Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?
(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
OA B
Source: Official Guide
Machines X and Y produced identical bottles at different con
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SayBTGmoderatorDC wrote:Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?
(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
OA B
Source: Official Guide
Machine X filled X bottles in 4 hours; thus, Machine X's rate = X/4 bottles per hour; and
Machine Y filled X bottles in 3 hours; thus, Machine Y's rate = Y/3 bottles per hour
We have to find out in how many hours will Machine X will fill (X + Y) bottles. It will take (4 + 4Y/X) hours.
If we get the value of Y/X, we get the answer.
Question rephrased: What's the value of Y/X?
Let's take each statement one by one.
(1) Machine X produced 30 bottles per minute.
No information about Machine Y. Insufficient.
(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
=> X = 2Y => Y/X = 1/2. Sufficient.
Machine X will take 4 + 4Y/X = 4 + 4*(1/2) = 6 hours fill the entire production lot.
The correct answer: B
Hope this helps!
-Jay
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