skamran wrote:

I still don't understand how the statement 1 alone is sufficient, how can we find out the average score through Mathew??

Say we have 2 groups A and B, and each group has only 1 person. Average/Individual score of person in Group A = 50, and that of person in Group B = 70.

Thus, overall Average score = 60( which is exactly the mid-point between the 2 individual scores). Now imagine, I add 3 person each in both the groups, with the same exact indvidual score for that group : Thus, the overall average :

\frac{4*50+4*70}{4+4} = 60Hence, if the # of people on both the groups is exactly the same, the overall average will always be the mid-point of the 2 individual averages.

From F.S 1, we know that there are n girls and n+1(This is Matthews) boys, and the # of people on both sides is not the same. Thus, the overall average can never be the mid-point of the given individual averages, i.e. 61. As the # of boys is more than the no of girls, the overall average will be a little closer to 60. Had the # of girls been more than boys, the overall average would have been closer to 62.

Hope this helps.

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