If Machine B and Machine C work together at their constant

[BTGmoderatorDC]

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

[ceilidh.erickson]

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.

[fskilnik@GMATH]

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

\[?\,\,\,:\,\,\,{\text{in}}\,\,B \cup C\,\,\left( {{\text{any}}} \right)\,\,{\text{widget}}\,\,{\text{production}}\,,\,\,{\text{% }}\,\,{\text{done}}\,\,{\text{by}}\,\,{\text{B}}\]
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.