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# Machine A, operating alone at its constant rate, produces 50 feet of

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Joined: 29 Jan 2015
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WE: General Management (Non-Profit and Government)
Machine A, operating alone at its constant rate, produces 50 feet of  [#permalink]

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05 Jan 2019, 02:14
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95% (hard)

Question Stats:

34% (02:18) correct 66% (01:39) wrong based on 114 sessions

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Machine A, operating alone at its constant rate, produces 50 feet of a particular fiber per hours. Machine B, operating alone at its constant rate, produces 30 feet of the same fiber per hour. If A and B each produces n feet of fiber, n=?

(1) Machine A and machine B spent 16 hours in total.

(2) Machine B spent 4 hours more than A to finish the work.

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Re: Machine A, operating alone at its constant rate, produces 50 feet of  [#permalink]

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05 Jan 2019, 06:57
1
1
we can answer this questions using Logic.
1) we get the following two equations:
30x=n
50(16-x)=n
two equations, two variables - definitely one solution! sufficient!

2)
30x=n
50(x+4)=n
two equations, two variables - definitely one solution! sufficient!
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Re: Machine A, operating alone at its constant rate, produces 50 feet of  [#permalink]

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14 Jan 2019, 12:16
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Top Contributor
rohan2345 wrote:
Machine A, operating alone at its constant rate, produces 50 feet of a particular fiber per hours. Machine B, operating alone at its constant rate, produces 30 feet of the same fiber per hour. If A and B each produces n feet of fiber, n=?

(1) Machine A and machine B spent 16 hours in total.
(2) Machine B spent 4 hours more than A to finish the work.

Given:
Machine A, operating alone at its constant rate, produces 50 feet of a particular fiber per hours.
Machine B, operating alone at its constant rate, produces 30 feet of the same fiber per hour.
A and B each produces n feet of fiber

Target question: What is the value of n?

Statement 1: Machine A and machine B spent 16 hours in total.
Time = output/rate

So, machine A's working time = n/50 hours
And machine B's working time = n/30 hours

Since the TOTAL work time is 16 hours, we can write: n/50 + n/30 = 16
To eliminate the fractions, we'll find the least common multiple of 50 and 30 (LCM = 150)
Multiply both sides by 150 to get: 3n + 5n = 2400
Solve: n = 300
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Aside: If you were able to see that the equation n/50 + n/30 = 16 has exactly ONE solution, you could have saved time, and just concluded that statement 1 is sufficient (without solving the equation).

Statement 2: Machine B spent 4 hours more than A to finish the work
In other words, Machine A's work time was LESS than Machine B's work time.
So, in order to make the two quantities EQUAL, we must add 4 hours to Machine A's work time.
That is: (Machine A's work time) + 4 = (Machine B's work time)
Time = output/rate
So, we can write: (n/50) + 4 = (n/30)
At this point, we might recognize that, IF we were to solve this equation, we'd arrive at exactly one solution.
So, we can save some time and just recognize that we COULD answer the target question with certainty.
So, statement 2 is SUFFICIENT

Cheers,
Brent

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Re: Machine A, operating alone at its constant rate, produces 50 feet of  [#permalink]

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12 Jan 2019, 04:03
DavidTutorexamPAL wrote:
H Davd,
Good solution!! But, please see the below mentioned change in statement 2.

[color=#ff0000]2)
30(x+4)=n
50(x)=n
[/color]
two equations, two variables - definitely one solution! sufficient!
Re: Machine A, operating alone at its constant rate, produces 50 feet of   [#permalink] 12 Jan 2019, 04:03
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