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Andy, George and Sally are a team of consultants

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by conquistador » Tue Oct 13, 2015 4:48 am
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Andy, George and Sally are a team of consultants working on Project Alpha. They have an eight hour deadline to complete the project. The team members work at constant rates throughout the eight hour period. If the team of three has to begin work now and no one else can work on this project, will Project Alpha be completed by the deadline?


(1) Sally can finish the project alone in 4k+7 hours, where k is a positive integer with a minimum value of 1 and a maximum value of 5.

(2) Working alone, George will take 2k+1 hours and Andy will take 3+2k hours, where k is a positive integer with a minimum value of 1 and a maximum value of 5

OA B
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by [email protected] » Tue Oct 13, 2015 8:47 am
Hi Mechmeera,

As complex-looking as this prompt might appear, it's just a Work Formula question, and can be dealt with using the Work Formula and TESTing VALUES.

Work = (A)(B)/(A+B) where A and B are the individual times it takes two entities to complete a task.

We're told that 3 people - Andy, George and Sally are going to work on a task together. We're told that each works at a constant rate for 8 hours. We're asked if the project will be completed in 8 hours. This is a YES/NO question.

At first glance, you might think that you need to know the rates for all 3 people to answer the question, but the prompt is NOT asking how long it took the three of them to complete the job - it's asking IF they completed the job in 8 hours....

1) Sally can finish the project alone in 4k+7 hours, where k is a positive integer with a minimum value of 1 and a maximum value of 5.

IF....
K = 1, then it takes Sally 11 hours to complete the job by herself. If K is HIGHER, then it takes Sally LONGER to complete the job. Without any information about how long it takes Andy and George, there's no way to know if the job was completed in 8 hours or not.
Fact 1 is INSUFFICIENT

2) Working alone, George will take 2k+1 hours and Andy will take 3+2k hours, where k is a positive integer with a minimum value of 1 and a maximum value of 5.

This Fact is interesting - it gives us information on 2 of the workers. MAYBE these 2 could complete the job on their own in 8 hours (and Sally's rate wouldn't matter).....

The LONGEST amount of time would be if K=5, so let's start there...

IF...
K = 5, then it takes George 11 hours and Andy 13 hours to complete the job individually. Working together, that would be...

(11)(13)/(11+13) hours...
143/24 hours =
LESS than 6 HOURS

Since Andy and George could complete the job on their own in less than 6 hours, any work that Sally does would decrease the total time spent working. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

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by Matt@VeritasPrep » Wed Oct 14, 2015 11:05 pm
We know that Work = Rate * Time. Let's say that Andy, George, and Sally have rates a, g, and s, respectively.

If we knew all three rates, we could say that

Work = (a + g + s) * t

or, since we only have one job (i.e. Work = 1),

1 = (a + g + s) * t

We can isolate t:

1/(a + g + s) = t

We want to know if t ≤ 8, so the question is really

"Is 1/(a + g + s) ≤ 8?", or

"Is 1/8 ≤ (a + g + s)?"

S1 tells us s can be any of 1/(4*1+7), 1/(4*2+7), ..., 1/(4*5+7). None of these is greater than 1/8 on its own, so we still need to know about a and g: NOT SUFFICIENT.

S2 is trickier. Since we have a lot of cases to work with, let's start with the LARGEST k, or the SLOWEST time. If this gives us something over 1/8, we're done: any of the others (all of which represent faster rates, i.e. less time) will be fine.

If k = 5, we have George's rate = 1/11 and Andy's rate = 1/13. Since 1/16 + 1/16 ≥ 1/8, and 1/11 + 1/13 ≥ 1/16 + 1/16, we know this is big enough, and statement 2 is SUFFICIENT.

Great question!
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