(x-x_1)*(x-x_2)*(x-x_3)........(x-x_n)

Dear MacFauz
OK, I see what you mean. As odd as this may sound, a good riddle or puzzle typically is not a valid basis for a good GMAT question. I know that may sound paradoxical, since so many GMAT math questions can be puzzling, and many are designed to exploit common misunderstanding. I'm not sure I will be able to explain this distinction.
I guess what makes a good GMAT math problem --- it relies on properties that a mathematician would recognize as important, although it may be framed in a way so as to induce folks to fall into a predictable mathematical trap. By contrast, a riddle or puzzle will often rely on emphasizing the importance of something that others would typically overlook. In this particular problem, the "trick" consisted in the names assigned to the variables. From a purely mathematical point of view, what names we assign to variables is entirely arbitrary, and doesn't affect the underlying mathematics at all. In fact, this is ultimately one of the defining characteristics of mathematical thinking, one hardest for non-mathematicians to appreciate: the absolute arbitrariness of external notation, the absolute fungibility of one variable/symbol for another. Therefore, I imagine that most people skilled with mathematics would entirely overlook the significance of the variable names, as I did. A question that "fools" people who understand mathematics well --- that may well be the characteristic of a good puzzle or riddle, but doesn't not constitute a good GMAT math question. The mark of a good GMAT math question is that it finely discriminates between those who understand math well and those who think about math superficially. In a way, this puzzle-question rewards a kind of superficial thinking (attachment to the names of the variables), which is the opposite of what a good GMAT question does.
I want to say: I really appreciate your effort in putting a question out there. I would say this question is not an appropriate basis for a GMAT question, but don't give up. It's actually excellent practice to understand how GMAT questions are constructed. Let me know if you create any more questions.
Mike

Thanks Mike... And will do for sure...
Just curious though... Is there any way to reframe this question to make it GMAT worthy??

I would say no. It seems the whole question depends so specifically on the choice of letters for variables, something very superficial from a mathematical perspective.

Here's something that occurs to me, two questions that would be GMAT worthy, on the hard side for the GMAT, but they're changed so much from the original that I don't know if you would consider them anything like a reframing:

What is the value of x^8 + 7x^6 - 3x^4 + 14x^2 - 5?
Statement #1: x^2 = 4
Statement #2: x^3 = 8

What is the value of x^7 + 7x^5 - 3x^3 + 14x?
Statement #1: x^2 = 4
Statement #2: x^3 = 8

Mike

Understood..
And my answers to these questions are D and B..

Posted from my mobile device