• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

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

This topic has 4 expert replies and 5 member replies
factor26 Senior | Next Rank: 100 Posts
Joined
13 Mar 2011
Posted:
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!

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
samirpassi Guest
Wed Mar 21, 2012 6:48 am
I totally agree with your explanation. Now I see the trouble with my approach.

Danny@GMATAcademy Junior | Next Rank: 30 Posts
Joined
28 Jun 2016
Posted:
24 messages
Followed by:
3 members
8
GMAT Score:
780
Wed Jan 11, 2017 8:07 am
A couple of ways to solve this question:

Logic/Time-Formula approach:

Rates/Algebra approach:

_________________

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

Danny@GMATAcademy Junior | Next Rank: 30 Posts
Joined
28 Jun 2016
Posted:
24 messages
Followed by:
3 members
8
GMAT Score:
780
Wed Jan 11, 2017 8:07 am
A couple of ways to solve this question:

Logic/Time-Formula approach:

Rates/Algebra approach:

_________________

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
625
Target GMAT Score:
V51
GMAT Score:
780
Wed Jan 18, 2017 6:09 pm
Not a great idea to revive five year old topics unless students are asking about them, IMHO

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
Followed by:
3 members
43
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.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

moneyball29 Junior | Next Rank: 30 Posts
Joined
24 Feb 2012
Posted:
12 messages
Followed by:
1 members
2
GMAT Score:
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
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.

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13608 messages
Followed by:
1796 members
13060
GMAT Score:
790
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.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Thanked by: factor26
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### Best Conversation Starters

1 lheiannie07 116 topics
2 LUANDATO 67 topics
3 swerve 66 topics
4 ardz24 61 topics
5 AAPL 59 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

213 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

177 posts
3 Jeff@TargetTestPrep

Target Test Prep

168 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

133 posts
5 GMATGuruNY

The Princeton Review Teacher

126 posts
See More Top Beat The GMAT Experts