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## Three machines, K, M, and P, working simultaneously

This topic has 4 expert replies and 5 member replies
factor26 Senior | Next Rank: 100 Posts
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99 messages

#### Three machines, K, M, and P, working simultaneously

Wed Dec 07, 2011 5:58 pm
Three machines, K, M, and P, working simultaneously
and independently at their respective constant rates,
can complete a certain task in 24 minutes. How long
does it take Machine K, working alone at its constant

(1) Machines M and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 36 minutes.

(2) Machines K and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 48 minutes.

OG answer is A ... can someone shed some light on how to solve this problem? thanks!

Danny@GMATAcademy Junior | Next Rank: 30 Posts
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Wed Jan 11, 2017 8:07 am
A couple of ways to solve this question:

Logic/Time-Formula approach:

Rates/Algebra approach:

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Scott@TargetTestPrep GMAT Instructor
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Mon Jan 16, 2017 5:01 pm
factor26 wrote:
Three machines, K, M, and P, working simultaneously
and independently at their respective constant rates,
can complete a certain task in 24 minutes. How long
does it take Machine K, working alone at its constant

(1) Machines M and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 36 minutes.

(2) Machines K and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 48 minutes.
We are given that machines K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. If we consider the entire task to be equal to 1, and the time in minutes for machines K, M, and P to complete the task to be k, m, and p, respectively, then the rates of machines K, M, and P are:

1/k = rate of machine K to complete the task

1/m = rate of machine M to complete the task

1/p = rate of machine P to complete the task

Since it takes machines K, M, and P, working simultaneously and independently, 24 minutes, the combined rate of machines K, M, and P is 1 task per 24 minutes. That is:

1/k + 1/m + 1/p = 1/24

We need to determine how long it takes machine K to complete the task, or in other words, the value of k. Since 1/k + 1/m + 1/p = 1/24, the rate of machine K is:

1/k = 1/24 - 1/m - 1/p

1/k = 1/24 - (1/m + 1/p)

Thus, if we can determine the value of (1/m + 1/p), we can determine the value of 1/k and hence the value of k.

Statement One Alone:

Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.

From statement one we know:

1/m + 1/p = 1/36

Thus, the rate for machine K to complete the task is 1/24 - 1/36 = 3/72 - 2/72 = 1/72, and therefore, the time for machine K to complete the task is 72 minutes.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.

From statement two we know:

1/k + 1/p = 1/48

Since we donâ€™t know the value of p, this is not enough information to determine the value of k.

Statement two alone is not sufficient to answer the question.

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Scott Woodbury-Stewart Founder and CEO

chufus Master | Next Rank: 500 Posts
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Wed Dec 07, 2011 6:19 pm
Here is the thing. Always remember that rates are additive. Lets rework the original statement.

Let Rate of K be = 1/K
Let rate of M be = 1/M
Let rate of N be = 1/N

We are assuming here that the complete job = 1 . It will work for all positive number. You can take 10 or 100 if you like. When we set the equation up, you will see it does not matter. So we know that together to complete the One job it takes 24 minutes. So rate of K, M and N would add up to 1/24.

So:

1/k+1/m+1/n = 1/24

Now lets look at our statement.

A. It gives us the value of (1/m + 1/n) = 1/36

Substitute it in the equation and solve for 1/k = 72

SUFFICIENT

B. its gives us the value of (1/k+1/p)

We still can't solve for 1/k

INSUFFICIENT

Pick A

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Anurag@Gurome GMAT Instructor
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Wed Dec 07, 2011 7:05 pm
factor26 wrote:
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

(1) Machines M and P, working simultaneously and independently at their respective constant rates,
can complete the task in 36 minutes.

(2) Machines K and P, working simultaneously and independently at their respective constant rates,
can complete the task in 48 minutes.

OG answer is A ... can someone shed some light on how to solve this problem? thanks!
The question body says that 1 minute task of 1/K + 1/M + 1/P = 1/24...Equation 1
We have to find 1/K

(1) 1/M + 1/P = 1/36
Put the above value in equation 1, 1/K + 1/36 = 1/24, we can find the value of 1/K from here; SUFFICIENT.

(2) 1/K + 1/P = 1/48, but we cannot find 1/K from this; NOT sufficient.

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Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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GMATGuruNY GMAT Instructor
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Thu Dec 08, 2011 9:09 am
factor26 wrote:
Three machines, K, M, and P, working simultaneously
and independently at their respective constant rates,
can complete a certain task in 24 minutes. How long
does it take Machine K, working alone at its constant

(1) Machines M and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 36 minutes.

(2) Machines K and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 48 minutes.

OG answer is A ... can someone shed some light on how to solve this problem? thanks!
Let the task = 72 units.
Rate for K+M+P = w/t = 72/24 = 3 units per minute.
In order to determine K's time to complete the task alone, we need to know K's rate.

Question rephrased: What is K's rate?

Statement 1: M+P = 36 minutes.
Rate for M+P = w/t = 72/36 = 2 units per minute.
Since K+M+P = 3 units per minute, and M+P = 2 units per minute, K = 1 unit per minute.
SUFFICIENT.

Statement 2: K+P = 48 minutes.

The time for K+P enables us to determine the rate for K+P and thus the rate for M.
No way to determine K's rate.
INSUFFICIENT.

