should be option D. Since, if we use the boundary condition of 3x, this ratio gives us the upper limit of the averages that is 82. So the average could be lower than that, if more than 3x boys are present, but certainly not more than 82.

Average of class = (78*3x + 94x)/(3x+x) = 82, when we have Boys atleast 3 times of girls, if Boys are higher in numbers then Denominator will increase more and Average will reduce further.

Say, boys = 4x and girls = x, Average of class = (78*4x + 94x)/(4x+x) = 81.5

So, I think D.

There are at least three times as many boys as girls in a class. On a test, the boys’ average score is 78, and the girls’ average score is 94. Which of the following could be the average test score for the entire class?

I. 84
II. 82
III. 80

Tricky one .. Importnat to notice the word at least and could be
so b > 3g

so avg =\( \frac{ (78 * 3g + 94 * g )}{ (3g + g) }\)=> 82 .

Hence if we increase denominator .. the overall value will be decreased ..
e..g.. lets take b=10g
avg = \( \frac{(78 * 10g + 94 * g) }{ (10g + g) }\)=> 79.XX.

Hence ans will be 82 or 80 ... D

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
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