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Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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01 Apr 2021, 02:04
01 Apr 2021, 02:04
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Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
A. 18
B. 36
C. 72
D. 90
E. 108
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 18
B. 36
C. 72
D. 90
E. 108
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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02 Apr 2021, 07:23
02 Apr 2021, 07:23
2
Carcass wrote:
Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
A. 18
B. 36
C. 72
D. 90
E. 108
A. 18
B. 36
C. 72
D. 90
E. 108
\(P = 2K\)
\(\frac{P}{K} = \frac{2}{1}\)
\(P = \frac{1}{3}M\)
\(\frac{P}{M} = \frac{1}{3}\)
Let's make \(P\)s equal;
\(\frac{P}{K} = \frac{2}{1}\), \(\frac{P}{M} = \frac{1(2)}{3(2)}\)
Therefore, \(P : K : M = 2 : 1 : 6\)
Now, \(M - K = \frac{(6 - 1)}{(2 + 1 + 6)}(162) = \frac{5}{9}(162) = 90\)
Hence, option D
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Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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02 Apr 2021, 09:16
02 Apr 2021, 09:16
1
We can see that Kate charged the fewest hours, so...
Let x =the number of hours Kate charged
Pat charged twice as much time to the project as Kate
So, 2x = the number of hours Pat charged
Pat charged 1/3 as much times as Mark
In other words, Mark charged THREE TIMES as much time as Pat
So, 3(2x ) = the number of hours Mark charged
In other words, 6x = the number of hours Mark charged
Pat, Kate and Mark charged a total of 162 hours to a certain project.
We can write: x + 2x + 6x = 162
Simplify: 9x = 162
Solve: x = 18
So, Kate charged 18 hours
When we plug x = 18 into 6x, we see that Mark charged 108 hours
How many more hours did Mark charge to the project than Kate?
Answer = 108 - 18
= 90
= D
Let x =the number of hours Kate charged
Pat charged twice as much time to the project as Kate
So, 2x = the number of hours Pat charged
Pat charged 1/3 as much times as Mark
In other words, Mark charged THREE TIMES as much time as Pat
So, 3(2x ) = the number of hours Mark charged
In other words, 6x = the number of hours Mark charged
Pat, Kate and Mark charged a total of 162 hours to a certain project.
We can write: x + 2x + 6x = 162
Simplify: 9x = 162
Solve: x = 18
So, Kate charged 18 hours
When we plug x = 18 into 6x, we see that Mark charged 108 hours
How many more hours did Mark charge to the project than Kate?
Answer = 108 - 18
= 90
= D
