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 Post subject: GMAT Percentage
PostPosted: Fri May 03, 2013 10:00 am 
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Posts: 483
Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the company’s average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A?

A. 25%
B. 30%
C. 37.5%
D. 56.25%
E. 75%

(D) This is a tricky weighted average problem. If there are only two price levels, $75 and $175, and the average customer pays $100, then the number of customers who pay $75 must be 3 times the number of customers who pay $175, since $100 is 3 times as close to $75 as it is to $175.

We can show this algebraically:
If there are A customers with plan A, and B customers with plan B, then the total revenue is $75A + $175B.
Since the average customer pays $100, we know that
$100 = ($75A + $175B) / (A + B)
$100(A + B) = ($75A + $175B)
$100A + $100B = $75A + $175B
$25A = $75B
A = 3B.

Since there are 3 times as many $75 clients as $175 clients, for every $175 received from Plan B customers, 3($75) = $225 is received from Plan A customers, and the percent of revenue from customers with Plan A is:
$225/($225 + $175) = $225/$400 = 56.25%.

The correct answer is choice (D).
----------
Could anyone explain this in more detail....
I do not understand why there are 3 times as many $75 clients as $175 clients.


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 Post subject: Re: GMAT Percentage
PostPosted: Fri May 03, 2013 10:02 am 
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The algebraic explanation provided above is the most detailed and sufficient. I suggest, you go through it again, line by line:

If there are x customers with plan A, and y customers with plan B, then the total revenue is $75x + $175y.
Since the average customer pays $100, we know that
$100 = ($75x + $175y) / (x + y)
$100(x + y) = ($75x + $175y)
$100x + $100y = $75x + $175y
$25x = $75y
x = 3y.

So there are 3 times as many $75 clients as $175 clients.

If there is some specific line you do not understand - let me know which one.


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 Post subject: Re: GMAT Percentage
PostPosted: Thu Dec 19, 2013 2:39 am 
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Read the question carefully. It is asking for % of revenue, not % of subscribers.


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 Post subject: Re: GMAT Percentage
PostPosted: Thu Dec 19, 2013 2:42 am 
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questioner wrote:
Read the question carefully. It is asking for % of revenue, not % of subscribers.
Indeed. That is why we use dollars at the end of the explanation:

Quote:
Since there are 3 times as many $75-clients as $175-clients, for every $175 received from Plan B customers, 3($75) = $225 is received from Plan A customers …
$225/($225 + $175) = 56.25%


We used the relative values. You may use the total values as well:

Total revenue from customers A:
$75 × A or $ 75 × 3B, because we know that A = 3B.

Total revenue from customers B:
$175 × B

Total revenue from ALL customers:
$75 × 3B + $175 × B

The desired percentage is:
($75 × 3B) / ($75 × 3B + $175 × B)

Simplifying B (plus multiply $75 × 3 = $225), we get the same relative formula, that we use in the explanation:
$225 / ($225 × $175)


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