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

Question

A class consists of boys and girls only. On a final exam in physics, the average score of the girls is 62 and the average score of the boys is 60. Is the average score of the class 61 ?

(1) Mathew is one of the classmates and he has the same number of boy classmates as girl classmates.
(2) The number of students in the class is 151 .

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mau5 · Answer

The given average of all the boys= 60 and the average of all the girls = 62. For an average score of the class to be 61, the no of girls will have to be the same as the no of boys.

From F.S 1, we know that there are n+1 boys and n girls. Thus, the average can't be 61. Sufficient.

From F.S 2, we know that the sum is an odd number and the no of girls and boys can't be the same.Sufficient.

D.

kalrac · Answer

From the question (60 + 62)/2 = 61 , i.e the no.of boys and girls should be equal to get the avg as 61
1. Mathew + n boys , n girls implies n+1 boys and n girls -- suffice
2. 151 is odd -- suffice

IMO D

skamran · Answer

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

mau5 · Answer

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.

skamran · Answer

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

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

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