swerve wrote: ↑

Mon Feb 22, 2021 2:55 pm

In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of \(q\) units of product Y. Which of the following CANNOT be the difference between product Y's sale price and cost per unit?

A. $3
B. $4
C. $7
D. $11
E. $51

The OA is D

Solution:

The difference between Product Y’s sale price and cost per unit is the profit per unit. Notice that the profit for the first week of last month, in dollars, is 5304 x 7. Assuming each unit has a profit of a whole number of dollars, we see that q must be a factor of 5304 x 7. So let’s prime factorize 5304 x 7:

5304 x 7 = 4 x 1326 x 7 = 2^2 x 2 x 663 x 7 = 2^3 x 3 x 221 x 7 = 2^3 x 3 x 13 x 17 x 7

Looking at the answer choices, we see that A) 3, B) 7, C) 4 = 2^2, and E) 3 x 17 = 51 are factors of 5304 x 7. However, D) 11 is not. Therefore, 11 is the correct answer.

Answer: D