Three machines, K, M, and P, working simultaneously and : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 04:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 5

Kudos [?]: 2322 [2] , given: 0

Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

03 Dec 2012, 02:40
2
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

75% (02:01) correct 25% (01:18) wrong based on 943 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36552
Followers: 7078

Kudos [?]: 93158 [2] , given: 10553

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

03 Dec 2012, 02:42
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
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?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that $$\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}$$.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> $$\frac{1}{m}+\frac{1}{p}=\frac{1}{36}$$, thus $$\frac{1}{k}+\frac{1}{36}=\frac{1}{24}$$ --> we can find the value of $$k$$. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> $$\frac{1}{k}+\frac{1}{p}=\frac{1}{48}$$. The value of k cannot be determined from the data we have. Not sufficient.

_________________
Senior Manager
Joined: 22 Nov 2010
Posts: 288
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 137 [0], given: 75

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

04 Mar 2013, 01:57
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.
RATE K + M + P) - RATE : (M+P) = RATE : K. SUFFICIENT
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.
RATE K + M + P) - RATE : (K+P) = RATE : M. NOT SUFFICIENT
_________________

YOU CAN, IF YOU THINK YOU CAN

Intern
Joined: 23 Oct 2012
Posts: 29
Followers: 0

Kudos [?]: 12 [0], given: 3

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

28 Nov 2013, 05:29
Bunuel 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?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that $$\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}$$.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> $$\frac{1}{m}+\frac{1}{p}=\frac{1}{36}$$, thus $$\frac{1}{k}+\frac{1}{36}=\frac{1}{24}$$ --> we can find the value of $$k$$. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> $$\frac{1}{k}+\frac{1}{p}=\frac{1}{48}$$. The value of k cannot be determined from the data we have. Not sufficient.

I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way?

Let Rk, Rm and Rp be the rates for the machines K,M and P respectively.
Then 1/Rk +1/Rm+1/Rp = 24

St 1 gives ---> 1/Rm + 1/Rp = 36

So, we get 1/Rk + 36 = 24.

Solving, 1/Rk = 24-36=-12

Why am I getting a negative value?
Math Expert
Joined: 02 Sep 2009
Posts: 36552
Followers: 7078

Kudos [?]: 93158 [0], given: 10553

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

29 Nov 2013, 09:12
audiogal101 wrote:
Bunuel 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?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that $$\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}$$.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> $$\frac{1}{m}+\frac{1}{p}=\frac{1}{36}$$, thus $$\frac{1}{k}+\frac{1}{36}=\frac{1}{24}$$ --> we can find the value of $$k$$. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> $$\frac{1}{k}+\frac{1}{p}=\frac{1}{48}$$. The value of k cannot be determined from the data we have. Not sufficient.

I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way?

Let Rk, Rm and Rp be the rates for the machines K,M and P respectively.
Then 1/Rk +1/Rm+1/Rp = 24

St 1 gives ---> 1/Rm + 1/Rp = 36

So, we get 1/Rk + 36 = 24.

Solving, 1/Rk = 24-36=-12

Why am I getting a negative value?

1/Rk, 1/Rm, and 1/Rp are the numbers of minutes machines K, M, and P take to complete the task alone. Each must be greater than the time needed for three machines to complete a certain task together (24 minutes), thus 1/Rk +1/Rm+1/Rp = 24 is not right. The same for 1/Rm + 1/Rp = 36.

Hope it's clear.
_________________
Intern
Joined: 23 Oct 2012
Posts: 29
Followers: 0

Kudos [?]: 12 [0], given: 3

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

29 Nov 2013, 21:35
Bunuel wrote:
audiogal101 wrote:
Bunuel 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?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that $$\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}$$.

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> $$\frac{1}{m}+\frac{1}{p}=\frac{1}{36}$$, thus $$\frac{1}{k}+\frac{1}{36}=\frac{1}{24}$$ --> we can find the value of $$k$$. Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> $$\frac{1}{k}+\frac{1}{p}=\frac{1}{48}$$. The value of k cannot be determined from the data we have. Not sufficient.

I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way?

Let Rk, Rm and Rp be the rates for the machines K,M and P respectively.
Then 1/Rk +1/Rm+1/Rp = 24

St 1 gives ---> 1/Rm + 1/Rp = 36

So, we get 1/Rk + 36 = 24.

Solving, 1/Rk = 24-36=-12

Why am I getting a negative value?

1/Rk, 1/Rm, and 1/Rp are the numbers of minutes machines K, M, and P take to complete the task alone. Each must be greater than the time needed for three machines to complete a certain task together (24 minutes), thus 1/Rk +1/Rm+1/Rp = 24 is not right. The same for 1/Rm + 1/Rp = 36.

Hope it's clear.

Got it. So would it be correct to say that 1/ (Rk+Rm+Rp) = 24? (since the denominator has combined rate now)?
Manager
Joined: 18 May 2014
Posts: 63
Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
Followers: 0

Kudos [?]: 12 [0], given: 6

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

18 May 2014, 09:47
st 1:

After rephrase :

n = (3^n)/9

No idea about "t". so Insufficient

St 2 :
t = 3^n

Insufficient

Combining st1 & st 2

t= 9n

Plug in few numbers to cross check is n a factor of t??

let n = 2 ; t = 9 *2 = 18

yes n is a factor of t

n= 7; t = 9*7 = 63

yes n is a factor of t

IMO C
Math Expert
Joined: 02 Sep 2009
Posts: 36552
Followers: 7078

Kudos [?]: 93158 [0], given: 10553

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

19 May 2014, 01:59
gmatkum wrote:
st 1:

After rephrase :

n = (3^n)/9

No idea about "t". so Insufficient

St 2 :
t = 3^n

Insufficient

Combining st1 & st 2

t= 9n

Plug in few numbers to cross check is n a factor of t??

let n = 2 ; t = 9 *2 = 18

yes n is a factor of t

n= 7; t = 9*7 = 63

yes n is a factor of t

IMO C

I think this post is about some other question.
_________________
Chat Moderator
Joined: 19 Apr 2013
Posts: 748
Concentration: Strategy, Healthcare
Schools: Sloan '18 (A)
GMAT 1: 730 Q48 V41
GPA: 4
Followers: 14

Kudos [?]: 166 [0], given: 537

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

05 Apr 2015, 07:22
Bunuel, does wording seem confusing for you, too? When it writes independently it seems they work separately with the same rate.
_________________

If my post was helpful, press Kudos. If not, then just press Kudos !!!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13444
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Three machines, K, M, and P, working simultaneously and [#permalink]

### Show Tags

18 Apr 2016, 20:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Three machines, K, M, and P, working simultaneously and   [#permalink] 18 Apr 2016, 20:47
Similar topics Replies Last post
Similar
Topics:
3 Three machines, K, M, and P, working simultaneously and 3 01 Jun 2012, 20:01
4 If two copying machines work simultaneously at their 4 28 Jan 2012, 03:01
5 Three machines, K, M, and P, working simultaneously and 8 04 Sep 2011, 08:45
1 If two copying machines work simultaneously at their 3 08 Sep 2010, 10:40
21 If two copying machines work simultaneously at their 16 08 Sep 2009, 11:35
Display posts from previous: Sort by