Beat The GMAT a GMAT & MBA community

IMO B is the answer here. What is the OA?

Yeah Your are very much correct!
We need to apply Weighted Average Concepts:

{(A1 * N1) +(A2 *N2)}/ (N1+N2) eqauls Total weighted average Aw.

St 1 gives only number of Men. Insufficient.

St2 : gives a relation between men & women . But not exact figures which we are looking for. Let us equate them as of now. N1=2*N2

Combining both of them, we can fing the Weighted average!

Pick C

_________________
R&D on GMAT algorithm:

http://www.beatthegmat.com/r-d-on-gmat-prep-t67692-15.html#305739

Can you please solve this for me in more clarity, i have solved it in simple logical sense. but i want to know how you apply the weighted average concept. Thanks

gmatmachoman - As per the statement 2 N1= 2*N2 -- N2 actually cancels out. I don't think we need statement 1. agree?

How ? i dint get u? please help me understand. I was expecting this answer since its mentioned that we dont require the statement 1 but im looking out for explanation.

Now that from St 2 we know N1 = 2 *N2

N1 +N2 = 3*N2

Apply this one in the main equation

{(A1 * N1) +(A2 *N2)}/ (N1+N2) eqauls Total weighted average Aw.
{150 * 2N2 + 120 * N2}/3*N2

As Boazkhan said N2 cancels out: (Sorry for my mistake)

(150 * 2 +120) *N2/(3*N2)

=140

Lesson Learnt : Dont be so hasty when it comes to Weighted average concepts..Knowing them is one part but applying them is also as equal as "knowing them".

_________________
R&D on GMAT algorithm:

http://www.beatthegmat.com/r-d-on-gmat-prep-t67692-15.html#305739

Nice Question. I got it wrong I thought we need both infomation.

I don't know if this is the approved solution on how to solve it but it gave me the right answer.

F=Total of Females
M=Total of Males
TFW = Total Female Weight
TMW = Total Male Weight
Sum/n = Avg

Setup:
(TFW+TMW)/(F+M) = The Avg weight of all competitors (what we're trying to find)

Given: (TFW)/(F) = 120 or TFW = 120F
Given: (TMW)/(M) = 150 or TMW = 150M

They gave us a 2:1 ratio of men to women so I just said 2/1 = M/F, therefore M=2 and F=1

Plug all the numbers into the first equation...
(TFW+TMW)/(F+M) = The Avg weight of all competitors
(120F + 150M)/(F+M) = The Avg weight of all competitors
now plug in 2 & 1 for M & F...
(120*1+150*2)/(3)= The Avg weight of all competitors = 140; since I have an answer I know (B) is sufficient. Answer is B.

There is a neat little trick, which I learned in a MGMAT study hall from the great Lunarpower, for this problem. Basically the principle is, if we know the average weight of X and the average weight of Y, and the average weight of X+Y, we know the ratio of X to Y. The ratio of X to Y is the inverse of the distance X is from the average to the distance Y is from the average.

For example, let's say we have a room full of football and basketball players. The average weight of basketball players is 180 pounds and the average weight of football players is 210 pounds. The average of both basketball and football players is 200 pounds. Using the principle listed above, since the weight of basketball players is 20 away from 200, and the weight of basketball players is 10 away from 200, we know that the ratio of basketball players to football players is 10 to 20, or 1:2. We can always figure out the ratio of X to Y, as long as we know the average of X, average of Y, and the average of both.

We can apply that principle to this problem. The problem gives us the average weight of men, 150, and the average weight of women, 120, in the problem.

Statement 1 gives us the total # of men. Just using basic principles of weighted average we know that we need to know the # of women, thus insufficient.

Statement 2 gives us the ratio of men to women, 2 to 1. Since we know the average weight of men as 150, the average weight of women as 120, and we are given a ratio of 2 to 1 for men to women, we know we can calculate the average using the trick we just learned. Instead of figuring out a ratio, we are working "backwards" for an average. Sufficient.


Hopefully you guys can understand my rambling, if you have any questions feel free to ask.

How did you get 1/3 and 2/3?

1/3 is the ratio of women. 2/3 is for men. since there are twice as many men as women, that is why the ratio is as such.

Stuart, when you say we need to know the "weight" of each group, you then use the fractions 1/3 and 2/3, which clearly refer to the w:m ratio of 1:2. To clarify, then, by "weight" you mean the ratio of one to the other?

Just want to make sure I'm clear, because it's a really elegant solution.

Thanks!