## 'Average' problem

##### This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 35
Joined: 31 Jul 2011
Thanked: 2 times
Followed by:1 members

### 'Average' problem

by Elena89 » Mon Nov 14, 2011 2:13 am
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? Community Manager Posts: 1060 Joined: 13 May 2011 Location: Utrecht, The Netherlands Thanked: 318 times Followed by:52 members by neelgandham » Mon Nov 14, 2011 2:49 am 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?

Let total number of sales prior to the big sale be S and
the average commission prior to the big sale be A
Total commission earned prior to the big sale = A*S
Total commission earned after the big sale = A*S + 2000
Total number of sales including the big sale = S+1

Question can be rephrased to What is the value of S+1 ?

900 = Average commission prior to the big sale + 100 = A+100
Implies A = 800

Average commission after the big sale be A = Total commission earned after the big sale/Total number of sales including the big sale
=> (A*S + 2000) / (S+1) = 900
=> (800S + 2000)/(S+1) = 900
=> 800S + 2000 = 900S + 900
=> 100S = 1100
=> S = 11

S+1 = 12 = Total number of sales he made !

p.s: For quick responses,
Please post PS questions here: https://www.beatthegmat.com/problem-solving-f6.html
Please post DS questions here: https://www.beatthegmat.com/data-sufficiency-f7.html
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

Legendary Member
Posts: 966
Joined: 02 Jan 2010
Thanked: 230 times
Followed by:21 members
by shankar.ashwin » Mon Nov 14, 2011 3:48 am
You could also do this using allegations.

New commission = Old + 100 = 900.

Old = 800. Resultant = 900 and Addition is 2000. ( 8 and 20 mixed to give 9)

So, (20-9) / (9-8) = 11/1. ( 11 of 8 and 1 of 20)

So, 11 + 1= 12 commissions.

### GMAT/MBA Expert

GMAT Instructor
Posts: 6578
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

### Re: 'Average' problem

by [email protected] » Tue Sep 08, 2020 9:24 am
Elena89 wrote:
Mon Nov 14, 2011 2:13 am
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? 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: 12 ### GMAT/MBA Expert GMAT Instructor Posts: 16140 Joined: 08 Dec 2008 Location: Vancouver, BC Thanked: 5254 times Followed by:1268 members GMAT Score:770 ### Re: 'Average' problem by [email protected] » Sat Feb 26, 2022 6:33 am Elena89 wrote: Mon Nov 14, 2011 2:13 am 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?
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 = 800n

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 $2,000 commission). So the total number of sales made = 11 + 1 = 12 Answer: 12 Newbie | Next Rank: 10 Posts Posts: 2 Joined: 02 Jan 2022 ### Re: 'Average' problem by GmatPoint » Thu Jun 02, 2022 1:53 am New average =$ 900
Since average is increased by $100, Old average =$ 800

If the total sales were x(before the big sale),
Then, Total commission = $800x By adding the new commission of$ 2000,
Total comission(after the big sale) = $800x + 2000 Also, total sales will be x+1. Thus,$ 2000 + 800x = \$ 900(x+1)
100x = 1100
x = 11.

Total sales = x + 1 = 12

• Page 1 of 1