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Machine M and Machine N working alone at their constant rate

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Machine M and Machine N working alone at their constant rate

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Machine M and Machine N working alone at their constant rates, non-stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?

1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate.

The OA is B

Source: GMAT Prep

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swerve wrote:
Machine M and Machine N working alone at their constant rates, non-stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?

1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate.

The OA is B

Source: GMAT Prep
Say Machine M works for x hours and Machine N works for y hours.

We have to determine whether x > y.

Let's take each statement one by one.

1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.

=> 2000 = 8000/y - 6000/x

1 = 4/y - 3/x

=> 4/y > 3/x

x/y > 3/4

Case 1: Say x/y = 4/5 > 3/4, then we have y > x.
Case 2: Say x/y = 5/4 > 3/4, then we have x > y.

No unique answer. Insufficient.

2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate.

=> 8000/y = 2*(6000/x)

x/y = 3/2

=> x > y. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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Manhattan Review

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swerve wrote:
Machine M and Machine N working alone at their constant rates, non-stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?

1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate.
Statement 1:
Case 1: N = 4000 nails per hour, M = 2000 nails per hour
Since N's rate = 4000 nails per hour, the time for N to produce 8000 nails = 8000/4000 = 2 hours.
Since M's rate = 2000 nails per hour, the time for M to produce 6000 nails = 6000/2000 = 3 hours.
In this case, M works longer than N, so the answer to the question stem is YES.

Case 2: N = 12000 nails per hour, M = 10000 nails per hour
Since N's rate = 12000 nails per hour, the time for N to produce 8000 nails = 8000/12000 = 2/3 hour = 40 minutes.
Since M's rate = 10000 nails per hour, the time for M to produce 6000 nails = 6000/10000 = 3/5 hour = 36 minutes
In this case, N works longer than M, so the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
In other words, N is twice as fast as M.
If N and M were to work for the same amount of time, then N's 8000-nail production would imply a 4000-nail production for M.
Since M actually produces 6000 nails -- more than 4000 -- M must work for LONGER than N.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.

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