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Averages!

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by kamu » Wed Mar 11, 2009 3:12 pm
Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean)
price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?
(1) The five most expensive items each increased in price by 10%.
(2) The five least expensive items each decreased in price by 10%.

OA : C

I took 4 minutes for this!
any suggestions..
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by cramya » Wed Mar 11, 2009 4:20 pm
Stmt I

No idea on what happenned to the 5 least expensive items. They could have given away for free or could have increased/decreased.

ISNUFF

Stmt II

No idea on what happenned to the 5 most expensive items


I would pick 10 numbers which are multiples of 10


10 20 30 40 50 60 70 80 90 100

As u can see a increase by 10% to the larger elements(>=50) of the list keeps getting more and more whereas a decrease on the smaller elements(<=50) keeps getting less and less. So overall sum/total increase and the no of elements remains the same and hence the average will definitely increase.

Choose C


Some useful concepts on averages:

If a constant k is added to each of the elements in a list then the new average = old average + k.


If a constant k is subtracted to each of the elements in a list then the new average = old average - k.

If each element is multiplied by a constant k then the new average = old average * k


If each element is divided by a constant k then the new average = old average / k


I just included these concepts as an FYI for this problem the 10% increase and decrease will not be a constant as explained in my post above.


Hope this helps and I have not misstated something! Experts please correct me if so.


Regards,
CR
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