Multiple choice

What is Rick’s age now? 1) Ricky is now twice as old as he was exactly 8 years ago. 2) Ricky’s sister Teresa is now 3 times as old as Ricky was exactly 8 years ago.

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

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

  3. Both statements (1) and (2) TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient.

  4. Each statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are not sufficient to answer the question, and additional data is required.
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A Correct answer
Explanation

Statement 1 gives the equation R = 2(R - 8), which uniquely solves to R = 16, making it sufficient. Statement 2 introduces a second variable for Teresa's age, T = 3(R - 8), which cannot be solved for R without additional information, making it insufficient.

AI explanation

Let Ricky's current age be R. Statement (1) provides the equation R = 2(R - 8), which simplifies to R = 16, proving his current age can be found using this statement alone. Statement (2) gives Teresa's age in terms of Ricky's past age but provides no information to determine the absolute value of Ricky's age without additional data. Because the first statement yields a single numerical value and the second does not, statement (1) alone is sufficient.

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