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# Working alone, machine X can manufacture 1,000 nails in 12 hours. Work

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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27 Dec 2015, 10:15
3
1
00:00

Difficulty:

25% (medium)

Question Stats:

78% (02:09) correct 22% (02:25) wrong based on 130 sessions

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Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?

A. 3 9/17
B. 5 1/3
C. 7
D. 7 1/5
E. 8 4/7

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Manager
Joined: 15 Feb 2015
Posts: 92
Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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27 Dec 2015, 10:48
Bunuel wrote:
Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?

A. 3 9/17
B. 5 1/3
C. 7
D. 7 1/5
E. 8 4/7

Rate of machine X = 1000/12 = 250/3
Rate of machine Y = 1/Y
Rate of machine X and Y together = 1000/5 = 200

250/3 + 1/y = 200

after solving this equation we get Y= 3/350

Rate of Y = 1/y = 1/ (3/350) = 350/3

Machine Y has to manufacture 1000 nails. So work is 1000. Putting the values;

time required for machine Y = 1000/(350/3) = 1000* 3/(350) = 60/7 = 8 4/7
VP
Joined: 07 Dec 2014
Posts: 1222
Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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27 Dec 2015, 21:55
let 1000 nails=1 unit
Y's rate=1/5-1/12=7/60 units per hour
inverting, 60/7=8 4/7 hours for Y to complete one unit
Senior Manager
Joined: 28 Feb 2014
Posts: 291
Location: United States
Concentration: Strategy, General Management
Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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27 Dec 2015, 22:20
Bunuel wrote:
Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?

A. 3 9/17
B. 5 1/3
C. 7
D. 7 1/5
E. 8 4/7

rate of machine x = 1000/12

(1000/12 + y)5=1000
y=350/3

350/3 * t = 1000
t=8 4/7

E. 8 4/7
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Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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29 Dec 2015, 11:12
3
1
Hi All,

We're given the rates of two entities that will share a job together - this is the standard "set-up" for a Work Formula question. This question does come with a minor 'twist' though - we have to 'work backwards' to find one of the two original rates....

Work Formula = (A)(B)/(A+B) where A and B are the respective amounts of time needed to individually complete a job.

Machine X = 12 hours to complete the job
Machine Y = Y hours to complete the job
Together = 5 hours to complete the job

Using the Work Formula, and those values, we have...

(12)(Y)/(12 + Y) = 5 hours to complete the job

12Y = (5)(12+Y)
12Y = 60 + 5Y
7Y = 60
Y = 60/7 = 8 4/7

GMAT assassins aren't born, they're made,
Rich
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Intern
Joined: 22 Oct 2017
Posts: 19
Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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20 Feb 2019, 08:58
Bunuel wrote:
Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?

A. 3 9/17
B. 5 1/3
C. 7
D. 7 1/5
E. 8 4/7

Why is it wrong to set up the following equation?:

1000/12 + 1000/y = 1000/5

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
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Location: United States (CA)
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GRE 1: Q170 V170
Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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20 Feb 2019, 10:56
1
Hi paolodeppa,

You can approach this question using the formula that you've created. How "easy" did you find the calculation though? What answer did you end up with?

GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 22 Oct 2017
Posts: 19
Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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20 Feb 2019, 11:26
EMPOWERgmatRichC wrote:
Hi paolodeppa,

You can approach this question using the formula that you've created. How "easy" did you find the calculation though? What answer did you end up with?

GMAT assassins aren't born, they're made,
Rich

Sorry, I wasn't able to recognize that 60/7 is equivalent to 8 + 4/7, my bad
Working alone, machine X can manufacture 1,000 nails in 12 hours. Work   [#permalink] 20 Feb 2019, 11:26
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