PSAT Math Multiple-Choice Question 191: Answer and Explanation

Question: 191

If (a, b) is a solution to the equation above, what is the ratio , given that a ≠ 0?

• A. - 3
• B. - 2
• C.
• D.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra/Linear Equations

Getting to the Answer: When you're given only one equation but two variables, chances are that you can't actually solve the equation (unless one variable happens to cancel out), but rather that you are going to need to manipulate it to look like the desired expression (which in this question is ). This type of question can't be planned out step-by-step—instead, start with basic algebraic manipulations and see where they take you. First, distribute the on the left side of the equation to get 2 a + 5 b = b. There are two terms that have a b, so subtract 5 b from both sides to get 2 a = - 4 b. You're hoping for plain b in the numerator, so divide both sides by - 4 to get . Finally, divide both sides by a to move the a into a denominator position under b. The result is , which means the ratio is , or , making (C) correct.