Data Sufficiency: The Question Stem - What is the Issue?
Working together without taking breaks, Michael and Donna painted the sidewalk in 6 hours. How long would it take Michael to paint the sidewalk by himself?
>(1) If Michael had left when the job was one-third done, it would have taken Donna 8 hours to finish the job by herself.
>(2) If Donna had to paint two identical sidewalks by herself, it would have taken her 24 hours to finish.
Remember, you don't need to arrive at a numerical answer in a data sufficiency problem. Just figure out if it can be solved. If you did want to see the calculations, here they are quickly:
Let's say the sidewalk is 60 feet long. The first sentence of the question stem says that the combined rate is 60 feet/6 hours, or 10 feet per hour. The combined rate is just the sum of the rates, so if you find Donna's rate, you can get Michael's rate by subtraction.
>For Stat. (1), when Michael leaves, 40 feet remain. It takes Donna 8 hours to finish. Her rate is $$\frac{40}{8} = 5$$ feet/hour. So Michael's rate is $$10 - 5 = 5$$ feet/hour.
>For Stat. (2), if Donna paints 120 feet of sidewalk, it takes her 24 hours to finish. Her rate is $$\frac{120}{24} = 5$$ feet/hour. So Michael's rate is $$10 - 5 = 5$$ feet/hour.
Incorrect.
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Stat. (1) provides data regarding Donna's rate, enabling you to get Michael's rate. Therefore, **Stat.(1) → S → AD**.
But what about Stat. (2)? Does it allow you to find Michael's rate as well?
Incorrect.
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Stat. (2) allows you to find Donna's rate, with a small twist from GMAC Land, which in turn allows you to find Michael's rate, therefore **Stat.(2) → S**.
But what about Stat. (1)?
Incorrect.
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Incorrect.
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Correct.
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Stat. (1) provides data regarding Donna's rate, enabling you to get Michael's rate. Therefore, **Stat.(1) → S → AD**.
Stat. (2) does the same, only with a small twist from GMAC land. Therefore, **Stat.(2) → S → D**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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