Sam earned a $2,000 commission on a big sale, raising his average comm

Question

Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?

a) 12
b) 13
c) 15
d) 21
e) 8

hasanratul22 · Accepted Answer

An alternative solution, 
Let, total sales before=s
Then, total revenue=800s
New average,900= (800s+2000)/(s+1)
Solve for, s= 11
Total sale=11+1 (new sale)=12 (Answer)

sam9312 · Answer

Okay, So we need to consider a few variables here:

Total Sales = Ts
Total commission (before $2000) =T1

New Average Commission = 900 =  \frac{T1+2000}{Ts}  = Old Average Commission + 100 ------ (According to the question)
Old Average Commission = \frac{T1}{(Ts-1)}

Therefore we have 2 equations now

900 =  \frac{T1+2000}{Ts}  ----- (i)
900 =  \frac{T1}{(Ts-1)}  + 100 -----(ii)

Simplifying them..

900xTs = T1 + 2000 ----- (i)
800xTs = T1 + 800 -----(ii)

Subtracting eq(ii) from eq(i), we eliminate T1

We get, Ts = 12;

ANSWER: (A) 12

ksrutisagar · Answer

By Rule of Alligations :

\frac{n_1}{n_2}  =  \frac{(A_2-A)}{(A-A_1)}

Here,  n_1  is unknown,  n_2  = 1,  A_2  = 2000,  A_1  = 800, and A = 900

\frac{n_1}{1} =  \frac{(2000-900)}{(900-800)}

n_1  =11

So, total number of Sales =  n_1 + n_2  = 11 + 1 = 12

Choice A

EncounterGMAT · Answer

Let total sales before the new commission be x. If you notice, Sam earned a this new commission on  A  big sale that means he made additional 1 more sale, which makes the total sales after this new commission be x+1-> this is what you need to find...

Let commission be C

Old commission average: 800 =  \frac{C}{x}  ...............(1)
and,
new commission average: 900 =  \frac{(2000+C)}{(x+1)}  => C= 900x-1100 ......(2)
putting the value of eq.2 in 1
800x= 900x-1100 =>  x=11----old sale

Since  the total sales after the new commission=x+1=11+1 =  12 ............option A

SchruteDwight · Answer

Treat it as a mixture question

2000*1+800x=900(x+1) –>x+1=12

Kinshook · Answer

Given:  Sam earned a $2,000 commission on a big sale, raising his average commission by $100.

Asked:  If Sam's new average commission is $900, how many sales has he made?

Let us assume that Sam has made x sales

900 = \frac{800(x-1) + 2000}{x} 
900x = 800x - 800 + 2000
100x = 1200
x =12
Sam has made 12 sales.

IMO A

sgaaa · Answer

Sam's old average commission is 800. Hence,
800= x/n
800n= x ..1

900= (x+2000)/n+1
900n+900=x+2000 ..2

After solving and putting 1 in 2,
100n=1100
n=11

ScottTargetTestPrep · Answer

Solution:
 
Since his new average commission is $900, his old average commission must be $800. We can create the equation where n is the number of sales Sam has made before the big sale.

(800n + 2000) / (n + 1) = 900

800n + 2000 = 900n + 900

1100 = 100n

11 = n

Including the big sale, Sam has made 12 sales.

Answer: A

BrentGMATPrepNow · Answer

Note: If Sam's average commission increased by $100 to $900, then his FORMER average commission was   $800   and his NEW average commission is   $900

When it comes to averages, we know that  average value = (sum of n values)/n 
We can rewrite this into a useful formula:   sum of n values = (average value)(n)

Let n = the  number  of sales Sam made to calculate his FORMER average commission. 
When we apply the above  formula , we get: sum of FORMER commissions =   800  n

Once Sam collects his $2,000 commission, the NEW sum of commissions =  800n + 2000 
At this point,  n + 1  = the total number of commissions  (since we just added the $2000 commission)

Since Sam's NEW average commission is   $900  , we can write:  800n + 2000 / (n + 1)  =   $900

Multiply both sides of the equation by (n + 1) to get:  800n + 2000 = 900(n + 1) 
Expand the right side:  800n + 2000 = 900n + 900 
Subtract 800n from both sides:  2000 = 100n + 900 
Subtract 900 from both sides:  1100 = 100n  
Solve:  n = 11

The question asks us to determine how many sales Sam HAS made, which means we must include the latest sale. 
Since n represents the  number  of sales Sam made to calculate his FORMER average commission, we must add the latest sale (the one that landed Sam a $2,000 commission). 
So the total number of sales made =  11 + 1 = 12

Answer: A

GinoRako · Answer

BrentGMATPrepNow

Your excellent and clear explanations are highly appreciated from 1000s of miles away, in my case The Netherlands!

BrentGMATPrepNow · Answer

Thanks for the kind words,  GinoRako !!

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Sam earned a $2,000 commission on a big sale, raising his average comm

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