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Manager  Joined: 20 Nov 2009
Posts: 122
Class A and class B took the same test. The average  [#permalink]

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7 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:18) correct 28% (01:03) wrong based on 122 sessions

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Class A and class B took the same test. The average (arithmetic mean) score for class A was 79.5. What was the average score for all the students in both classes?

(1) The average score for class B was 80.5.
(2) Class B had 25 fewer students than class A.

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SVP  Status: Three Down.
Joined: 09 Jun 2010
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Concentration: General Management, Nonprofit
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Statement 1 gives you the average arithmetic mean for class B but then it doesn't mention how many students were there in the classes. So insufficient.

Statement 2 gives you the comparison between the number of students in the two classes but no information about the mean in class B. So insufficient again.

Putting together, we still don't know the absolute numbers of the number of students in the classes. Hence the answer is E.
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Re: Class A and class B took the same test. The average  [#permalink]

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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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Re: Class A and class B took the same test. The average  [#permalink]

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To find average we need 4 things: Av of Class A, Average of Class B, Total No. of students in Class A & Total No. of students in Class B.
Even with both statements together, we don't get all the 4 variables so insufficient.
Senior Manager  G
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Joined: 05 Feb 2018
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Re: Class A and class B took the same test. The average  [#permalink]

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This is a weighted average problem, so we can use the formula Avg=Avg1*weight1+Avg2*weight2 / weight1+weight 2
We have Avg 1 (Class A's average).

1) Gives us Avg 2, but we don't have the weights (amount of students). The trap here is that IF the weights were the same we could simply do Avg1+Avg2/2, but since we don't know this for certain it's insufficient.

2) We are given that weight 1 = weight 2 + 25. No info about Avg 2, insufficient

3) Combining the two doesn't help because we still don't have a concrete value for weight 1 or weight 2. Insufficient.
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Re: Class A and class B took the same test. The average  [#permalink]

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_________________ Re: Class A and class B took the same test. The average   [#permalink] 29 Apr 2019, 08:10
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