PSAT Math Multiple-Choice Question 603: Answer and Explanation

Question: 603

What is the solution with the least possible y-value that satisfies both of the following inequalities?

y ≥ 2x + 5
and
4 - y ≤ x

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

(D) First, get the second inequality in the same form as the first. To do this, subtract 4 from both sides of the second inequality:

-y ≤ x - 4

Then divide by -1, remembering to flip the inequality since you're dividing by a negative:

y ≥ -x + 4

If you graph these two inequalities, you'll see that the point where the lines intersect is the solution that they share that has the lowest y-value.

We can use this knowledge to set both inequalities equal to one another and solve:

2x + 5 = -x + 4

To solve for x, add an x to both sides to get all of the x-terms on the left. Subtract 5 from both sides to get all constants on the right:

3x = -1

Dividing by 3 tells us that . That's enough to narrow it down to choice (D).

However, if we wanted to know the y-value, we could plug the x-value into the equation for either of the two lines:

This also agrees with choice (D).

Alternatively, you can plug in the values of the answers and see which set works for both ­equations.