Problem Solving

Can someone please explain how to solve this problem. I guessed correctly on a practice GMAT, but I am not exactly sure how to solve the problem.

Q24:
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A. 80
B. 96
C. 160
D. 192
E. 240


[spoiler]Answer: D[/spoiler]

should be D.

Let ratios be 2x,3x,5x & 6x

if 2x = 30, then total hours = 30 + 45 + 75 +90 = 240
if 3x = 30, then total hours = 20 + 30 + 50 +60 = 160
if 5x = 30, then total hours = 12 + 18 + 30 + 36 = 96
if 6x = 30, then total hours = 10 + 15 + 25 + 30 = 80

only option left out is D

Thanks. I started to do that on the test, but I felt that it took to long. Does anyone know a faster methodology, or is that way simply the fastest.

jba05d wrote:Thanks. I started to do that on the test, but I felt that it took to long. Does anyone know a faster methodology, or is that way simply the fastest.

So the previous post listed all the hours for each of 4 employees such as

if 2x = 30, then total hours = 30 + 45 + 75 +90 = 240

If we do this then we have to spend a lot of time calculating each employees hours...

One way to make this quicker is to understand that the sum of all hours = 2x + 3x + 5x + 6x = 16x.

So if 2x = 30; 16x = 240
If 3x = 30; 16x = 160
If 5x = 30; 16x = 96
If 6x = 30; 16x = 80

Hence this only leaves out 192...so the answer is D.

Hopefully this helps make it quicker!

hope below method will take lesser time for you

start with 2x, this will give the time = 240 ....(1)
next with 3x this will give the time = 160 .....(2)
Now, if you will take the higher ratio, amount if time will be decrease. You may deduce this pattern from the equ 1 and 2. Hence the only option that is inbetween 240 and 160 is 192(option D). You cnt get this answr as time is gettting decreased.