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). ---------- [color=#FF0000]Could anyone explain this in more detail.... I do not understand why there are 3 times as many $75 clients as $175 clients.[/color]

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.

[quote="questioner"][color=#FF0000]Read the question carefully. It is asking for % of revenue, not % of subscribers.[/color]

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)

Users browsing this forum: No registered users and 1 guest

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.