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rohan2345
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Machine A, operating alone at its constant rate, produces 50 feet of 05 Jan 2019, 02:14
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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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D
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Machine A, operating alone at its constant rate, produces 50 feet of 05 Jan 2019, 06:57
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The answer is D.
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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Machine A, operating alone at its constant rate, produces 50 feet of 12 Jan 2019, 04:03
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DavidTutorexamPAL
The answer is D.
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!
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Machine A, operating alone at its constant rate, produces 50 feet of Updated on: 02 Apr 2020, 07:57
Originally posted by BrentGMATPrepNow on 14 Jan 2019, 12:16.
Last edited by BrentGMATPrepNow on 02 Apr 2020, 07:57, edited 1 time in total.
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rohan2345
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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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

Answer: D

Cheers,
Brent
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Machine A, operating alone at its constant rate, produces 50 feet of 13 Feb 2020, 11:52
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rohan2345
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.
Show more

Rate and time have a RECIPROCAL RELATIONSHIP.
Since the rate ratio for A and B = (50 feet per hour):(30 feet per hour) = 5:3, the time ratio for A and B = 3:5.

Statement 1:
Time ratio for A and B = 3:5 = 6:10, implying that's A's time = 6 hours and B's time = 10 hours, for a total of 16 hours.
Since A works for 6 hours at a rate of 50 feet per hour, n = (rate)(time) = 50*6 = 300 feet of fiber.
SUFFICIENT.

Statement 2:
Same values as those yielded by Statement 1:
B's time = 10 hours and A's time = 6 hours, for a difference of 4 hours.
Since A works for 6 hours at a rate of 50 feet per hour, n = (rate)(time) = 60*5 = 300 feet of fiber.
SUFFICIENT.

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Machine A, operating alone at its constant rate, produces 50 feet of 19 Jan 2026, 14:20
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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=?


Rate of A - 50 feet/hr
Date of B- 30 ft/hr
Work done by both- n each
Find n

Time for A - n/50
Time for B - n/30

S-1
n/50 + n/30 - 16
3n+ 5n - 2400
8n-2400
N- 300
Sufficient

S-2
N/30 = 4 + n/50
5n-3n - 600
2n - 600
N - 30
Sufficient

D

(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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