Digital PSAT Math Practice Question 275: Answer and Explanation

Question: 275

The costs of packages of generic brand soda, G, and name brand soda, N, at a grocery store are directly proportional to each other. If the relationship between the two is modeled by the equation N = 2G, where 2 represents the constant of proportionality, which of the following statements would be true?

• A. The name brand soda is twice as expensive as the generic soda.
• B. The name brand soda is half as expensive as the generic soda.
• C. The prices of the generic and name brand sodas are equivalent.
• D. The average number of packages sold of the generic brand soda is twice that of the name brand.

Correct Answer: A

Explanation:

(A) You can determine the answer by assigning particular values to G. For instance, suppose the generic brand soda costs $1 (i.e., G = 1). Since N = 2G, it follows that N = 2(1) = 2. Thus, the name brand soda is twice as expensive as the generic brand. Similarly, trying other values for G, you always multiply G by 2 to find N, so N is always twice the cost of G, or choice (A).