PSAT Math Multiple-Choice Question 215: Answer and Explanation

Question: 215

In the legal field, "reciprocity" means that an attorney can take and pass a bar exam in one state and be allowed to practice law in a different state that permits such reciprocity. Each state bar association decides with which other states it will allow reciprocity. For example, Pennsylvania allows reciprocity with the District of Columbia. It costs $25 less than 3 times as much to take the bar in Pennsylvania than in D.C. If both bar exams together cost $775, how much less expensive is it to take the bar exam in D.C. than in Pennsylvania?

• A. $200
• B. $275
• C. $375
• D. $575

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra/Systems of Linear Equations

Getting to the Answer: Use the Kaplan Method for Translating English into Math. Write a system of equations with p = the cost in dollars of the Pennsylvania bar exam and d = the cost of the D.C. bar exam. The Pennsylvania bar exam (p) costs $25 less (-25) than 3 times as much (3 d) as the D.C. bar exam, or p = 3 d - 25. Together, both bar exams cost $775, so d + p = 775. The system is:

The top equation is already solved for p, so substitute 3 d - 25 into the second equation for p, and solve for d:

Be careful—that's not the answer. The D.C. bar exam costs $200, which means the Pennsylvania bar exam costs $775 - $200 = $575. This means the D.C. bar exam is $575 - $200 = $375 less expensive than the Pennsylvania bar exam. Choice (C) is correct.