Pat, Kate and Mark

[Viper83]

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

a) 18
b) 36
c) 72
d) 90
e) 108

D

[rishab1988]

Answer is D

Here is why:

Let no. of hours charged by Pat be =x
Then no of hours charged by Kate =x/2 [ Pat charged for twice as many hours as Kate charged].So if Kate =1 Pat =2.
Then no. of hours charged by Mark =3x [pat charged for 1/3 as many hours as Mark charged].So if Mark =3 Pat = 1

Question is Mark-Kate or 3x-x/2= 5x/2 =?
Now, x+x/2+3x =162 [ Pat,Kate,and Mark charged for a cumulative 162 hours]

4x+x/2= 162
9x/2=162
x/2 =18
5x/2= 90

What is the OA?

[Night reader]

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

a) 18
b) 36
c) 72
d) 90
e) 108

D

P=2K=1/3M OR P=2K; K=K; M=6K

M-K=?

2K+K+6K=162
K=18

M=6*18=108

M-K=108-18=90

LOOK UP THE ANSWER CHOICES:)

IT'S D

[GMATGuruNY]

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

a) 18
b) 36
c) 72
d) 90
e) 108

D

We can plug in values in order to determine the ratio of K: P :M.

If K=1, then P=2 (since Pat charged twice as much), and M=6 (since Pat charged 1/3 as much as Mark).
Thus, K: P :M = 1:2:6. Since 1+2+6=9, Kate charged 1/9 of the total time.
K = 1/9 * 162 = 18.
Following the ratio above, M = 6K = 6*18 = 108.
M-K = 108-18 = 90.

The correct answer is D.