<< This Month's Problem
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, 2nd edition, p. 212, examples mid-page). You may also wish to read our discussion of square roots on our blog.