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by raju232007 » Thu Jan 21, 2010 2:36 pm
For a certain company X, the average daily payroll for each 30-day payroll cycle is the average (arithmetic mean) of the daily payroll totals for each of the 30 days. During the first part of a recent 30-day payroll cycle, the daily payroll was a constant $5,750. When a new employee was hired during this 30-day cycle, the total payroll for each day rose by $280. If the new daily payroll total remained constant for the remainder of the cycle, what was the average daily payroll for the 30-day cycle?

(1) The new employee was hired on the 11th day of the payroll cycle.

(2) The average daily payroll was $5,890 through the first 20 days of the cycle.

OA is D..

I don't understand how the second statement is sufficient to answer the question. Could somebody help me with this?
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by KapTeacherEli » Fri Jan 22, 2010 1:52 pm
Hi Raju,

We have a data sufficiency problem. The first step in the Kaplan Method for data sufficiency is to analyze the stem, figuring out what information we need. Given the title of this thread (weighted averages) you've already done that; we need to know how many days of that 30 day payroll cycle are spent without the new employee, and how many are spent with him. That will let us figure out the total amount of money spent on payroll, and therefore the average daily payroll that the problem asks for.

Once we've figured that out, evaluating (1) is simple enough; it gives us exactly the information that we predicted we'd need. Remember, eliminate choice B, C, and E as soon as we know (1) is sufficient.

(2) is a little trickier. Kaplan's advice for these situations is to take a step back and look at the big picture. On average problems, it often helps to write out the average formula out, even if you're already comfortable with it. If we do so, we get:

Average = Sum of terms/number of terms.

When evaluating (2), it's easy enough to plug in two of those values.

5,890 = Sum of terms / 20

We're trying to get the number of days before the new employee joined. We'll call that number x. So, for x of those 20 days, the company payed $5,750 to its employees, and for the remaining 20-x days, they payed $5,750 + $280. That lets us set up a mathematical formula for the total amount of money payed. Plugging it in to our previous work, we get:

5,890 = {5750x +(5,750 + 280)(20-x)} / 20

Not that we don't even bother to do the addition, let alone solve the algebra. Our goal is to show whether there is only a single possible value. By writing out a first-degree, single-variable algebraic expression, we have definitely proven that there can be only one possible answer for the day the new employee joined--and therefore, only one possible answer for the average 30-day payroll. (2) is sufficient, and our final answer is (D)
Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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