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Mean Changes

by sampath » Sun Aug 14, 2011 11:30 am
X is the average price of 10 items of which no two cost the same. If each of the cheapest 5 items loses 10% in price while each of the most expensive 5 items gains 10% in price, which of the following is possible about ?
I. X will decrease
II. X will not change
III. X will increase
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by GmatKiss » Sun Aug 14, 2011 11:33 am
IMO: X will increase
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by gmatboost » Mon Aug 15, 2011 9:40 am
Each change is 10% of the previous price.
The 5 increases are EACH bigger than ANY of the 5 decreases, since the increases are taken from LARGER initial amounts.
This means the total increase > total decrease, so X goes up.
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by GmatKiss » Tue Aug 16, 2011 12:11 am
Can you post the OA please!
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by zouril » Tue Aug 16, 2011 12:47 am
If A is the sum of the cheapest items and B the sum of the most expensive items, then

A decrease of 10% in A and an increase of 10% in B would result in a value change of the average as follows

X + 10% (B-A) which is a positive number since B>A

X will therefore increase
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