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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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17 00:00

Difficulty:   75% (hard)

Question Stats: 59% (02:31) correct 41% (02:53) wrong based on 199 sessions

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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

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Senior Manager  G
Joined: 24 Apr 2016
Posts: 321
Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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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

Manager  S
Joined: 05 Oct 2017
Posts: 65
GMAT 1: 560 Q44 V23 Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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1
Bunuel 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

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

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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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Bunuel 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

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

[5000(n - 1) + 4000]/n = 4800

5000n - 5000 + 4000 = 4800n

200n = 1000

n = 5

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Intern  B
Joined: 09 Apr 2018
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In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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3
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 Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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quantumliner wrote:
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

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.
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Quote which i can relate to.
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Veritas Prep GMAT Instructor V
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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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KanishkMehta wrote:
quantumliner wrote:
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

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.

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) _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Director  G Joined: 09 Mar 2018 Posts: 994 Location: India Re: In her position as a real estate agent, Sarah receives a bonus for eac [#permalink] Show Tags VeritasKarishma wrote: KanishkMehta wrote: quantumliner wrote: 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 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. 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)

After going through the highlighted i realized my gap.

Thank you Karishma for your help on this.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4019
Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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Bunuel 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

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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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.

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_________________ Re: In her position as a real estate agent, Sarah receives a bonus for eac   [#permalink] 04 Dec 2018, 15:58
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