Rate Problems: Plugging in Rate Problems - Work as an Invisible Variable

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 sidewalk was one-third painted, it would have taken Donna 8 hours to finish painting the sidewalk by herself. >(2) If Donna, by herself, were to paint two sidewalks identical to the original, it would take 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. [[snippet]] 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. [[snippet]] Stat. (2) allows you to find Donna's rate, which in turn allows you to find Michael's rate, therefore **Stat.(2) → S → BD**. But what about Stat. (1)?

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Correct. [[snippet]] Stat. (1) provides data regarding Donna's rate, enabling you to get Michael's rate. Remember that you don't need to actually find Donna's rate, just that you have the ability to. If the size of the sidewalk was 60, then there was 40 left when Michael left, giving you two values in the equation: $$\text{Rate} \times \text{Time} = \text{Work} \rightarrow \text{Rate} \times 8 = 40$$ Therefore, **Stat.(1) → S → AD**. Stat. (2) does the same. 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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