I dont understand this DS

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nhai2003: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Tue Feb 10, 2009 11:30 pm

I dont understand this DS

by nhai2003 » Sun May 31, 2009 3:29 am

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.

The answer is E,

but I think the answer is A. Average score of all students = Average of class A + Average of class B

Is it right?

Thanks guys

Quote

Source: Beat The GMAT — Data Sufficiency | Sun May 31, 2009 3:29 am

Sher1: Master | Next Rank: 500 Posts; Posts: 116; Joined: Fri Feb 20, 2009 9:26 am; Location: New Jersey; Thanked: 7 times; GMAT Score:660

by Sher1 » Sun May 31, 2009 4:29 am

The answer can't be A because to get the average of the class you need two things.
1. Average scores
2. Number

This is a weighted average problem.

If you add averages the answer is 161. Average of the two can not be higher than either the two numbers. Has to be in the middle, depending on which class has more people or weight in other words

1 is insufficient

2 by itself doesnt tell us B's average

Together you sill don't know the number of people

Try a few examples and you will understand

if A has 1 person who scored 79.5 and B had 26 with average of 80.5, weithed average = (Average A * #A + Average B*#B)/Total #

or A is 2 people and B has 27. Using the formula above you will get a different result.

Hope this helps