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In her position as a real estate agent, Sarah receives a bon

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In her position as a real estate agent, Sarah receives a bon

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In her position as a real estate agent, Sarah receives a bonus for each sale she makes. Last week, she earned a $4,000 bonus, which decreased her average bonus amount to $4800. If this represents a decrease of 4%, how many sales has Sarah made?

A 4
B. 5
C. 8
D. 16
E. 25

OA B

Source: Veritas Prep

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BTGmoderatorDC wrote:
In her position as a real estate agent, Sarah receives a bonus for each sale she makes. Last week, she earned a $4,000 bonus, which decreased her average bonus amount to $4800. If this represents a decrease of 4%, how many sales has Sarah made?

A 4
B. 5
C. 8
D. 16
E. 25
Last week, Sarah earned a $4,000 bonus, which decreased her average bonus amount to $4800. This represents a decrease of 4%.
Let x = OLD average bonus amount
We can write: x - 0.04x = $4800
Simplify: 0.96x = $4800
Solve: x = $4800/(0.96) = $5000

How many sales has Sarah made?
Let n = the TOTAL number of sales that Sarah has made.
This means (n-1) sales had an average bonus amount of $5000, and 1 sale had an bonus amount of $4000
All of this results in an AVERAGE bonus amount of $4800
We can write: [(n-1)($5000) + (1)($4000)]/n = $4800
Multiply both sides by n to get: (n - 1)(5000) + (1)(4000) = 4800n
Expand: 5000n - 5000 + 4000 = 4800n
Simplify: 5000n - 1000 = 4800n
Solve: n = 5

Answer: B

Cheers,
Brent

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Original average = 4800/0.96 = 5000

New bonus = 4000

Everyone was 5000 before and now by adding 4000, everyone becomes 4800. The new 4000 also become 4800.

The new bonus of 4000 got 800 from others to become 4800 (new average).

All the old one (5000) became 4800, so all gave 200 to new guy 4000, so that he becomes 4800. It means 4 old guys gave 200 each.

So there were 4 old and 1 new
total =5

The correct answer is B.

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GMAT/MBA Expert

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Hi All,

We're told that Sarah receives a bonus for EACH sale she makes - and that last week, she earned a $4,000 bonus, which decreased her AVERAGE bonus amount to $4800 (which represents a decrease of 4%). We're asked for the number of sales Sarah made. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, since both the $4800 and 4% are whole numbers (notice that there are no decimal points), Sarah's prior number of sales AND her total number of sales are likely numbers that do NOT lead to repeating decimals when they are divided into a larger number. For example, when dividing an integer by 1 or 2, the result will NOT be a repeating decimal (whereas when dividing by 6 or 7, most of the time the result will be a repeating decimal). Thus, we are likely looking for a total AND '1 less' than the total that both create a non-repeating decimal. The only answer choice that fits THAT pattern is B (re: 4 sales and 5 sales), so we'll TEST that answer first:

Answer B: 5 total sales
Average = $4800/sale, so TOTAL sales = ($4800)(5) = $24,000
Most recent sale = $4000, so prior total = 24,000 - 4000 = $20,000
Prior average = $20,000/4 = $5000
A decease from 5000 to 4800 = (5000 - 4800)/5000 = 200/5000 = 2/50 = .04 = 4%

This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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