Statistics Problem

[briology]

The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

a. 1.5 b. 3.0 c. 3.9 d. 4.0 e. 6.0

This problem is a bit confusing for me. I understand how to solve it now (setup two equations), but still don't fully grasp the concept. Specifically, I don't understand why you can't find the difference between the two means and divide by 3 (which would give you 4 as your answer). Any help would be much appreciated!

[cans]

let sum of other 4 numbers=x and 5th number be y.
then x+y = 6.8*5 = 34
also x+3y = 5*9.2 = 46
2y = 12 and y=6

(take difference between means and divide by 3 is incorrect because mean is not multiplied by 3)

[gmatclubmember]

The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

a. 1.5 b. 3.0 c. 3.9 d. 4.0 e. 6.0

This problem is a bit confusing for me. I understand how to solve it now (setup two equations), but still don't fully grasp the concept. Specifically, I don't understand why you can't find the difference between the two means and divide by 3 (which would give you 4 as your answer). Any help would be much appreciated!

1. Summation of 5 no. = 5*6.8=34
When one no. is multiplied by 3 then the new mean is 9.2, so the new summation of the 5 nos. is 5*9.2=46.
So the sum of nos. increased from 34 to 46, that is by 12.
So multiplication of the no. increased the sum by 12. If that no. is x then
3x-x=12=>x=6.

Is OA E.

Cheers
Ami/-

[briology]

Thank you both for the replies! Although I'm still not 100% sure why you can't say 3x=12, when you know the increase was 12 and nothing changes except x becomes 3x