What is the two-digit positive integer whose tens digit is a and whose units digit is b? (1) 2a > 3b > 6 (2) a > 2b > 6

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(B) Statement (1) is not sufficient because there are many 2-digit numbers that satisfy the inequality given in Statement (1). For example, both 63 and 53 are possible numbers for ab. For 63, 2(6) > 3(3) > 6 For 53, 2(5) > 3(3) > 6. So Statement (1) is not sufficient by itself.

Statement (2) is sufficient by itself. For 2b to be greater than 6, b must be greater than 3. However, b cannot be 5 or greater, because 2b would then be greater than 10, which is impossible because a is a digit.

Therefore, b must be 4, and a must be 9, and the number ab must be 94.

Since Statement (1) is not sufficient, and Statement (2) is sufficient, the correct answer is choice (B). ---------- This does not explain why Statement 2 tells us that a = 9. If b = 4, then the statement merely suggests that 2(4) < 3a, so 8/3 < a, which only tells us that a can be anything between 3 and 9 (the same thing as 6 < 3a).

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