For a basic monthly fee of F yen, Noak's first cell phone allowed him

We are given T = F + xM, in which T = the total charge for the month, F = the monthly fee, x = the excess minutes over 420, and M = the amount charged for each of the x additional minutes.

Statement One Alone:

Naoko used 450 minutes on calls the first month, and the total charge for the month was 13,755 yen.

Using the information in statement one, we can determine that Naoko used 30 excess minutes beyond the 420 minutes allowed by the basic monthly fee, so we can create the following equation:

13,755 = F + 30M

However, since we don’t know the value of F, we do not have enough information to determine the value of M. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Naoko used 400 minutes on calls the second month and the total charge for the month was 13,125 yen.

Since 400 < 420, we know that 13,125 yen must be the basic monthly free. That is,

13,125 = F

However, we still do not have enough information to determine the value of M. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we have the following equations:

13,755 = F + 30M

AND

13,125 = F

Thus, we have:

13,755 = 13,125 + 30M

630 = 30M

21 = M

Answer: C