GMAT Math : Calculating arithmetic mean
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Example Question #51 : Arithmetic Mean
Give the arithmetic mean of 
Statement 1:
Statement 2:
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
The arithmetic mean of 
Statement 1 alone provides insufficient information to find the mean. For example:
If
then
and
But if
then
and
Statement 2 alone provides sufficient information:
Example Question #52 : Arithmetic Mean
Give the arithmetic mean of 
Statement 1: A trapezoid with bases of length 
Statement 2: If 
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
The arithmetic mean of two numbers is half their sum.
Assume Statement 1 alone. The area of a trapezoid can be calculated from its height 
Setting 
Therefore, the arithmetic mean of 
Assume Statement 2 alone. A geometric sequence is one in which the ratio of each term to the previous term is constant - a common ratio. Consider these two sequences:
Both sequences have 810 as their third term. Both are geometric; the common ratio of the first sequence is 9, and that of the second is 10. The arithmetic means of the first two terms, however, are different. In the first sequence it is
In the second sequence, it is
Therefore, Statement 2 alone gives insufficient information.
Example Question #521 : Arithmetic
Some balls are placed in a large box, which include one ball marked "10", two balls marked "9", and so forth up to ten balls marked "1".
A carnival wants to set up a game by which a player can pay to draw a ball and win an amount of money equal to the number marked on the ball drawn. What should the carnival charge per play in order to make the expected value $1 per game in the carnival's favor?
The total number of balls in the box will be
Since
it follows that the number of balls is
The frequencies out of 55 of each outcome from 1 to 10, in order, is as follows:
Their respective probabilities are their frequencies divided by 55:
The expected value of the payment that the church will have to make per game can be calculated by multiplying the frequency of each outcome by the respective payment:
...and then adding these products.
The carnival should expect to pay a prize of $4 per draw, so to expect an average profit of $1 per game, it should charge $5 per play.
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