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For a basic monthly fee of F yen (¥F), Naoko’s first cell phone plan allowed him to use a maximum of 420 minutes on calls during the month. Then, for each of x additional minutes he used on calls, he was charged ¥M, making his total charge for the month ¥T, where T = F + xM. What is the value of F ?


1. Naoko used 450 minutes on calls the first month and the total charge for the month was

¥13,755.

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


    A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    D. EACH statement ALONE is sufficient.

    E. Statements (1) and (2) TOGETHER are NOT sufficient.


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答案:
B
="font-size: 14px;">Algebra Simultaneous Equations

1. Given that Naoko used 450 minutes and was charged ¥13,125, it follows that F + (450 − 420)M = 13,755, or F + 30M = 13,755. However, the value of F cannot be determined. For example, F = 13,005 and M = 25 is possible, and F = 13,035 and M = 24 is possible; NOT sufficient.

2. Given that Naoko used 400 minutes and was charged ¥13,125, it follows that F = 13,125, since Naoko did not use more than 420 minutes; SUFFICIENT.

 

The correct answer is B; 
statement 2 alone is sufficient.


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