AAPL wrote:Veritas Prep

Mr. McCall selects a number that is two-digit and positive. If the number is prime, he assigns that many problems for homework. If the number is not prime, he assigns 8 more problems than the number for homework. If he assigns 97 problems for homework, which of the following could be the number he selected?

I. 89
II. 97
III. 105

A. I only
B. I and II only
C. II only
D. II and III only
E. I and III only

OA C

Since 97 is a prime, he could have selected 97 and thus assigned 97 problems for homework.

He could also have selected a composite number (i.e., number that is not a prime) and assigned 97 problems for homework. To do so, let's let x be the composite number he has selected, and thus we have:

x + 8 = 97

x = 89

However, 89 is not composite (89 is a prime), so he couldn't have selected the number 89. Lastly, he couldn't have selected 105, since 105 is not a two-digit number.

Answer: C