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555-605 (Medium)|   Statistics and Sets Problems|                     
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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AbdurRakib
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?

(1) x - y = y - z

(2) x^2 - y^2 = z

Answer: Option E

Video solution by GMATinsight

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A lot of people are saying that the statements can not be sufficient since they have no numerical value. This is NOT entirely true, and it is therefore dangerous to make a conclusion on this premise alone even though it is true for this exact question.

For example, IF one of statements where xy+xz=y, this would give us x+z=1. And since we are looking for (x+z)/2, we can conclude that the arithmetic mean of x and z is 1/2.
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Q. what is x+z/2 ?

1. after solving, x+z/2 = y. Since we don't know y. (Insufficient)
2. same as a three variables, can't solve for AM
1&2, we have 2 equation but we have 3 variables. Hence E.
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