GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2019, 19:16 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Machine M, N, O working simultaneously Machine M can produce

Author Message
TAGS:

### Hide Tags

Manager  Status: mba here i come!
Joined: 07 Aug 2011
Posts: 182
Machine M, N, O working simultaneously Machine M can produce  [#permalink]

### Show Tags

3
10 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:43) correct 32% (02:45) wrong based on 250 sessions

### HideShow timer Statistics

Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

Spoiler: :: Solution
N produces x units in ‘t’
M produces x units in ¾ t
O produces x units in 3/2t

In 1 minute total units produced by M,N,O working together = 1/t + 4/3t + 2/3t = 3/t
Ratio of work done by N in 1 minute = (1/t) / (3/t) = 1/3
This ratio will be the same no matter how long M, N, O work together.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9874
Location: Pune, India
Re: machines m,n,o working simaltaneously  [#permalink]

### Show Tags

11
2
MBAhereIcome wrote:
Machine M,N,O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

Think in terms of ratios for a quick clean solution.
Time taken by M : time taken by N = 3:4
So speed of M : speed of N = 4:3
Similarly, speed of N:speed of O = 3:2
Speed of M: Speed of N : Speed of O = 4:3:2
So N will produce 3/(2+3+4) = 1/3rd of the output
_________________
Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Intern  Status: GMAT - A logic game! Enjoy it!!
Joined: 19 Apr 2011
Posts: 7
Re: machines m,n,o working simaltaneously  [#permalink]

### Show Tags

1
MBAhereIcome wrote:
Machine M,N,O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

Spoiler: :: Solution
N produces x units in ‘t’
M produces x units in ¾ t
O produces x units in 3/2t

In 1 minute total units produced by M,N,O working together = 1/t + 4/3t + 2/3t = 3/t
Ratio of work done by N in 1 minute = (1/t) / (3/t) = 1/3
This ratio will be the same no matter how long M, N, O work together.

Okieee..

Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4

Mach O makes x units in 12 hrs
So, Mach N = 2/3 of O = 2/3*12 = 8 hrs to make x units
and Mach M = 3/4 of N = 3/4*8 = 6 hrs to make x units

No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = x/8 units
Mach M = x/6 units

In 1 hr, together they make - x/12+x/8+x/6 = 3x/8
So what ratio of this has Mach N made?

(x/8) / (3x/8) = 1/3

Ans: B=1/3
Manager  Joined: 21 Aug 2010
Posts: 161
Location: United States
GMAT 1: 700 Q49 V35 Re: machines m,n,o working simaltaneously  [#permalink]

### Show Tags

1
Work done by O = 1/O
Work Done by N = 1/N = 1/(2/3)O = 3/2O

Work done by M = 1/M = 1/(3/4)N = 1/(3/4)(3/2O) = 12 /6 O = 2 /O

Worn done y N = 1/O + 3/2 O + 2/O = 2 + 3 + 4 / 2O = 9 /2O
= 1/3 part of whole work done
_________________
-------------------------------------
Senior Manager  B
Joined: 11 May 2011
Posts: 284
Re: machines m,n,o working simaltaneously  [#permalink]

### Show Tags

@MBAhereIcome - Kudos to you for this excellent question.

_________________
-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------
Intern  Joined: 06 Nov 2011
Posts: 34
Location: Germany
Concentration: Entrepreneurship, General Management
GMAT Date: 03-10-2012
GPA: 3
Re: machines m,n,o working simaltaneously  [#permalink]

### Show Tags

Let O --> T = 12 hours to finish the job
Let N --> $$N = \frac{2}{3}*T = 8$$ hours the job
Let M --> $$M = \frac{3}{4}*\frac{2}{3} * T = 6$$ hours to finish the job
Combine their rates: $$\frac{1}{6}+\frac{1}{8}+\frac{1}{12} = \frac{3}{8}$$ Rate to finish one job together
We are looking for the fraction of N on the whole output.
Rate of N is $$\frac{1}{8}$$, multiply it with the total time of all machines $$*\frac{8}{3} = \frac{1}{3}$$

Hope its correct. Took me 10 minutes Intern  Joined: 01 Dec 2010
Posts: 2
Re: machines m,n,o working simaltaneously  [#permalink]

### Show Tags

I know we are supposed to say thank you by just pressing kudos but I must add here that your methods are very efficient.

VeritasPrepKarishma wrote:
MBAhereIcome wrote:
Machine M,N,O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

Think in terms of ratios for a quick clean solution.
Time taken by M : time taken by N = 3:4
So speed of M : speed of N = 4:3
Similarly, speed of N:speed of O = 3:2
Speed of M: Speed of N : Speed of O = 4:3:2
So N will produce 3/(2+3+4) = 1/3rd of the output
SVP  Joined: 06 Sep 2013
Posts: 1545
Concentration: Finance
Re: Machine M, N, O working simultaneously Machine M can produce  [#permalink]

### Show Tags

I would go with smart numbers on this one. Say that N=4, M=3 and O = 6. Therefore all working together will finish x in 4/3 hour. Now in 4/3 hour N does 1/4 so (4/3)(1/4) = 1/3. B is the correct answer

Peace
VP  P
Joined: 07 Dec 2014
Posts: 1217
Re: Machine M, N, O working simultaneously Machine M can produce  [#permalink]

### Show Tags

Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

M,N,O respective times=t/2, 2t/3, t
M,N,O combined rates=2/t+3/2t+1/t=4.5/t
N's fraction of total output=(3/2t)/(4.5/t)=1/3
B
Non-Human User Joined: 09 Sep 2013
Posts: 13743
Re: Machine M, N, O working simultaneously Machine M can produce  [#permalink]

### Show Tags

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: Machine M, N, O working simultaneously Machine M can produce   [#permalink] 27 Jan 2019, 14:27
Display posts from previous: Sort by

# Machine M, N, O working simultaneously Machine M can produce  