PSAT Math Multiple-Choice Question 204: Answer and Explanation

Question: 204

	Jan	Feb	Mar	Apr
Company A	54	146	238	330
Company B	15	30	60	120

Company A and company B are selling two similar toys. The sales figures for each toy are recorded in the table above. The marketing department at company A predicts that its monthly sales for this particular toy will continue to be higher than company B's through the end of the year. Based on the data in the table, and assuming that each company sustains the pattern of growth the data suggests, which company will sell more of this toy in December of that year and how much more?

• A. Company A; 182
• B. Company A; 978
• C. Company B; 29,654
• D. Company B; 60,282

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Problem Solving and Data Analysis/Functions

Getting to the Answer: Look for a pattern for the sales of each company. Then, apply that pattern to see which one will sell more in the last month of the year. Writing a function that represents each pattern will also help, but you have to be careful that you evaluate the function at the correct input value. Company A's sales can be represented by a linear function because each month the company sells 92 more of the toy than the month before, which is a constant difference. The sales can be represented by the function f(t) = 92 t + 54, where t is the number of months after January. December is 11 months (not 12) after January, so during the last month of the year company A should sell f(11) = 92(11) + 54 = 1,066 of the toy. Company B's sales can be represented by an exponential function because the sales are doubling each month, which is a constant ratio (2 for doubling). The function is g(t) = 15(2)t, where t is again the number of months after January. In December, company B should sell g(11) = 15(2)¹¹ = 30,720. This means that in December, company B should sell 30,720 - 1,066 = 29,654 more of the toy than company A. Choice (C) is correct.