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

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

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New post 27 Dec 2015, 10:15
3
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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

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

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New post 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




answer should be E

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

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New post 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
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Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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New post 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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New post 29 Dec 2015, 11:12
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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

Final Answer:

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

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New post 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

Please help me, kudos guaranteed
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Re: Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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New post 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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Working alone, machine X can manufacture 1,000 nails in 12 hours. Work  [#permalink]

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New post 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
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Working alone, machine X can manufacture 1,000 nails in 12 hours. Work   [#permalink] 20 Feb 2019, 11:26
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