Data Sufficiency

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!

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

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!

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.

The correct answer is A.

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
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!

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.

The correct answer is A.

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.

Shouldn't the answer be D?

Please explain. Thanks.

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.

A couple of ways to solve this question:

Logic/Time-Formula approach:

https://www.youtube.com/watch?v=8OGY5xcYqDM

Rates/Algebra approach:

https://www.youtube.com/watch?v=B2PAbu157fw

Not a great idea to revive five year old topics unless students are asking about them, IMHO