Quote:
A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number of tickets sold by the male members of the association
This is a weighted average question, to solve it quickly, we should realize that the formula is as follows:
\(\frac{X(1) + 70(2)}{1+2}=66\)
But, you don't need to use it like that! This is a sub-600 question, so it's easy to make an actual calculation, but it will still take your time, better to understand the following:
If there are more of X, then weighted average WILL BE closer to X.70 - 66 =
4, we have 2 of 70, so the overall effect is +8, that is how much X(females) drags average away from Y(males). So, we should take that and divide by number of males and subtract from average.
So the formula:
\(66 - \frac{4*2}{1} = 66 - 8 = 58\). Answer: And that's why it doesn't matter if we have 2 females and 1 male, or 800 females and 400 males.
This is important, because sometimes absolute values might be huge and many, while differences between the values and averages are usually small on GMAT (my experience).
To better understand the importance of using a deviation from average instead of absolute values see the following question:
if-the-average-of-116741.html