Problem Solving

BTGmoderatorLU wrote: ↑

Thu Aug 06, 2020 10:59 am

Source: GMAT Prep

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

The OA is D

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

BTGmoderatorLU wrote: ↑

Thu Aug 06, 2020 10:59 am

Source: GMAT Prep

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

The OA is D

Solution:

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