# If x is a positive integer, what is the value of √(x+24) – …

## Solution:

We are given that x is a positive integer and must determine the value of √(x+24) – √x.

**Statement One Alone:**

√x is an integer.

Using the information in statement one, we could obtain multiple values for √(x+24) – √x. If x = 1, then √(x+24) – √x = √25 – √1 = 5 – 1 = 4; however, if x = 4, then √(x+24) – √x = √28 – √4 = √28 – 2. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone**

√(x+24) is an integer.

Using the information in statement two, we could obtain multiple values for √(x+24) – √x. If x = 1, then √(x+24) – √x = √25 – √1 = 5 – 1 = 4; however, if x = 12, then √(x+24) – √x = √36 – √12 = 6 – √12. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together:**

Using the information in statements one and two, we still could obtain multiple values for √(x+24) – √x. If x = 1, then √(x+24) – √x = √25 – √1 = 5 – 1 = 4; however, if x = 25, then √(x+24) – √x = √49 – √25 = 7 – 5 = 2.

**Answer: E**