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 Post subject: GMAT Percentage
PostPosted: Wed Jan 12, 2011 3:13 pm 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
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: Wed Jan 12, 2011 3:28 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
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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