The value of x is one quarter of z. The sum of x, y, and z is equal to 26. If the value of y is twice the value of z, what is the largest factor of the sum of y and z? Pick:	A) 2	B) 3	C) 8	D) 12	E) 24 IS ANSWER
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= 
<gadget id="calculator">2+16+8</gadget>
<output>26</output>
26   All of the numbers 'fit' what we were told, so this MUST be the answer.   24 IS ANSWER
<result>E</result>
The value of x is one quarter of z. The sum of x, y, and z is equal to 26. If the value of y is twice the value of z, what is the largest factor of the sum of y and z?