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Updated on: 08 May 2011, 12:43
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A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is$75,000, what is the average income of the other 40 customers?

(A) $27,500 (B)$35,000
(C) $37,500 (D)$42,500
(E) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? Originally posted by Yalephd on 07 May 2011, 09:02. Last edited by Yalephd on 08 May 2011, 12:43, edited 3 times in total. CEO Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2659 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: A survey reveals that the average income of a company’s customers is$ [#permalink]

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07 May 2011, 09:09
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Yalephd wrote:
A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers responded to the survey and the average income of the wealthiest 10 of those customers is$75,000, what is the average income of the other 40 customers?

(A) $27,500 (B)$35,000
(C) $37,500 (D)$42,500
(E) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? 45*50 = 10*75 + 4x => 4x = 2250-750 = 1500 =? x = 375 Hence C _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Director Joined: 01 Feb 2011 Posts: 686 Re: A survey reveals that the average income of a company’s customers is$ [#permalink]

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07 May 2011, 09:32
1
KUDOS
let x be the average of 40 customers

40*x + 10* 75000 = 50*45000

solving this we have x= 37500

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Joined: 03 Aug 2010
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07 May 2011, 09:37
you can even solve this by weighted average. Here is the approach. you can use either one of the above approaches.

$$(10/50)(75000) + (40/50)*x = (50/50)*45000$$

=> 750000 + 40x = 45000*50

=> x = 375000

Yalephd wrote:
A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers responded to the survey and the average income of the wealthiest 10 of those customers is$75,000, what is the average income of the other 40 customers?

(A) $27,500 (B)$35,000
(C) $37,500 (D)$42,500
(E) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? VP Status: There is always something new !! Affiliations: PMI,QAI Global,eXampleCG Joined: 08 May 2009 Posts: 1146 Re: A survey reveals that the average income of a company’s customers is$ [#permalink]

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07 May 2011, 13:24
total amount of the 40 people = [45,000 *50 - 75,000 *10] divided by 40 gives the average.

[45,000 *50 - 75,000 *10]/40

= 375000.
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08 May 2011, 11:50
Expert's post
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Yalephd wrote:
A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers responded to the survey and the average income of the wealthiest 10 of those customers is$75,000, what is the average income of the other 40 customers?

(A) $27,500 (B)$35,000
(C) $37,500 (D)$42,500
(E) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? Use: $$\frac{w1}{w2} = \frac{(A2 - Avg)}{(Avg - A1)}$$ $$\frac{40}{10} = \frac{(75,000 - 45,000)}{(Avg - 30,000)}$$ $$Avg - 30,000 = \frac{(30,000)}{4}$$ Avg = 37,500 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A survey reveals that the average income of a company’s customers is $[#permalink] ### Show Tags 08 May 2011, 12:22 Total income of all 50 customer = 45,000 * 50 =$2,250,000
Total income of top 10 customers = 75,000 * 10 = $750,000 Total income of rest 40 = 2250000-750000-->$1,500,000

Average income of 40 customers = 1,500,000 / 40 = $37,500 Senior Manager Joined: 03 Mar 2010 Posts: 401 Schools: Simon '16 (M) Re: A survey reveals that the average income of a company’s customers is$ [#permalink]

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08 May 2011, 23:38
VeritasPrepKarishma wrote:
Use:
\frac{w1}{w2} = \frac{(A2 - Avg)}{(Avg - A1)}

\frac{40}{10} = \frac{(75,000 - 45,000)}{(Avg - 30,000)}

Avg - 30,000 = \frac{(30,000)}{4}

@Karishma in above formula, u have substituted avg=45000 in numerator but in denominator u haven't substituted same for avg. can i please know how so?
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Re: A survey reveals that the average income of a company’s customers is $[#permalink] ### Show Tags 09 May 2011, 04:28 1 This post received KUDOS Expert's post jamifahad wrote: @Karishma in above formula, u have substituted avg=45000 in numerator but in denominator u haven't substituted same for avg. can i please know how so? That's something I messed up. I actually meant to say: $$\frac{w1}{w2} = \frac{(A2 - Avg)}{(Avg - A1)}$$ $$\frac{40}{10} = \frac{(75,000 - 45,000)}{(45,000 - A1)}$$ $$45,000 - A1 = \frac{(30,000)}{4}$$ $$A1 = 37,500$$ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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16 Dec 2016, 17:15
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Re: A survey reveals that the average income of a company’s customers is $[#permalink] ### Show Tags 08 Feb 2018, 16:43 1 This post received KUDOS Expert's post Yalephd wrote: A survey reveals that the average income of a company’s customers is$45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 40 customers? (A)$27,500
(B) $35,000 (C)$37,500
(D) $42,500 (E)$50,000

The total income of all customers is 45,000 x 50 = $2,250,000. The total income of the wealthiest 10 of those customers is 75,000 x 10 =$750,000.

So the total income of the remaining 40 customers is 2,250,000 - 750,000 = $1,500,000 leaving us with an average of: 1,500,000/40 =$37,500

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