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samirpassi Guest
Tue Mar 06, 2012 7:39 am
GMATGuruNY wrote:
factor26 wrote:
Three machines, K, M, and P, working simultaneously
and independently at their respective constant rates,
can complete a certain task in 24 minutes. How long
does it take Machine K, working alone at its constant

(1) Machines M and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 36 minutes.

(2) Machines K and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 48 minutes.

OG answer is A ... can someone shed some light on how to solve this problem? thanks!
Let the task = 72 units.
Rate for K+M+P = w/t = 72/24 = 3 units per minute.
In order to determine K's time to complete the task alone, we need to know K's rate.

Question rephrased: What is K's rate?

Statement 1: M+P = 36 minutes.
Rate for M+P = w/t = 72/36 = 2 units per minute.
Since K+M+P = 3 units per minute, and M+P = 2 units per minute, K = 1 unit per minute.
SUFFICIENT.

Statement 2: K+P = 48 minutes.

The time for K+P enables us to determine the rate for K+P and thus the rate for M.
No way to determine K's rate.
INSUFFICIENT.

I understand your reasoning but taking it forward, the initial data tells us that:
1/k + 1/m + 1/p = 72/24 = 3 units

Choice-1:
Yes, pretty clear you can solve for K's rate.

Choice-2:
It is true that you cannot use simply this to get the value of K. However, what if you do it in the following way:
Step-1: Plug this into main given equation (1/k + 1/m + 1/p) and get the value of m.
Step-2: Substitute P in terms of K, in the main equation and plug in the value of m received from Step-1.
Step-3: Get the value of K.

moneyball29 Junior | Next Rank: 30 Posts
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690
Mon Mar 12, 2012 2:16 am
samirpassi wrote:
GMATGuruNY wrote:
factor26 wrote:
Three machines, K, M, and P, working simultaneously
and independently at their respective constant rates,
can complete a certain task in 24 minutes. How long
does it take Machine K, working alone at its constant

(1) Machines M and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 36 minutes.

(2) Machines K and P, working simultaneously and
independently at their respective constant rates,
can complete the task in 48 minutes.

OG answer is A ... can someone shed some light on how to solve this problem? thanks!
Let the task = 72 units.
Rate for K+M+P = w/t = 72/24 = 3 units per minute.
In order to determine K's time to complete the task alone, we need to know K's rate.

Question rephrased: What is K's rate?

Statement 1: M+P = 36 minutes.
Rate for M+P = w/t = 72/36 = 2 units per minute.
Since K+M+P = 3 units per minute, and M+P = 2 units per minute, K = 1 unit per minute.
SUFFICIENT.

Statement 2: K+P = 48 minutes.

The time for K+P enables us to determine the rate for K+P and thus the rate for M.
No way to determine K's rate.
INSUFFICIENT.

I understand your reasoning but taking it forward, the initial data tells us that:
1/k + 1/m + 1/p = 72/24 = 3 units

Choice-1:
Yes, pretty clear you can solve for K's rate.

Choice-2:
It is true that you cannot use simply this to get the value of K. However, what if you do it in the following way:
Step-1: Plug this into main given equation (1/k + 1/m + 1/p) and get the value of m.
Step-2: Substitute P in terms of K, in the main equation and plug in the value of m received from Step-1.
Step-3: Get the value of K.

The best way that I know how to explain it, and someone more knowledgeable can correct me if I'm wrong, is to compare it to the question in which you're trying to find the value of one of the three angles inside of a triangle. I believe the scenario is exactly the same, but the math makes a bit more sense

For example:

There are three angles inside a triangle, X Y and Z. What is the value of angle Z?

1) X + Y = 108

2) Y + Z = 108

So you'd obviously set up the equation X + Y + Z = 180, right?

So The first statement gives you the value of X + Y, which you substitute in and get the value of 72 for Z, which is SUFFICIENT

But for the second statement, I tried to do the same thing as you the first time I saw this question. This is how I worked it out:

X + Y + Z = 180 again.
Then this time, X = 72, right?
Also, as you did with the machines question, I took the second statement and rearranged it so that Y is in terms of Z, like so:

Y = 108 - Z

I then combined these equations:

72[which is X] + (108 - Z)[which is Y] + Z = 180

If we simplify this down, we get

180 - Z + Z = 180

180 = 180

When I finally started to understand it was when I thought about it logically. The triangle question gave us no constraints on what type of triangle it is, so as much as we'd like to be able to rearrange expressions and plug them back in to find the answer, the fact remains that Z in statement two is some part of that 108 degrees, and we simply do not have the requisite information necessary to deduce what that angle is.

From what I can tell, the situation with the 3 machines is exactly the same. Unless they give you the combined rate along with the rates of the other 2 machines besides K (as they do in statement 1), there is no way to solve it. In statement 1, K can only be the third part of the equation that makes the final task complete in 24 minutes. In statement two, it could be either of the two rates that add up to 48, and there is no way to deduce how that 48 is broken down.

Being able to solve it could be as simple as them adding the stipulation "and K works twice as fast as P" to statement 2, but what they give us just isn't enough to go on.

As I said before, if I'm wrong, hopefully someone will correct me, but I believe these problems go hand in hand, and I've seen the same concept phrased many different ways in my studying.

samirpassi Guest
Wed Mar 21, 2012 6:48 am
I totally agree with your explanation. Now I see the trouble with my approach.

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Matt@VeritasPrep GMAT Instructor
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Wed Jan 18, 2017 6:09 pm
Not a great idea to revive five year old topics unless students are asking about them, IMHO

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