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

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

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New post 21 Mar 2017, 04:10
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Question Stats:

58% (04:10) correct 42% (02:02) wrong based on 178 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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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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New post 21 Mar 2017, 10:15
3
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
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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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New post 03 Oct 2018, 21:32
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

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

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New post 04 Oct 2018, 18:30
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

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

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New post 05 Oct 2018, 03:19
2
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 :)
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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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New post 15 Oct 2018, 19:36
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.
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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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New post 16 Oct 2018, 00:28
1
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)
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Re: In her position as a real estate agent, Sarah receives a bonus for eac  [#permalink]

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New post 16 Oct 2018, 02:29
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.
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Be a good critique, If you don't like my approach.

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

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New post 04 Dec 2018, 07:24
Top Contributor
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

Answer: B

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

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New post 04 Dec 2018, 14:58
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 &nbs [#permalink] 04 Dec 2018, 14:58
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