In her position as a real estate agent, Sarah receives a bonus for eac

Question

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

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

laulau · Accepted Answer

Using the % change formula, with x representing sales: \frac{800}{4000}=\frac{4}{100}x \frac{1}{5}*\frac{100}{4}=x \frac{100}{20}=x 5=x Please hit Kudos if you liked this approach

quantumliner · Answer

Let the initial average Bonus be 100x
Decrease of 4% on initial average Bonus, should make the new average bonus as = 96x
New Average bonus = $4800

Therefore 96x = 4800, x = 50. 
Initial Average Bonus = $5000

Let prior sales = n

Therefore (n*5000 + 4000)/(n+1) = 4800

5000n + 4000 = 4800n + 4800
200n = 800
n = 4

Therefore total number of sales made by Sarah is 5

Answer B. 5

aa008 · Answer

Original average=4800/0.96=5000
new bonus=4000

My thinking process of calculating average.

think that, everyone was 5000 before and now by adding 4000, everyone becomes 4800. the new 4000 also became 4800.
new bonus of 4000 got 800 extra 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

answer is B

ScottTargetTestPrep · Answer

The old average was 4800/0.96 = 5,000. We can let n = the number of sales she made and create the equation:

/n = 4800

5000n - 5000 + 4000 = 4800n

200n = 1000

n = 5

Answer: B

KanishkM · Answer

Can someone please tell me why we divided by n + 1 ?? I was able to calculate till the average i.e. Average = 5000 ( It took me 5 mins to come to this step

) x = Number of sales and made this equation, by using average = \frac{initial value * number of sales}{total number of sales} \frac{5000x + 4000}{x} = 4800 after that step i was stumped.

KarishmaB · Answer

When you assume x = Number of sales, is this the new number of sales or previous (before the $4000 bonus sale)?
If this is new number of sales, then you need to use 5000*(x - 1) in the numerator.
If this is previous number of sales, you need to use (x + 1) in the denominator since that is the total number of sales now.

Also, use some observation to figure out 
4800 = A - (4/100)*A = (96/100)*A
A = 4800*100/96 = 100*100/2 = 5000 (note that 96 is twice of 48)

KanishkM · Answer

After going through the  highlighted  i realized my gap.

Thank you Karishma for your help on this.

BrentGMATPrepNow · Answer

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

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EMPOWERgmatRichC · Answer

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

dave13 · Answer

VeritasKarishma if $4,000 bonus decreased her average bonus amount to $4800, why would people assume that that Sarah received exactly same bonus per each sale, different numbers could yield average bonus amount to $5000

EMPOWERgmatRichC · Answer

Hi dave13,

Since this prompt refers to her AVERAGE bonus, it's just convenient to assume that all of the prior bonuses are for the same amount. They obviously might not be exactly the same, but that doesn't really matter as long as you can calculate the TOTAL of those prior bonuses. As an aside, thinking about all of the various ways that you might get to that TOTAL does not help you at all with this question (and doing so would make the whole process of working through this question take longer).
 
GMAT assassins aren't born, they're made,
Rich

ishita27 · Answer

This is my approach,

Initial sale amount be "x" and number of sales by "n"
x + 4000/n = 4800 -(i)

By %decrease formula,
4 = x - 4000/4000
16000 = x - 4000
x = 20000

Put the value of x in (i)
20000+4000/n = 4800
n= 24000/4800
 n = 5

KarishmaB · Answer

dave13  - We are not assuming that all previous bonuses were same. The average was 5000 (so there could have been a bonus of 3800 and another of 6200 etc). Just that the average was 5000 so if she received x bonuses, the total amount she received is 5000x.

Adding a bonus of 4000 brought the average down to 4800 because this bonus was 1000 less than average.
Since the average came down by 200, it means there are total 5 bonuses.

Mathematically,

4800 = (5000x + 4000)/(x + 1) 
x = 4
So x + 1 = 5 (the total number of bonuses she has received now)

Ismail12 · Answer

Can some one please help me out?

Why are we assuming the number of sales last week to be 1?

My approach was, Sarah made m number of sales before last week, average bonus was 5000 ( 5000m) (Found by decrease of 4% mentioned)
She made n number of sales last week, for which she earned 4000 (4000n).

Therefore, 5000m+4000n/m+n= 4800
which gives m=4n.

Both answer choices A and E satisfy the above equation.
Did I misinterpret the question? I don't see where I have faltered.

bumpbot · Answer

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In her position as a real estate agent, Sarah receives a bonus for eac

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