Hard SAT question, have the answer, but do not understand why?

Question

If:

XYZ

+XYZ

________

WZXX

What is the value of 2x?

The answer key says it is 12, therefore x=6 but I do not understand how they got this answer.

Please explain.

Answer 1

are you sure this is a SAT question because i have no idea.

sorry

Answer 2

This may be something of a guess-and-check situation. They give you a list of answers, so you check to see which one works in the problem.

For the answer 2x = 12, you are absolutely correct that x = 6. Plug that in:

6YZ

+6YZ

________

WZ66

There two ways to get 6 (the last one) with z + z...either z = 3 or z = 8. Try z = 3. Plug that in:

6Y3

+6Y3

________

W366

On the assumption that y and z are not equal, try y = 8:

683

+683

________

W366

That would leave W = 1. Since this works, 2x = 12 is a valid answer. I assume that none of the other answers would work.

I hope that helps some!