Hi,
First i like to thank
VeritasKarishma, for teaching weighted averages. if you master that concept ,it could be used in variety of problems. It finds applications in most of the question on GMAT. Most importantly if you can find the scenarios you can use the concept you would be saving 5 to 7 mins on the exam. Similar example is this question.
What are we asked. Does n lie closer to 50 than to 75. If i know the weights of 50 and weights of 75 i could say where would n lie. Say weight on 50 side were to be more than n would lie closer to 50 than to 75. But if weights on 75 side were more than we could conclude that n would be closer to 75 than to 50.
if you knew the allegation or weighted averages technique. This is how it would turn out . Let weights on 50 side be \(w_1\)and weights on 75 side be \(w_2\), then we know that \(\frac{ 75-n}{n-50}=\frac{w_1}{w_2}\). Can we say that \(75-n=w_1\) and \(n-50=w_2\)
Now Statement A: This statement precisely says that \(w_1>w_2\). so we can conclude that n will be closer to 50 than to 75
Statement B: n>60 Since n takes any value more than 60 we can't conclude conclusively that n will be closer to 50 than to 75
I did not do any of the calculations for this question and yes people did solve it in < 60sec. But I have learnt one point brain uses energy during the real battle. We must learn to use this energy so that for the fierce enemy we do have enough to conquer and win.
Probus