shiftcourse wrote:If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the assessed values of y other houses is $194,000, what is the average of the assessed values of x + y houses?
1) x + y = 36
2) x = 2y
Answer: B
The way I read this question it seems like the average of x + y houses would just be ($212,000 + $194,000)/2.
Why is that not true?
Hi shiftcourse,
Computing the average as ($212,000 + $194,000)/2 underlies an assumption that x = y, ie, the number of type 1 houses (x in number) is equal to the number of type 2 houses (y in number); however, it is not stated in the question.
Had this been the case, you do not need any statement at all. On a funny note, the question is self-sufficient to be solved!
This question tests the concept of Weighted Average. When the number of quantities is not equal, one must take into account their relative importance, ie, their count!
Weighted average = Total value / Total numbers
Total value of (x+y) number of houses = 212000*x + 194000*y
We have, Total number of houses = (x+y)
Thus, Weighted average = (212000*x + 194000*y) / (x+y)
Statement 1: x+y = 36
In Weighted average = (212000*x + 194000*y) / (x+y), we only know the value of the denominator (x+y), thus we cannot calculate the value of Weighted average. Insufficient!
Statement 2: x = 2y
We can put x = 2y in Weighted average = (212000*x + 194000*y) / (x+y)
=> Weighted average = (212000*x + 194000*y) / (x+y) = (212000*2y + 194000*y) / (2y+y)
=> Weighted average = (414000y + 194000y) / 3y
=> Weighted average = (414000 + 194000) / 3; y cancels
Weighted average = a unique value. There is no need to calculate if you are satisfied that you get a unique value. Sufficient.
The correct answer:
B
Hope this helps!
Relevant book:
Manhattan Review GMAT Data Sufficiency Guide
-Jay
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