PSAT Math Multiple-Choice Question 613: Answer and Explanation

Question: 613

An employee at a company has the following rules for days off from work:

-Employees are granted 30 flex days paid time off in a year for non-weekend and holiday days.

-Sick days with a doctor's note count as half a flex day.

-Personal days count as a full flex day.

If an employee wants to use at least half of the flex days but less than of them, what inequality would express the total number of sick days, S, and personal days, P, he or she could take in a year?

• A.
• B.
• C. 15 ≤ 2S + P < 25
• D. 15 ≤ S + 2P < 30

Correct Answer: B

Explanation:

(B) First, figure out what and of 30 are so that you know what range of flex days an employee wants to take:

and (30) = 25

So the employee wants to take at least 15 days but fewer than 25 days. If we consider F to be the number of flex days taken, this can be expressed as:

15 ≤ F < 25

Now we need an expression for flex days using sick days, S, and personal days, P. A sick day counts as half of a flex day, and a personal day counts as a total flex day. So the number of flex days used will be represented by:

We can plug in this expression for F in our previous inequality:

This is choice (B).