manik11 wrote:If the average (arithmetic mean) annual income for a group of people is x, where x >0, and the annual income of one of the members of the group, Joe, increases by 25%, by what percent does the average income of the whole group increase?
(1) There are 8 people in the group.
(2) The total initial income of the group is 9 times Joe's initial income.
OA : B
Let Joe's initial income = 100.
Increase in Joe's new income = 25% of 100 = 25.
Question stem, rephrased:
What is the value of (new average)/(old average)?
Statement 1:
No way to determine the new average or the old.
INSUFFICIENT.
Statement 2:
Total old income = 9*100 = 900.
After Joe's income increases, new total income = 900+25 = 925.
Case 1: 10 people in the group
Old average = 900/10 = 90.
New average = 925/10 = 92.5
Resulting ratio:
(new average)/(old average) = 92.5/90 = 185/180.
Case 2: 5 people in the group
Old average = 900/5 = 180.
New average = 925/5= 185.
Resulting ratio:
(new average)/(old average) = 185/180.
Since the ratio is THE SAME in each case, SUFFICIENT.
The correct answer is
B.
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