What is the ratio x:y:z?

[GayaneP973]

This question comes from the FDP Strategy Guide, 5th Edition. Chapter 6, page 100, Question #9.

It is a data sufficiency question.

What is the ratio x:y:z?

(1) x+y=2z
(2) 2x+3y=z

The answer was C, both together are sufficient, neither is sufficient alone.

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Is there a faster way of solving this question without actually manipulating the equations as suggested by the answer page?

The FDP strategy suggests the following for ratio DS questions:

1- If a Data Sufficiency question asks for the relative value of two pieces of a ratio, ANY statement that gives the relative value of ANY two pieces of the ratio will be sufficient.

2- If a DS question asks for the concrete value of one element of a ratio, you will need BOTH the concrete value of another element of the ratio AND the relative value of two elements of the ratio.

Do these tips apply to this question? If so, how? And if not, is there a general rule that we can apply to these questions that will help us reach the answer quickly?

Thank you.

[RonPurewal]

Please post your question in the correct folder (MGMAT non-CAT math).

Thanks.