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

A class consists of boys and girls only. On a final exam in History, the average score of the girls is 72 and the average score of the boys is 70. Is the average score of the class 71?

(1) Smith is one of the classmates and Smith has the same number of boy classmates as girl classmates.

(2) The number of students in the class is 101.

IMO C
1) Smith is one of the classmates and Smith has the same number of boy classmates as girl classmates.
we do not know about the number of boys and girls , we just know that g+1=b (Insuff)
(2) The number of students in the class is 101.
We just know about the total number, cant find the average with it (Insuff)
Combining :
g+b=101
g+1+g=101
g=50 and b=51
From this we can find the weighted average (suff)

Mutiply gxgirls average plus g+1 x boys average. Then divide by g+(g+1).

A is sufficient

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Looking at the two statements given below, we are not told the individual total scores for each sex. This means that we need to look at ratios. Because the girls have an average 72 and the boys have an average of 70, for their combined average to be 71 the number of girls and boys in the class needs to be equal.

(1) Smith is one of the classmates and Smith has the same number of boy classmates as girl classmates.

This tells us that there is 1 more boy than the total number of girls. This means that it is impossible for their combined average to be 71.

SUFFICIENT

(2) The number of students in the class is 101.

As there are a total of 101 students in the class, it is impossible for their to be an equal number of boys or girls which means that once again it is impossible for the classes combined average to be 71.

SUFFICIENT

Answer D

From the question statement we do not know whether Smith is a boy or a girl.
Hence, Combining 1 & 2 we can have
g=50 and b=50+1 (Smith) or g=50+1(Smith) and b=50
And, average score could be
\(\frac{50*72+51*70}{101}\) OR \(\frac{51*72+50*70}{101}\)
= \(\frac{7170}{101}\) OR \(\frac{7172}{101}\)

Hence IMO answer: E

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