The value of x is one quarter of z. The sum of x, y, and z

Hi All,

While most Test Takers would treat this as a 'system' algebra question and solve it that way, there are some interesting Number Property patterns in this prompt that will actually allow you to use the answer choices (and some pattern-matching) to get to the solution.

To start, I'm going to deal with the last piece of information first:

Y is twice Z

The prompt asks for the BIGGEST factor of the SUM of Y and Z. Since Y = 2Z, the sum of Y and Z is (2Z) + Z = 3Z. This means that the BIGGEST factor is a MULTIPLE OF 3 (and likely one of the larger multiples of 3 in the answer choices).

The second piece of information tells us...

X+Y+Z = 26

By extension...

X+(Y+Z) = 26
X+(larger multiple of 3) = 26

From the answer choices, there are really only 2 options that make any sense: Answers D and E....

With Answer D:
IF....Y+Z = 12, then X= 14, but....

The first piece of information tells us that X = 1/4 of Z, so X has to be relatively small....In this example, it's LARGER than Z, so D is NOT the answer. At this point, the answer would have to be E, but here's the proof...

IF...Y+Z = 24 and Y= 2Z....
Y = 16
Z = 8

X is 1/4 of Z, so X = (1/4)(8) = 2

X+Y+Z=26
2+16+8=26

All of the numbers 'fit' what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich