ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8
This is a wonderful problem to make an educated guess on. Rates & work problems are great for guessing in general.
Four machines make a certain amount of stuff in 6 days. We want to make
three times as much stuff. That means we need at least three times as many machines, unless we also get extra time! (We don't.) So, eliminate 8.
We also have fewer days to spend making the stuff than we did originally. So, we can't get away with just having three times as many machines. We need
more than three times as many. Eliminate 12.
Do we need 24 machines, though? That's 6 times as many as we had before. If you have six times as many machines, and you're only trying to make three times as much stuff, you should need half as much time. But we needed 4 days, not 3. Eliminate 24.
Guess 16 or 18 and move on!
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