PSAT Math Multiple-Choice Question 298: Answer and Explanation

Question: 298

If x > 0, which of the following is equivalent to ?

• A. (x + 5)²
• B.
• C. 3(x + 4)
• D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Rational Expressions and Equations

Strategic Advice: Pick a number for x to determine the numerical value of the given expression, then plug the same number into the answer choices to find the one that matches.

Getting to the Answer: Pick something easy, like x = 1: . This simplifies to . This fraction can be rewritten as .

Now, plug 1 in for x in each of the answer choices to see which one gives you the same value:

(A):(1 + 5)² = 36. Eliminate.

(B): . Correct! Just to be sure, check the other two answers.

(C): 3(1+ 4) = 3(5) = 15. Eliminate.

(D): . Eliminate.

Since (B) is the only answer that matched the calculated value, it must be the correct answer.