If Machine B and Machine C work together at their constant individual rates to produce x widgets, what percent of the widgets will be produced by Machine B?
(1) Machine A and Machine B, working together at their constant individual rates, can produce x widgets in 9 hours.
(2) Machine A and Machine C, working together at their constant individual rates, can produce x widgets in 12 hours.
OA E
Source: Veritas Prep
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If Machine B and Machine C work together at their constant
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BTGmoderatorDC
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ceilidh.erickson
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Machines working together will work at the SUM of their individual rates. Since the question is asking us for the proportion of the work that Machine B completed, we would need to know the proportion that A & C together completed.
(1) Machine A and Machine B, working together at their constant individual rates, can produce x widgets in 9 hours.
Since we don't know how long it took at 3 machines to make x widgets working all together, it doesn't help us to know how long it took A and B together. There's no way to distinguish which portion of this was Machine B alone. Insufficient.
(2) Machine A and Machine C, working together at their constant individual rates, can produce x widgets in 12 hours.
If we knew how long all 3 of them spent together to make x widgets, this would be helpful. But since we don't have that information, we don't know if 12 hrs is way longer or just slightly longer than all 3 working together. This won't help us to determine the proportion of the total that B did. Insufficient.
(1) & (2) Together
Even with both pieces of information together, we don't have enough. What if Machine A is so slow that it effectively does almost nothing, so B does the whole job in almost 9 hrs and C does the whole job in almost 12 hrs? Or maybe C does almost nothing, A does it alone in almost 12 hrs, so B makes up whatever that difference is? In those 2 cases, Machine B would account for different proportions of the total. Insufficient.
The answer is E.
(1) Machine A and Machine B, working together at their constant individual rates, can produce x widgets in 9 hours.
Since we don't know how long it took at 3 machines to make x widgets working all together, it doesn't help us to know how long it took A and B together. There's no way to distinguish which portion of this was Machine B alone. Insufficient.
(2) Machine A and Machine C, working together at their constant individual rates, can produce x widgets in 12 hours.
If we knew how long all 3 of them spent together to make x widgets, this would be helpful. But since we don't have that information, we don't know if 12 hrs is way longer or just slightly longer than all 3 working together. This won't help us to determine the proportion of the total that B did. Insufficient.
(1) & (2) Together
Even with both pieces of information together, we don't have enough. What if Machine A is so slow that it effectively does almost nothing, so B does the whole job in almost 9 hrs and C does the whole job in almost 12 hrs? Or maybe C does almost nothing, A does it alone in almost 12 hrs, so B makes up whatever that difference is? In those 2 cases, Machine B would account for different proportions of the total. Insufficient.
The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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fskilnik@GMATH
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\[?\,\,\,:\,\,\,{\text{in}}\,\,B \cup C\,\,\left( {{\text{any}}} \right)\,\,{\text{widget}}\,\,{\text{production}}\,,\,\,{\text{% }}\,\,{\text{done}}\,\,{\text{by}}\,\,{\text{B}}\]BTGmoderatorDC wrote:If Machine B and Machine C work together at their constant individual rates to produce x widgets, what percent of the widgets will be produced by Machine B?
(1) Machine A and Machine B, working together at their constant individual rates, can produce x widgets in 9 hours.
(2) Machine A and Machine C, working together at their constant individual rates, can produce x widgets in 12 hours.
Source: Veritas Prep
Let´s present a BIFURCATION for (1+2), that is, two EXPLICIT VIABLE scenarios, each one giving a different answer to our FOCUS!
One possible scenario is the following:
A does x/2 widgets in 9 hours (hence x/6 in 3 hours and 2x/3 in 12 hours) , B does x/2 widgets in 9 hours and C does x/3 widgets in 12 hours.
Conclusion: in 12h, B does 2x/3 widgets and C does x/3 widgets , hence our FOCUS is 2x/3 divided by x , that is , 2/3.
Another possible scenario is the following:
A does x/4 widgets in 9 hours (hence x/12 in 3 hours and x/3 in 12 hours) , B does 3x/4 widgets in 9 hours (hence x widgets in 12h) and C does 2x/3 widgets in 12 hours.
Conclusion: in 12h, B does x widgets and C does 2x/3 widgets , hence our FOCUS is x divided by (x+2x/3 = 5x/3), that is 3/5 (NOT equal to 2/3).
The correct answer is therefore (E).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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