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
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M - K = ?

P + K + M = 162

P = 2K
P = 1/3 M <=> 3P = M

=> P + P/2 + 3P = 162
9P = 324
P=36

M - K = 3P - P/2 = 2,5 P = 90

The correct answer is D.

Another approach.

Let Mark be 'M' time on th project
Pat = 1/3M
Kate = 1/6M (as it twic less then Pat)

So 1/6M + 1/3M + M = 162 hours.
From here M = 108 hours, Kate = 18 hours
And the answer is 90 (108-18).

Very quick solution about 30 seconds.

D.

P+K+M = 162

K = 1/2P
M = 3P

P+1/2P+3P = 162
P=36

K = 36/2 = 18
M = 3*36 = 108

108-18 = 90

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 \(P = \frac{162*2}{9} = 36\)

So from this, we get K = 18 and M = 108

So \(M-K = 108-18 = 90\)

Hope this helps.

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.

hope it helps.
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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

p/a=2/1
p/m=1/3


p:a:m
2:1:-
2:-:6

p:a:m
2:1:6

2x+x+6x=162
x=18

(6-1)*18=90
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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

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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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
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dave13

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 or

1/3(Mark) = Pat -> 1/3 (Mark) = 2x So, the number of hours Mark charged = 3(2x)

In other words, 6x = the number of hours Mark charged

P + K + M = 162

Using Ratios
P: 2x
K: x
M: 6x

Need= 6x - x = 5x = ?

9x = 162
x = 18

5x = 90

ANSWER: D

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