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Re: If 4x = 5y = 10z, what is the value of x + y + z ? [#permalink]
05 Apr 2015, 14:50

Expert's post

Hi All,

As 'layered' as this DS question looks, it's actually based on a standard Algebra rule that you WILL be tested on at least once when you take the Official GMAT: "system math." Knowing this rule will provide you with a shortcut so that you can avoid most of the work involved in this question....

We're told that 4X = 5Y = 10Z. We're asked for the value of X + Y + Z.

Fact 1: X - Y = 6

From the prompt, we also know that 4X = 5Y. We now have a "system" of equations (2 variables and 2 unique equations) involving X and Y; since there are no special situations to consider (re: absolute values, squared terms), we CAN solve for the value of X and Y and there will be just one value for each. With either of those values, we can then solve for the value of Z (since 4X = 10Z and 5Y = 10Z). With the individual values of X, Y and Z, we CAN answer the question. Fact 1 is SUFFICIENT

Fact 2: Y + Z = 36

Here we have a similar situation to the one we saw in Fact 1. From the prompt, we know that 5Y = 10Z, so we again have a "system" of equations. The exact same shortcut applies here, so we CAN answer the question. Fact 2 is SUFFICIENT

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