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A survey reveals that the average income of a company’s customers is $

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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?
[Reveal] Spoiler: OA

Last edited by Yalephd on 08 May 2011, 11:43, 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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New post 07 May 2011, 08:09
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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
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]

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New post 07 May 2011, 08:32
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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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New post 07 May 2011, 08:33
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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New post 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?
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]

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

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New post 08 May 2011, 07:00
(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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New post 08 May 2011, 10:50
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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
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Re: A survey reveals that the average income of a company’s customers is $ [#permalink]

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

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

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

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New post 16 Dec 2016, 16:15
Here is my solution to this one =>

Sum(50)=450000*50
Sum(10)=75000*10

Sum(40)= 1500000

Hence Average = 1500000/4 => $37,500

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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New post 08 Feb 2018, 15:43
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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Re: A survey reveals that the average income of a company’s customers is $   [#permalink] 08 Feb 2018, 15:43
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