When a certain positive number is subtracted from 15, the resulting number is 2 times the positive square root of the original number. Which of the following could be the original number?

Indicate __all__ such original numbers.

Translate the text into math, using *x* for the original number.

“a certain positive number is subtracted from 15” = 15 – *x* = “the resulting number”

“2 times the positive square root of the original number” =

These two expressions are equal to each other, so set them equal and solve. Note that , so there is a hidden quadratic.

Since the question explicitly states “the positive square root,” is the only solution and *x* = 9.*

Check this answer:

As an alternative to solving the quadratic, you could test all of the choices. The correct answer was tested above, so what follows is the test of the remaining choices:

No, so *x* = 3 is not a correct answer.

No, so *x* = 15 is not a correct answer.

No, so *x* = 16 is not a correct answer.

No, so *x* = 25 is not a correct answer.

The correct answer is 9 only.

* Even if the problem had not specified “the positive square root,” there is some indication in the OG that when taking the square root of an ordinary number (which *x*, ultimately, is), the positive root is the only solution (see GRE Official Guide, 2^{nd} edition, p. 212, examples mid-page). You may also wish to read our discussion of square roots on our blog.