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
Machine M and Machine N working alone at their constant rate
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Say Machine M works for x hours and Machine N works for y hours.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
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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Global Stats
Statement 1: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.
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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