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05 Sep 2015, 14:41
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:32) correct
27%
(01:42)
wrong
based on 427
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Cameron can paint a room in c hours. Cameron and Mackenzie, working together, can paint the room in d hours. In terms of c and d, how long in hours would it take Mackenzie, working alone, to paint the room?
(A) 2d - c
(B) \(\frac{c+d}{cd}\)
(C) \(\frac{c-d}{cd}\)
(D) \(\frac{cd}{c+d}\)
(E) \(\frac{cd}{c-d}\)
Source: GMAT HACKS 1800 - Guide 1 - Rates, Ratios & Percents
(A) 2d - c
(B) \(\frac{c+d}{cd}\)
(C) \(\frac{c-d}{cd}\)
(D) \(\frac{cd}{c+d}\)
(E) \(\frac{cd}{c-d}\)
Explanation: While it may be easier to work with actual numbers, this question is an explicit test of your knowledge of the work formula. If you know the time it takes for two individuals to do a job, you can plug those times into the equation \(\frac{xy}{x+y}\) to get the time it would take them, combined. Thus, plugging c in for x and setting the whole thing equal to d:
\(\frac{cy}{c + y}= d\)
\(cy= d(c + y)\)
\(cy = dc + dy\)
\(cy - dy = dc\)
\(y = \frac{dc}{c-d}\)
which is equivalent to \(\frac{cd}{c-d}\), choice (E).
\(\frac{cy}{c + y}= d\)
\(cy= d(c + y)\)
\(cy = dc + dy\)
\(cy - dy = dc\)
\(y = \frac{dc}{c-d}\)
which is equivalent to \(\frac{cd}{c-d}\), choice (E).
Source: GMAT HACKS 1800 - Guide 1 - Rates, Ratios & Percents
05 Sep 2015, 16:22
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Hi gmatser1,
This prompt can be solved by TESTing VALUES and using the Work Formula:
Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'
Here, we're told that one person can paint a room in C hours and that two people (when WORKING TOGETHER) can paint the room in D hours. We're asked for the individual amount of time that it would take the second person to paint the room when working along.
IF...
the 1st person can paint the room in 3 hours
the 2nd person can paint the room in 6 hours
Combined, it would take (3)(6)/(3+6) = 18/9 = 2 hours to paint the room when working together
Using the above example, we can TEST VALUES....
C = 3
D = 2
And we're looking for an answer that equals 6....There's only one answer that fits....
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This prompt can be solved by TESTing VALUES and using the Work Formula:
Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'
Here, we're told that one person can paint a room in C hours and that two people (when WORKING TOGETHER) can paint the room in D hours. We're asked for the individual amount of time that it would take the second person to paint the room when working along.
IF...
the 1st person can paint the room in 3 hours
the 2nd person can paint the room in 6 hours
Combined, it would take (3)(6)/(3+6) = 18/9 = 2 hours to paint the room when working together
Using the above example, we can TEST VALUES....
C = 3
D = 2
And we're looking for an answer that equals 6....There's only one answer that fits....
Final Answer:
GMAT assassins aren't born, they're made,
Rich
