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Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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04 Jul 2006, 04:57

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Difficulty:

45% (medium)

Question Stats:

72% (02:24) correct 28% (02:21) wrong based on 614 sessions

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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?

Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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31 Jul 2010, 09:14

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So let us denote the hours charged by Pat as P, Kate as K and Mark as M.

\(P + K + M = 162\)

We are told that \(P = 2K\) and \(P = \frac{1}{3}M\). The easiest way to solve a problem like this would be to convert everything to one variable, which in this case, is P.

So we get \(K = \frac{1}{2}P\) and \(M = 3P\). Substituting this into the original equation we get: \(P + \frac{1}{2}P + 3P = 162\)

This tells us that \(\frac{9P}{2} = 162\) which implies \(P = \frac{162*2}{9} = 36\)

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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24 Mar 2011, 07:59

2

You may try my approach. It may be easier and may be faster.

P+M+K=162 we need to find M-K

Lets Kate charged 60 hours then Pat charged 60*2=120 hours Mark charged 3 times more than Pat or 120*3=360

Total 60+120+360=540. M-K= 360-60=300 Now look at the trick: We must have received 162 instead of 540 hours. and the difference (M-K) is 300 not one in the available answer choices.

Now guess what you need to do to obtain the correct answer choice? Exactly 162/540=3.33 , and 300/3.33=90.

Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.

Affiliations: University of Chicago Booth School of Business

Joined: 03 Feb 2011

Posts: 743

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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06 May 2011, 09:26

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P + K + M = 162

P = 2K, P = 1/3M

Hence K = 0.5P and M = 3P

P + 0.5 P + 3P = 162 or 4.5 P = 162

P = 18 * 2 = 36 K = 18 M = 108 M - K = 108 - 18 = 90

naveenhv 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 rd as much as Mark, how many more hours did mark charge to the project than Kate?

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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20 Jan 2018, 07:22

Top Contributor

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? Answer = 108 - 18 = 90 = D

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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20 Jan 2018, 10:35

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? Answer = 108 - 18 = 90 = D

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...

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"

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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08 Mar 2018, 16:51

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.

Answer: D
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Pat, Kate, and Mark charged a total of 162 hours to a certain project.
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03 Jul 2018, 04:10

1

Quote:

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?