If x is a positive integer, what is the value of

jjjinapinch wrote:If x is a positive integer, what is the value of √(x + 24) - √x?

(1) √x is an integer
(2) √(x + 24) is an integer

Official Guide question
Answer: E

Target question: What is the value of √(x + 24) - √x?

Given: x is a positive integer

Statement 1: √x is an integer
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1 (notice that √1 is an integer). In this case, √(x + 24) - √x = √(1 + 24) - √1 = 5 - 1 = 4
Case b: x = 4 (notice that √4 is an integer). In this case, √(x + 24) - √x = √(4 + 24) - √4 = √28 - 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √(x + 24) is an integer
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 1 (notice that √(1 + 24) = √25 = 5, which is an integer). In this case, √(x + 24) - √x = √(1 + 24) - √1 = 5 - 1 = 4
Case b: x = 25 (notice that √(25 + 24) = √49 = 7, which is an integer). In this case, √(x + 24) - √x = √(25 + 24) - √25 = 7 - 5 = 2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Case a: x = 1. In this case, √(x + 24) - √x = √(1 + 24) - √1 = 5 - 1 = 4
Case b: x = 25. In this case, √(x + 24) - √x = √(25 + 24) - √25 = 7 - 5 = 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent