PSAT Math Multiple-Choice Question 55: Answer and Explanation

Question: 55

The temperature, T, in degrees Celsius on a winter day can be written as a function of x, the time in hours since midnight (12:00 A.M.), as shown below.

If 100 = x² - 24x + 144 is an equivalent form of the equation when T(x) = 0, which of the following gives a time on that day when the temperature was 0°C?

• A. 6 P.M.
• B. 10 P.M.
• C. 3 A.M.
• D. 9 A.M.

Correct Answer: B

Explanation:

B

The question asks for a time when the temperature was 0°C. In the equation, T(x) represents temperature and x represents time, so the question is asking for some value of x that makes T(x) = 0. Notice that the question gives an equivalent form of the first equation when T(x) = 0. Solve this equation for x to find a time at which T(x) = 0. First, subtract 100 from both sides of the equation to set the left side equal to 0. The equation becomes 0 = x² - 24x + 44. This can be factored as 0 = (x - 22)(x - 2). To solve for x, set both factors equal to 0. There are two possible values of x : x = 22 and x = 2. Since x represents the time in hours since midnight, the temperature was 0°C at two times: 12:00 A.M. + 22 hours = 10:00 P.M. and at 12:00 A.M. + 2 hours = 2:00 A.M. Only 10:00 P.M. is an answer choice. The correct answer is (B).