Prep Swift - words to algebra - the sum of square root

GRE Quant Problem Solving
1

Hey guys!

Here’s a troubling task.
“The sum of the square root of two numbers is 18 and the difference of the square root of the two numbers is 12. What is the smaller number?”

I have 2 problems with the task.

  1. the wording
    Is it x^2 + y^2 = 18 or (x+y)^2 = 18 ?
    And a bigger question, what would be the wording in each case?

  2. the solution. It says the smaller number is 9. But I haven’t been able to make that work.

Here’s what I did.
x^2 + y^2 = 18
x^2 - y^2 = 12

I added both equations together. What I get is 2x^2 = 30, then x^2 = 15. If x^2 = 15, y^2 = 3, so y = √3.

2

It’s \sqrt{x} + \sqrt{y} = 18 - the question is saying that the sum of the square root of the two numbers is 18, not the squares.

4

I totally missed that. Thanks!