DS with Ratios, Shortcuts needs explanation

[shrivastava.rohit]

Can someone please explain how to solve this questions part 2 of the data sufficiency.

I was going through the Manhattan Verbal guide and found this example it states that combined average can be found based on the Ratious of the men and women along and no quantity is needed. I will need more explanation to understand this better.

Thanks is advance, Questions is below.

A group of men and women competed in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs, while the average weight of the men was found to be 150 lbs. What was the average weight of all of the competitors?

(1) 100 men competed in the marathon.
(2) There were twice as many men as women competing in the marathon.

[adiagr]

The question is on weighted average concept.


Average weight of the entire Group = [Total wt. of the group] divided by [Total members in the group]

We have average weight of males as well as females with us.


Taking Statement (2) First.

let there are w women. Thus there will be 2w men as per condition of statement 2.

The average weight of the combined groups will be given by;

[A/B] where


A: Total Weight

(i) Total wt. of men: [avg. wt. of men ] x [No. of men]
(ii) Total wt. of women: [avg. wt. of women ] x [No. of women]


A: (i) + (ii)


B: Total No.

{(No. of women) + (No. of men)}


A: {(w x 120) + (2w x 150)}

B: {w + 2w} = 3w


when we divide A by B we see that "w" cancels out.

Average weight of the entire group is 140.

Therefore (2) is sufficient.



Statement 1

We know the No. of males, however the No. of females are not known. therefore it is not sufficient to find average weight of the group.


(Please note that in DS questions we don't have to find exact solution. So in case of statement (2) we don't have to find the exact average weight. This has been done just to show that we don't require exact Nos. of Men and Women, their ratios will serve the purpose.

My suggestion would be to solve some problems of weighted average concept. With enough practice, you will soon figure out that statement (2) is sufficient to provide a solution.)

[shrivastava.rohit]

Thanks for explaining.

[RonPurewal]

the above post is a nice explanation of the full-on algebraic solution to this problem. however, as it turns out, there's a shortcut -- all that is necessary is the ratio of the number of men to the number of women.

the full explanation of the shortcut involves number lines, and can be found on the december 17 recording at the following link:
http://www.manhattangmat.com/thursdays-with-ron.cfm