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A survey reveals that the average income of a company’s customers is $ [#permalink]
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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?
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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.



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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 = 2250750 = 1500 =? x = 375 Hence C
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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07 May 2011, 09:32
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let x be the average of 40 customers
40*x + 10* 75000 = 50*45000
solving this we have x= 37500
Answer is C.
Are you sure the official answer is D? if not change please change the answer.



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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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07 May 2011, 09:33
Awesome. Thank you, Gurpreetsingh and Spidy001.
I selected the wrong OA. The correct answer is C



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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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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?



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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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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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08 May 2011, 08:00
(50*45  75 * 10)/40 = (2250  750)/40 = 1500/40 = 150/4 * 1000 (multiply by 1000 as 3 zeroes trimmed earlier) = 37.5 * 100 = 37500 Answer  C
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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08 May 2011, 11:50
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
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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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 = 2250000750000> $1,500,000
Answer is C
Average income of 40 customers = 1,500,000 / 40 = $37,500



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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]
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09 May 2011, 04:28
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: \(\frac{w1}{w2} = \frac{(A2  Avg)}{(Avg  A1)}\) \(\frac{40}{10} = \frac{(75,000  45,000)}{(45,000  A1)}\) \(45,000  A1 = \frac{(30,000)}{4}\) \(A1 = 37,500\)
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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09 May 2011, 15:04
we know that the highest salaries "pulled" the avg 7545 = 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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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]
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08 Feb 2018, 16:43
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
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