Multiple choice

Directions: The question below consists of a question and two statements, labeled (1) and (2), in which certain data is given. Decide whether the data given in the statements is sufficient for answering the question. Using the data provided in the statements and knowledge of mathematics and everyday facts, mark the following: If Andy and Sandy, working together, can paint a house in 5 days, can Andy paint the same house in 8 days? 1. Andy is faster than Sandy. 2. Sandy can paint the same house in 10 days.

  1. If statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question

  2. If statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question

  3. If both statements (1) and (2) together are sufficient to answer the question, but neither statement alone is sufficient

  4. If each statement alone is sufficient to answer the question

  5. If statements (1) and (2) together are not sufficient to answer the question and an additional data, that is specific to the problem, is needed
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and S be the rates of Andy and Sandy. 1/A + 1/S = 1/5. Statement 2 says S = 1/10. Substituting this: 1/A + 1/10 = 1/5 => 1/A = 1/10 => A = 10. So Andy takes 10 days, not 8. Statement 2 is sufficient to answer the question (the answer is no). Statement 1 is not sufficient as it only gives a relative comparison.

AI explanation

The question asks to determine if Andy takes exactly 8 days to paint the house alone, which requires knowing either Andy's exact work rate or Sandy's. Statement 1 only says Andy is faster than Sandy, which does not provide the exact numerical work rates needed to answer the question. Statement 2 provides Sandy's time of 10 days, so using the combined work rate of 1/5, Andy's rate is 1/5 minus 1/10, which equals 1/10, proving Andy takes 10 days rather than 8. Therefore, statement 2 alone is sufficient to answer the question, but statement 1 alone is not.

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