Problem Solving

BTGmoderatorLU wrote: ↑

Tue Apr 20, 2021 2:57 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 x = Kate’s time in hours. Then Pat’s time = 2x and Mark’s time = 6x (since Pat’s time is ⅓ of Mark’s time). We can create the equation:

x + 2x + 6x = 162

9x = 162

x = 18

Since Mark charged 6x hours, he charged 6(18) = 108 hours, and hence he charged 108 - 18 = 90 hours more than Kate.

Answer: D

BTGmoderatorLU wrote: ↑

Tue Apr 20, 2021 2:57 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