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If r and t are three-digit positive integers, is r greater than t ?

1. The tens digit of r is greater than each of the three digits of t.

2. The tens digit of r is less than either of the other two digits of r.


    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:
C
<="" div="">="font-size: 14px;">Arithmetic Properties of Numbers


1. Each of the examples below are such that the tens digit of r (equal to 4 in both examples) is greater than each of the three digits of t.

Example I: r = 242 and t = 222. Example II: r = 242 and t = 333.

Note that r is greater than t in Example I and r is not greater than t in Example II; NOT

sufficient.

2. Given that the tens digit of r is less than either of the other two digits of r, there is no information about the three-digit integer t ; NOT sufficient.

 

Taking (1) and (2) together, the hundreds digit of r is greater than the tens digit of r by (2) and the tens digit of r is greater than the hundreds digit of t by (1). Therefore, the hundreds digit of r is greater than the hundreds digit of t and it follows that r is greater than t.

 

The correct answer is C;

both statements together are sufficient.


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