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by parulmahajan89 » Tue Feb 11, 2014 5:46 pm
The average arthmetic mean(average monthly) income of four workers is $2200.After one worker's income increases by 25% the new average income is $2400. What was the original income of the worker whose monthly income was increased?

1)$800
2)$1200
3)$2400
4)$3200
5) It cannot be determined from above
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by Brent@GMATPrepNow » Tue Feb 11, 2014 6:02 pm
parulmahajan89 wrote:The average arthmetic mean(average monthly) income of four workers is $2200.After one worker's income increases by 25% the new average income is $2400. What was the original income of the worker whose monthly income was increased?

A)$800
B)$1200
C)$2400
D)$3200
E) It cannot be determined from above
When it comes to averages, we know that average value = (sum of n values)/n
We can rewrite this as a useful formula: sum of n values = (average value)(n)

The average monthly income of 4 workers is $2200.
So, the SUM of the 4 incomes = ($2200)(4) = $8800

After one worker's income increases by 25% the new average income is $2400.
So, the NEW SUM of the 4 incomes = ($2400)(4) = $9600

So, the increase = $9600 - $8800 = $800

Where did this increase come from? It came from the 25% raise.
If $800 represents a 25% raise, then the employee's original income was [spoiler]$3200[/spoiler] [since 800/3200 = 25%]

Answer: D

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by GMATGuruNY » Tue Feb 11, 2014 6:10 pm
parulmahajan89 wrote:The average arthmetic mean(average monthly) income of four workers is $2200.After one worker's income increases by 25% the new average income is $2400. What was the original income of the worker whose monthly income was increased?

1)$800
2)$1200
3)$2400
4)$3200
5) It cannot be determined from above
.

Old sum = (number of workers)(old average) = 4*2200 = 8800.
New sum = (number of workers)(new average) = 4*2400 = 9600.
New sum - old sum = 9600-8800 = 800.

Since one worker's income increases by 1/4, the $800 increase in the sum must be equal to 1/4 of this lucky worker's original income:
800 = (1/4)x
x = 3200.

The correct answer is D.
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