At a particular business school which requires applicants to submit GM

Hi,

you dont require the exact number here as you have the ratio as we are working on average of two sets of items..


lets take a simple scenario..
10 % of a class has average of 90 marks and 90% has an average of 50 marks..
combined average = \(50+40*\frac{100-90}{100}=50+4=54\)

Now say the strength is 50.
so 10% that is 5 have 90 and remaining 45 have 50..
combined average = \(\frac{5*90+45*50}{50}=54\)

Let Average admitted GMAT score=\(x_{avg}\), Average rejected GMAT score=\(y_{avg}\), \(n_1\)=no of applicants admitted, \(n_2\)=no of applicants rejected

Given, \(x_{avg}=y_{avg}+15\)
Question stem:- Average GMAT score of all applicants in 2017= \(\frac{n_1*x_{avg}+n_2*y_{avg}}{n_1+n_2}\) ?-----------(a)

St1:- \(x_{avg}=700\) so, \(y_{avg}=700-15=685\)

But , we have no information on no of students.
hence insufficient

St2:- Let 'n' be the total no of applicants in 2017.

Given, \(n_1\)=10% of n=0.1n, so \(n_2=n-n_1=n-0.1n=0.9n\)

We know only the ratio of \(n_1\) & \(n_2\), however, no information available on \(x_{avg}\) and \(y_{avg}\).

Hence insufficient.
(1)+(2),

from (a), we have, Average GMAT score of all applicants in 2017= \(\frac{700*0.1n+685*0.9n}{n}\)=70+616.5=686.5

Therefore, Answer is (C).

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