Sentence Correction

[BTGmoderatorRO]

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 times as Mark, how many more hours did Mark charge to the project than Kate.

18
36
72
90
108

OA isD
please, what is the mathematical approach to solve this problem? I need an Expert advice.

[EconomistGMATTutor]

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 times as Mark, how many more hours did Mark charge to the project than Kate.

18
36
72
90
108

OA isD
please, what is the mathematical approach to solve this problem? I need an Expert advice.

Hi Roland2rule,
Let's take a look at your question.

Let P, K and M represents the number of hours Pat, Kate and Mark charged to the project respectively.
Then the total number of hours can be represented as:
$$P+K+M=162...\left(i\right)$$

Also, Pat charged twice as much time to the project as Kate:
$$P=2K$$
$$K=\frac{P}{2}$$
and Pat charged1/3 as much times as Mark
$$P=\frac{1}{3}M$$
$$M=3P$$

Plugin the values of K and P in eq (i):
$$P+\frac{P}{2}+3P=162$$
$$2P+P+6P=2\left(162\right)$$
$$9P=324$$
$$P=36$$

Number of hours Kate charged = P/2 = 36/2 = 18
Number of hours Mark charged = 3P = 3(36) = 108

Number of hours Mark charged more to the project than Kate = 108 - 18 = 90

Therefore, option D is correct.

Hope it helps.
I am available if you's like any follow up.

[Brent@GMATPrepNow]

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 times as Mark, how many more hours did Mark charge to the project than Kate?

18
36
72
90
108

We can also solve the question using one variable

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

Cheers,
Brent