Pat, Kate, and Mark charged a total of 162 hours to a certain project.

Question

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

BrentGMATPrepNow · Accepted Answer

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

pi10t · Answer

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.

M8 · Answer

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.

amartin6165 · Answer

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

whiplash2411 · Answer

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.

PTK · Answer

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.

gmat1220 · Answer

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

LalaB · Answer

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

dave13 · Answer

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

BrentGMATPrepNow · Answer

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

JeffTargetTestPrep · Answer

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

seed · Answer

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

dabaobao · Answer

P + K + M = 162

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

Need= 6x - x = 5x = ?

9x = 162
x = 18

5x = 90

ANSWER: D

egmat · Answer

Let's break this down together in a way that makes sense.

Here's the key insight you need to see:

When the problem says "Pat charged 1/3 as much time as Mark," it means Pat's hours = (1/3) × Mark's hours. This is often where students get tripped up - they think it means the opposite!

Let's solve this step-by-step:

Since Pat's time relates to both Kate and Mark, let's use Kate's hours as our base. Call it  K .

Now, let's translate what we know:
- Kate worked  K  hours
- Pat worked twice as much as Kate, so Pat =  2K  hours
- Pat worked 1/3 as much as Mark, which means Pat = Mark/3

If Pat =  2K  and Pat = Mark/3, then:
 2K = \frac{Mark}{3}

Therefore, Mark =  6K  hours

Notice how this makes sense - Pat works more than Kate (double), but Mark works even more than Pat (triple).

Setting up our equation: 
Total hours = Kate + Pat + Mark = 162
 K + 2K + 6K = 162 
 9K = 162 
 K = 18

So:
- Kate: 18 hours
- Pat:  2 	imes 18 = 36  hours 
- Mark:  6 	imes 18 = 108  hours

The question asks how many  more  hours Mark charged than Kate:
 108 - 18 = 90  hours

Answer: D

You can check out the  step-by-step solution on Neuron by e-GMAT  to master the systematic framework for solving all ratio-based word problems. The full solution shows you three alternative approaches and reveals the common trap patterns that appear in similar GMAT questions. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice  here .

Pat, Kate, and Mark charged a total of 162 hours to a certain project.

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