A class consists of boys and girls only. On a final exam in

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 :\(\frac{4*50+4*70}{4+4} = 60\)

Hence, 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.

Thanks alot for this explanation. It helped me alot to understand how these questions work.

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