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 Post subject: GMAT PercentagePosted: Wed Jan 12, 2011 3:13 pm

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 PercentagePosted: Wed Jan 12, 2011 3:28 pm

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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