\
z = 5k \hfill \\
\end{gathered} \right\}\,\,\,\,\,k \ne 0\]
\[? = x = 3k\,\,\,\, \Leftrightarrow \,\,\,\boxed{? = k}\]
\[\left( 1 \right)\,\,4k = y = 16\,\,\,\, \Rightarrow \,\,\,k\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,{\text{SUF}}.\,\,\,\]
\[\left( 2 \right)\,\,4 = y - z = - k\,\,\,\, \Rightarrow \,\,\,k\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,{\text{SUF}}.\,\,\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

P.S.: It IS possible to have (D) in an official GMAT question even when the (unique) values obtained in each statement alone are different.
Proof: https://www.beatthegmat.com/data-suffic ... tml#491069

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method I s the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The original condition gives the proportion x : y : z = 3 : 4 : 5, so we can write x = 3k, y = 4k and z = 5k. We have 4 variables and 3 equations.
Therefore, D is most likely to be the answer.

Condition 1) is sufficient since 16 = y = 4k, and so k = 4. Then x = 3k = 12.

Condition 2) is also sufficient since 4 = z - y = 5k - 4k = k. So, x = 3k = 12.

Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) give similar information.

Therefore, D is the answer.
Answer: D