Vincen wrote:What is the value of x?

(1) x is the square of an integer.
(2) 577 < x < 675

We need to determine the value of x.

Statement One Alone:

x is the square of an integer.

x could be an infinite number of values, so statement one alone is not sufficient to answer the question.

Statement Two Alone:

577 < x < 675

Since x could be any value between 577 and 675, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we know that x is the square of an integer between 577 and 675. Since we know that 25^2 = 625, we know that 625 is one possible value of x. However, to determine whether 625 is the only value for x, we should test 24^2 and 26^2 to determine whether those numbers are between 577 and 675.

24^2 = 576 and 26^2 = 676

Since both 24^2 and 26^2 are outside the range of values from 577 to 675, x must be 25^2 or 625.

Answer: C