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# Pat, Kate, and Mark charged a total of 162 hours to a

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Director
Joined: 09 Mar 2016
Posts: 601
Re: Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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20 Jan 2018, 11:35
GMATPrepNow wrote:
likar 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

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?
= 90
= D

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Helllo GMATPrepNow

can you please explain the wording of 1/3 as much time as Mark, why are you multiplying 2 by 3 ? there is a fraction 1/3 if it said "Pat charged three times as much as Mark" then i would multiply...

thank you
CEO
Joined: 12 Sep 2015
Posts: 2561
Re: Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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20 Jan 2018, 12:07
Top Contributor
1
dave13 wrote:
Helllo GMATPrepNow

can you please explain the wording of 1/3 as much time as Mark, why are you multiplying 2 by 3 ? there is a fraction 1/3 if it said "Pat charged three times as much as Mark" then i would multiply...

thank you

For most word problems, the given situation can be expressed in 2 ways.
For example, saying that "Joe is 4 years older than Ann" is exactly the SAME as saying "Ann is 4 years younger than Joe"

Likewise, saying that "Peter is HALF as old as Sue" is exactly the SAME as saying "Sue is TWICE as old as Peter"
And saying that "Peter is 1/3 as old as Sue" is exactly the SAME as saying "Sue is THREE TIMES as old as Peter"

Does that help?

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

Director
Joined: 09 Mar 2016
Posts: 601
Re: Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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20 Jan 2018, 12:16
GMATPrepNow wrote:
dave13 wrote:
Helllo GMATPrepNow

can you please explain the wording of 1/3 as much time as Mark, why are you multiplying 2 by 3 ? there is a fraction 1/3 if it said "Pat charged three times as much as Mark" then i would multiply...

thank you

For most word problems, the given situation can be expressed in 2 ways.
For example, saying that "Joe is 4 years older than Ann" is exactly the SAME as saying "Ann is 4 years younger than Joe"

Likewise, saying that "Peter is HALF as old as Sue" is exactly the SAME as saying "Sue is TWICE as old as Peter"
And saying that "Peter is 1/3 as old as Sue" is exactly the SAME as saying "Sue is THREE TIMES as old as Peter"

Does that help?

Cheers,
Brent

Brent - thank you very much! It is an excellent explanation!
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: Pat, Kate, and Mark charged a total of 162 hours to a [#permalink]

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08 Mar 2018, 17:51
likar 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

We can let P, K, and M = the amount time spent on the project by Pat, Kate, and Marck, respectively, and create the equations:

P + K + M = 162

and

P = 2K

P/2 = K

and

P = (M)(1/3)

3P = M

Substituting, we have:

P + P/2 + 3P = 162

Multiplying by 2, we have:

2P + P + 6P = 324

9P = 324

P = 36, so M = 108 and K = 18.

M - K = 108 - 18 = 90.

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Jeffery Miller

GMAT Quant Self-Study Course
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Re: Pat, Kate, and Mark charged a total of 162 hours to a   [#permalink] 08 Mar 2018, 17:51

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