Have: The average (arithmetic mean) score for class A was 79.5.
NEED: What was the average score for all the students in both classes?
Inference: A = sum of Class A scores
B = sum of Class B scores
a= total students in class A
b= total students in class B
x= variable required, average score of students from both classes
Need to solve using this --> (A+B)/(a+b) = x
Have: arithmetic mean for Class A: (A)/(a) = 79.5 or (A)= 79.5(a)
Statement (1) The average score for class B was 80.5.
(B)/(b) = 80.5
In the equation from above we get B= (b)(80.5) but we don't know what (b) is, nor do we have a value for (a)
So the equation looks like this
[(79.5)(a) + (b)(80.5)]/(a+b) = x --> no value for a, or b, so no x
NO SUFFICIENT (not A or E)
Statement (2) Class B had 25 fewer students than class A. b = a-25
a = ?
Equation would look like this: [(A+B)]/[a+a-25] = [(A+B)]/[2a-25] = x; we don't have values for A, B, a, so we can't get x
<b>NO SUFFICIENT</b>
(not B)Together: From Statement 1: [(79.5)(a) + (b)(80.5)]/(a+b) = x
From Statement 2: b = a-25; a = ?; (A+B)/(2a-25)
[(79.5)(a) + (a-25)(80.5)]/(2a-25) = x where we still don't have a variable for a and not
sufficient to find x, so not together
(answer choice C) answer choice E
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