Working together, Michelle and John can type a manuscript in 60 hours. How long does it take Martha and Jeff, working together, to type the same manuscript? (1) Michelle types 60 words per minute and John types 40 words per minute. (2) Martha types 30 words per minute and Jeff types 80 words per minute.

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.

---------- I might be reading the problem wrong but it seems like the question is asking how long it takes Martha and Jeff, working together, to type the manuscript. #2 clearly gives you enough information to answer the question, if they are the only two people. Please let me know if I am reading the question wrong.

Post subject: Re: Math: test 4, question 27 (Data sufficiency, work/rate)

Posted: Sat Apr 24, 2010 9:43 am

Joined: Fri Apr 09, 2010 2:11 pm Posts: 454

You were reading question all right, but don't rush too quickly. Be attentive to information you need to answer the question and information you have using each additional statement by itself.

Yes, the question is asking how long it takes Martha and Jeff, working together, to type the manuscript. Statement (2) gives us rates for Martha and Jeff but we still do not know what the volume of the manuscript is. It can be 360 000 words, or 100 000 words, or any other number - we have no information about the size of the manuscript. So statement (2) alone is not sufficient.

Let's go over the solution again, step by step.

First, we read basic question statement:"Working together, Michelle and John can type a manuscript in 60 hours. How long does it take Martha and Jeff, working together, to type the same manuscript?".

What we need to do right away is to clearly state what needs to be found. "The time it takes Martha and Jeff to complete the manuscript." We should always keep that in mind while solving.

Secondly, we should "make a list" of all the facts we know from the basic statement. In this case the fact is only one:

- Michelle and John, working together, complete a manuscript in 60 hours.

After we finished analyzing the basic statement we need to ask ourselves a question "What are the simplest facts (most direct ones) we need to know to find the required time?". The answer to this question in this case is "Since work = rate × time, we need to know the rate of Martha and Jeff, working together, and volume of the work (volume of the manuscript). Knowing that we will be able to find the time."

Basic statement doesn't give any facts about Martha and Jeff, or volume of the manuscript.

Let's consider Statement (1): "Michelle types 60 words per minute and John types 40 words per minute." It gives us two facts: - Michelle's rate is 60 words/minute - John's rate is 40 words/minute We also can find rate of Michelle and John, working together, it is 100 words/minute.

Let's add fact from original statement and see what we have altogether: - Michelle and John can type a manuscript in 60 hours - Michelle's rate is 60 words/minute - John's rate is 40 words/minute We also can find rate of Michelle and John, working together, it is 100 words/minute.

From these facts, using formula work = rate × time we can find the volume of the manuscript: volume of the manuscript = [rate of Michelle and John working together] × [time it takes Michelle and John, working together, to complete the manuscript]

volume of the manuscript = 100 words/minute × 60 hours Be careful with units! 100 words/minute = (100 × 60) words/hour so volume of the manuscript = 6 000 words/hour × 60 hours = 360 000 words

Using statement one we have found the volume of the manuscript, but we have no information about the rates of Martha and Jeff. For example, the rate, if they work together, could be 6 000 words/hour or 3 000 words/hour. In first case it would take them 60 hours to complete the manuscript, in the second case - 120 hours. So Statement (1) alone is not sufficient.

Let's consider Statement (2): "Martha types 30 words per minute and Jeff types 80 words per minute."

It gives us two facts: - Martha's rate is 30 words/minute - Jeff's rate is 80 words/minute We also can find rate of Martha and Jeff, working together, it is 110 words/minute.

Let's add fact from original statement and see what we have altogether: - Michelle and John can type a manuscript in 60 hours - Martha's rate is 30 words/minute - Jeff's rate is 80 words/minute We also can find rate of Martha and Jeff, working together, it is 110 words/minute.

We know the rate of Martha and Jeff, working together, but we know nothing about the volume of the manuscript. It can be 110 000 words and the required time would be 1000 minutes, or it can be 220 000 words and the required time would be 2000. So statement (2) by itself is also insufficient.

Let's combine all the statements and see what facts we have:

- Michelle and John can type a manuscript in 60 hours - Michelle's rate is 60 words/minute - John's rate is 40 words/minute We also can find rate of Michelle and John, working together, it is 100 words/minute. - Martha's rate is 30 words/minute - Jeff's rate is 80 words/minute We also can find rate of Martha and Jeff, working together, it is 110 words/minute.

As we already know we can find the volume of the manuscript and rate of Martha and Jeff, working together. The required time = 360 000 words / (110 × 60) words/hour. So these facts are sufficient to find the required time. Therefore choice (C) is the right one.

Note, that you do not need to make actual calculations if you see they can be done using facts. You do not need to find the actual numbers but to assure there are enough facts to find what is required.

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