PSAT Math Multiple-Choice Question 317: Answer and Explanation

Question: 317

Which of the following statements is NOT true if the above equation is true?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Solving Equations

Strategic Advice: Watch out for the word NOT in the question stem.

Getting to the Answer: To find the answer using Picking Numbers, take advantage of the fact that the equation is a proportion (that is, two fractions equal to each other). If b = 5 and 2(a - 4) = 4, then both fractions will be the same and the numbers you've picked will be valid. Solve for a: a - 4 = 2, so a = 6. Now, plug b = 5 and a = 6 into the choices, looking for the one that is NOT true:

(A) , eliminate.

(B)

You're done: pick (B) and move on. For the record:

(C) , eliminate.

(D) , eliminate.

To solve this question using algebra, first cross-multiply and simplify the original equation:

Then, repeat this process for each answer choice, looking for the one that does NOT yield the same equation:

(A) , eliminate.

(B)

This equation is different from the one in the question, so (B) is correct. For the record:

(C) , eliminate.

(D) , eliminate.