PSAT Math Multiple-Choice Question 293: Answer and Explanation

Question: 293

Last month, Keith ran 18 more miles than Mick ran. If they ran a total of 76 miles, how many miles did Keith run?

• A. 29
• B. 38
• C. 42
• D. 47

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Systems of Linear Equations

Strategic Advice: Use the answer choices to your advantage to quickly find Keith's distance.

Getting to the Answer: The question gives two unknowns and enough information so that a system of equations could be formed. Traditional algebra could be used to solve this system of equations.

However, there is a more efficient way to answer the question: examine the answer choices to see which answers make sense for Keith's distance. The question states that Keith ran 18 more miles than Mick; thus, Keith must have run more than half of the 76 miles that the two of them ran. Since one-half of 76 is 38, you can eliminate (A) and (B) immediately.

Now, you just have to check either (C) or (D). For (C), if Keith ran 42 miles, then Mick ran 42- 18 = 24 miles, and 42 + 24 = 66 miles, which isn't correct. Thus, (D) is the correct answer. For the record, if Keith ran 47 miles, then Mick ran 47- 18 = 29 miles, and 47 + 29 = 76, which is correct.

If you are curious about the algebraic approach, let k represent the number of miles Keith ran. Since Keith ran 18 miles more than Mick, Mick ran 18 miles fewer, or k- 18 miles. They ran a combined 76 miles, so the following equation can be created and solved:

Again, this matches (D).