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Each customer of a networking company subscribes to one of two plans:

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Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 29 Jul 2015, 15:46
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Difficulty:

  95% (hard)

Question Stats:

41% (01:42) correct 59% (01:11) wrong based on 160 sessions

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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%

Kudos for a correct solution.

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Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 29 Jul 2015, 16:28
2
Bunuel wrote:
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%

Kudos for a correct solution.


The question asks for the amount of revenue from plan A, but before the amount of revenue can be calculated, the number of units from Plan A must be calculated. If the average revenue was $100\(x\), with \(x\) being the quantity of total plans, the weight between 75 and 175 is \(3:1\). Again, the question is asking what the revenue is. Thus, assume that 4 units were sold, three of the four units equals $225. \(\frac{225}{400}\) or \(56.25\)%.

Answer D.

To prove that's the correct answer choice, I went through the answer choices.
A. 25% Trick answer, paired with E. Out.
B. 30% Figured percentage must be a fourth or eight of something, so since the number of units a multiple of 4, 30% is out.
C. 37.5% Paired with D. Out
D. 56.25% Correct
E. 75% Trick answer if problem were half solved. Out
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Re: Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 17 Aug 2015, 09:47
2
2
Bunuel wrote:
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%

Kudos for a correct solution.


800score Official Solution:

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).
_________________

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 31 Aug 2015, 12:39
Bunuel wrote:
Bunuel wrote:
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%

Kudos for a correct solution.


800score Official Solution:

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).


Good Explanation Bunuel
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Re: Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 01 Sep 2015, 05:51
1
Bunuel wrote:
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%

Kudos for a correct solution.


This question can be easily solved by using allegation.
the ratio of plan A to plan B will be
(175-100)/(100-75) =75/25 = 3/1

for every 3 plan A there is 1 plan B
so company earns 225 from 3 plan A and 175 from 1 plan B.
total 400
revenue percent from plan A will be
(225/400)*100 = 56.25 %

Answer:- D
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Re: Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 03 Jan 2018, 07:24
consider this as a weighted mean situation:

Plan A costs: 75 & Plan B costs: 175
average costs: 100

A B
75-----------------175
100
ratio of quantities is
(175-100) : (100-75)
3 : 1

so total revenue = 3x(75) + x(175) = 400x
A's percentage = 225x/400x ----> 56.25%

Answer: D
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Re: Each customer of a networking company subscribes to one of two plans: [#permalink]

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New post 18 Mar 2018, 16:49
Hi All,

All Average Formula questions can be solved with that formula (just plug the numbers and variables into the formula). This question asks you to do MORE than just use the average formula though….

A = Number of customers for Plan A
B = Number of customers for Plan B

[75A + 175B] / [A + B] = 100

Now there's just a few algebra steps:

75A + 175B = 100A + 100B

75B = 25A

3B = A

This tells us that the number of people who bought Plan A is THREE TIMES the number of people who bought Plan B.

If B=1 and A=3 then the revenue would be:

1(175) + 3(75)

175 + 225 = 400 total dollars

The question asks "what percentage of revenue comes from Plan A"

225/400 = 9/16 = 56.25%

Final Answer:

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Re: Each customer of a networking company subscribes to one of two plans:   [#permalink] 18 Mar 2018, 16:49
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