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Difficulty:
55%
(hard)
Question Stats:
69% (02:43) correct
31%
(03:06)
wrong
based on 1021
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A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 250 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?
A. 400
B. 475
C. 550
D. 625
E. 700
A. 400
B. 475
C. 550
D. 625
E. 700
05 Jun 2015, 11:46
Kudos
Bookmarks
Hi All,
When dealing with complex-"looking" prompts, it's important to remember that they were DESIGNED to be solved, so sometimes you have to 'play around' with what you're given to get to the correct answer.
From this prompt, we can create two equations:
7A + 11B = 250/hour
8A + 22C = 600/hour
We're asked for (A+B+C)/hour over the course of 8 hours.
With the given equations, we have 3 variables but only 2 equations, so this is NOT a typical "system" question. The answers ARE numbers though, so there must be a way to get to A+B+C from the two equations that we have....
Notice how we have 11B in one equation and 22C an another? It's INTERESTING that they're both multiples of 11.....Maybe that's a 'clue' as to how we can proceed....
If we "double" the entire first equation, we get...
14A + 22B = 500/hour
Now I can add this equation to the second equation:
14A + 22B = 500/hour
8A + 22C = 600/hour
22A + 22B + 22C = 1100/hour
Dividing everything by 22, we get....
A+B+C = 50/hour
Over the course of an 8-hour day, that gives us...50(8) = 400 widgets.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
When dealing with complex-"looking" prompts, it's important to remember that they were DESIGNED to be solved, so sometimes you have to 'play around' with what you're given to get to the correct answer.
From this prompt, we can create two equations:
7A + 11B = 250/hour
8A + 22C = 600/hour
We're asked for (A+B+C)/hour over the course of 8 hours.
With the given equations, we have 3 variables but only 2 equations, so this is NOT a typical "system" question. The answers ARE numbers though, so there must be a way to get to A+B+C from the two equations that we have....
Notice how we have 11B in one equation and 22C an another? It's INTERESTING that they're both multiples of 11.....Maybe that's a 'clue' as to how we can proceed....
If we "double" the entire first equation, we get...
14A + 22B = 500/hour
Now I can add this equation to the second equation:
14A + 22B = 500/hour
8A + 22C = 600/hour
22A + 22B + 22C = 1100/hour
Dividing everything by 22, we get....
A+B+C = 50/hour
Over the course of an 8-hour day, that gives us...50(8) = 400 widgets.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
11 Jun 2013, 03:10
Kudos
Bookmarks
\(rate*time=work\)
\((7A+11B)*1h=250\)
\((8A+22C)*1h=600\) or \(4A+11C=300\). Sum those equations:
\(7A+11B+4A+11C=550\) or \(11A+11B+11C=550\)
\(A+B+C=50\) every hour, in 8 hours \(50*8=400\)
\((7A+11B)*1h=250\)
\((8A+22C)*1h=600\) or \(4A+11C=300\). Sum those equations:
\(7A+11B+4A+11C=550\) or \(11A+11B+11C=550\)
\(A+B+C=50\) every hour, in 8 hours \(50*8=400\)
