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01 Jul 2017, 03:50
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:32) correct
26%
(02:44)
wrong
based on 242
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Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?
(A) 12
(B) 16
(C) 18
(D) 24
(E) 39
(A) 12
(B) 16
(C) 18
(D) 24
(E) 39
01 Jul 2017, 04:19
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Lets assume the time they take to do the project to be x.
Hence the time taken by Mark will be x+12 and Kate will be x+27
The work done by both of them in an hour can be written by equation
\(\frac{1}{x} = \frac{1}{x+12} + \frac{1}{x+27}\)
\((x+12)(x+27) = x(2x+39)\)
\(x^2 + 39x + 324 = 2x^2 + 39x\)
\(x^2 = 324\)
\(x=18\)(because number of hours cannot be negative)
The correct answer is Option C(x=18)
Hence the time taken by Mark will be x+12 and Kate will be x+27
The work done by both of them in an hour can be written by equation
\(\frac{1}{x} = \frac{1}{x+12} + \frac{1}{x+27}\)
\((x+12)(x+27) = x(2x+39)\)
\(x^2 + 39x + 324 = 2x^2 + 39x\)
\(x^2 = 324\)
\(x=18\)(because number of hours cannot be negative)
The correct answer is Option C(x=18)
01 Jul 2017, 06:57
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Working through options, let's choose 18 first since it's the middle number.
We need to verify if this is true:
\(\frac{1}{18} = \frac{1}{18+12} + \frac{1}{18+27}\)
\(\frac{1}{18} = \frac{1}{30} + \frac{1}{45}\)
\(\frac{1}{18} = \frac{5}{90}\)
\(\frac{1}{18} = \frac{1}{18}\) - so, this is the correct answer. Ans - C.
We need to verify if this is true:
\(\frac{1}{18} = \frac{1}{18+12} + \frac{1}{18+27}\)
\(\frac{1}{18} = \frac{1}{30} + \frac{1}{45}\)
\(\frac{1}{18} = \frac{5}{90}\)
\(\frac{1}{18} = \frac{1}{18}\) - so, this is the correct answer. Ans - C.
