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Updated on: 08 May 2011, 11:43
3
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:52) correct 18% (02:11) wrong based on 95 sessions

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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) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? Originally posted by Yalephd on 07 May 2011, 08:02. Last edited by Yalephd on 08 May 2011, 11:43, edited 3 times in total. CEO Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2591 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: A survey reveals that the average income of a company’s customers is$  [#permalink]

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07 May 2011, 08:09
2
1
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) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? 45*50 = 10*75 + 4x => 4x = 2250-750 = 1500 =? x = 375 Hence C _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Director Joined: 01 Feb 2011 Posts: 658 Re: A survey reveals that the average income of a company’s customers is$  [#permalink]

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07 May 2011, 08:32
1
let x be the average of 40 customers

40*x + 10* 75000 = 50*45000

solving this we have x= 37500

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GMAT Date: 08-08-2011

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07 May 2011, 08:37
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) $50,000 Is there a way to solve this using weighted average concept instead of doing tedious calculations? VP Status: There is always something new !! Affiliations: PMI,QAI Global,eXampleCG Joined: 08 May 2009 Posts: 1015 Re: A survey reveals that the average income of a company’s customers is$  [#permalink]

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07 May 2011, 12:24
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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Joined: 16 Nov 2010
Posts: 1420
Location: United States (IN)
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08 May 2011, 10:50
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 Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 29 Mar 2011 Posts: 18 Re: A survey reveals that the average income of a company’s customers is$  [#permalink]

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08 May 2011, 11:22
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 Answer is C Average income of 40 customers = 1,500,000 / 40 =$37,500
Senior Manager
Joined: 03 Mar 2010
Posts: 374
Schools: Simon '16 (M$) Re: A survey reveals that the average income of a company’s customers is$  [#permalink]

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08 May 2011, 22:38
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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09 May 2011, 14:04
we know that the highest salaries "pulled" the avg
75-45 = 30 for each one. so total of 300 above the avg.

now - to go back down - we need to pull the avg back down (-300) so we need to divide
-300/40 = -7.5. so the avg of the other 40 will be 45+(-7.5) = 37.5

similar to the weight system of Karishma, but for some reason its easier for me to work by understanding.
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08 Feb 2018, 15:43
1
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 = $37,500 Answer: C _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: A survey reveals that the average income of a company’s customers is$ &nbs [#permalink] 08 Feb 2018, 15:43
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