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Weighted averages - To find the average income of the town

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by gmattesttaker2 » Sun Feb 09, 2014 12:03 am
Hello,

Can you please assist with this question? I was not sure how to solve Statement 2.

What is the average income at Town A?
(1) The combined income of the people at Town A is $42,000,000.

(2) 60 percent of the people at Town A have an average income of
$36,000 and the rest have an average income of $55,000.

OA: B


Thanks,
Sri
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Feb 09, 2014 4:44 am
gmattesttaker2 wrote: What is the average income in Town A?

(1) The combined income of the people in Town A is $42,000,000.

(2) 60 percent of the people in Town A have an average income of
$36,000 and the rest have an average income of $55,000.
Statement 1: The combined income of the people in Town A is $42,000,000.
Without knowing the number of people in Town A, we cannot determine the average income.
INSUFFICIENT.

Statement 2: 60 percent of the people in Town A have an average income of $36,000 and the rest have an average income of $55,000.
60% = 3/5.
Thus, of every 5 people, 3 earn an average of $36000, while the remaining 2 people earn an average of $55000.
Resulting average for every 5 people = (3*36000 + 2*55000)/5 = 43,600.
SUFFICIENT.

The correct answer is B.
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by [email protected] » Mon Feb 10, 2014 12:15 am
Hi Sri,

Mitch has provided a great explanation for this question. I want to add a bit more "proof" to Fact 2, in the (likely) event that you face something like this on the Official GMAT...

Fact 2 essentially tells you about a 60/40 ratio between people who average $36,000 and those who average $55,000.

That could be
3 @ $36,000
2 @ $55,000

Average = [3(36,000) + 2(55,000)]/5 = 43,600

It could also be
6 @ $36,000
4 @ $55,000

Average = [6(36,000) + 4(55,000)]/10 = 43,600

Since the average stays the same, Fact 2 is SUFFICIENT. If you're ever unsure about how to assess ratio "data", then just track two examples - if the answers are the same, then you're dealing with Sufficient information.

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