Digital PSAT Math Practice Question 137: Answer and Explanation

Question: 137

Out of all possible solutions (x, y) to the pair of equations below, what is the greatest possible product xy that can be obtained?

• A. 3
• B. 4
• C. 6
• D. 8

Correct Answer: D

Explanation:

(D) The second equation is simpler, so solve for y and then plug your expression for y back into the first equation:

Divide by 3 to solve for y:

Now you can plug x - 2 in for y in the first equality:

Combine like terms within the parentheses:

Combine like terms and bring the 12 to the left side:

Factor this, or use the quadratic equation if you're not great at factoring:

Set each factor equal to 0 to solve for the possible values of x:

Next, plug these values into either of the two equations to solve for y. It'll be easiest to plug them into the equation that you already solved for y:

So x can equal 3 or 4, and y can equal 1 or 2. Therefore, the greatest product xy will be:

Choice (D) is the answer.