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Machines X and Y

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Machines X and Y

by GmatKiss » Thu May 17, 2012 12:13 am
Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 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.
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Source: — Data Sufficiency |
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by neelgandham » Thu May 17, 2012 2:04 am
Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 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?
Let the number of hours required by X to complete the job be x
Let the number of hours required by Y to complete the job be y
Fraction of job completed by X in the first 4 hours = 4/x
Fraction of job completed by Y in the first 3 hours = 3/y and
(4/x)+(3/y) = 1

The question can be rephrased to 'If (4/x)+(3/y) = 1, then what is the value of x?'
1. Machine X produced 30 bottles per minute.
Irrelevant!
2. Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
(4/x)= 2*(3/y)
(2/x) = (3/y) and we know that (4/x)+(3/y) = 1
(4/x)+(2/x) = 1
6/x = 1 and x = 6
Statement 2 is sufficient to answer the question.

Answer B
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by GMATGuruNY » Thu May 17, 2012 5:00 am
GmatKiss wrote:Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 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.
Statement 1: X produced 30 bottles per minute.
Thus, the work produced by X in 240 minutes = r*t = 30*240.
No information about how much work was produced by Y.
INSUFFICIENT.

Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
Thus, for every bottle Y produced, X produced 2 bottles, implying that X produced 2 of every 3 bottles.
Since X produced 2/3 of the lot in 4 hours, X would need 2 more hours to produce the remaining 1/3 of the lot, for a total of 6 hours.
SUFFICIENT.

The correct answer is B.
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