What is the value of x?

[Vincen]

What is the value of x?

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

The OA is C.

How can I use the statement (2)?

[Brent@GMATPrepNow]

What is the value of x?

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

Target question: What is the value of x?

Statement 1: x is the square of an integer.
There are infinitely many values of x and y that satisfy statement 1.
x COULD equal 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 577 < x < 675
There are several values of x that satisfy statement 2.
x COULD equal 578, 579, 580, 581, etc
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
So, x is the square of an integer AND between 577 and 675
Let's look at some squares of integers near this range.
24² = 576 (576 is NOT in the given range)
25² = 625 (625 IS in the given range)
26² = 676 (676 is NOT in the given range)
So, x MUST equals 25
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

[Jeff@TargetTestPrep]

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