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A swim club that sold only individual and family memberships charged $

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Bunuel
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A swim club that sold only individual and family memberships charged $ [#permalink] New post   18 Dec 2014, 07:17
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A swim club that sold only individual and family memberships charged $300 for an individual membership. If the club’s total revenue from memberships was $480,000, what was the charge for a family membership ?

(1) The revenue from individual memberships was 1/4 of the total revenue from memberships.
(2) The club sold 1.5 times as many family member- ships as individual memberships.
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C
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tarikk
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Re: A swim club that sold only individual and family memberships charged $ [#permalink] New post   19 Dec 2014, 09:45
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



A swim club that sold only individual and family memberships charged $300 for an individual membership. If the club’s total revenue from memberships was $480,000, what was the charge for a family membership ?

(1) The revenue from individual memberships was 1/4 of the total revenue from memberships.
(2) The club sold 1.5 times as many family member- ships as individual memberships.

Kudos for a correct solution.


x+y=480,000
x= total revenue from individual memberships = Individual Memberships [i] * Individual Rate [r1]
y= total revenue from family memberships = Family Memberships [f] * Family Rate [r2]

(1) The revenue from individual memberships was 1/4 of the total revenue from memberships.

x= \(\frac{1}{4}\)*$480,000 = $120,000
x= i * r1 = i*$300 = $120,000 ==> i= 400 individual memberships

y= \(\frac{3}{4}\)*$480,000 = $360,000
y= f * r2 ==> two unknown variables, hence Not Sufficient.


(2) The club sold 1.5 times as many family member- ships as individual memberships.

x+y = $480,000; and r1=$300 ==> (i * $300) + (f * r2) = $480,000, where f = \(\frac{3}{2}\)i

(i * $300) + (f * r2) = (i*$300)+(\(\frac{3}{2}\)i*r2) = $480,000 ==> We still have two unknown variables and one equation, hence Not sufficient.

(1) + (2)

(1) i=400 memberships; and y=$360,000
(2) f= 1.5i = \(\frac{3}{2}\) * 400 = 600 family memberships

y= $360,000 ==> y = f*r2 ==> 600 * r2 = $360,000
r2=$600, thus Sufficient, Answer is C.
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Re: A swim club that sold only individual and family memberships charged $ [#permalink] New post   19 Dec 2014, 11:49
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Solution:

Statement 1: The revenue from individual memberships was 1/4 of the total revenue from memberships
Revenue from selling individual memberships = 480,000 / 4 = 120,000
Revenue from selling family membership = 480,000 - 120,000 = 360,000
- Insufficient to find the selling price of family membership

Statement 2: The club sold 1.5 times as many family member- ships as individual memberships
We don't know the total memberships sold or individual membership sold
- Insufficient to find the selling price of family membership

Combining statement 1 and 2:
Number of individual membership sold = 120,000 / 300 = 400
Number of family membership sold = 1.5 * 400 = 600

Charge for family membership = 360,000 / 600

Thus Statement A & B together are sufficient, Answer C
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Re: A swim club that sold only individual and family memberships charged $ [#permalink] New post   Updated on: 19 Dec 2014, 19:07
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The correct answer is C

Statement 1. - Let the revenue generated from individuals be i, Therefore that generated from families is f = 480,000 - i
The statement says that 480,000 - i = 3i, solving for i we can get the values of i & f.
This however does not provide us with the value of the charge for a family membership.
Hence insufficient.
Statement 2. - This statement too is insufficient as it gives us the numbers of the subscriptions as a proportion and not the exact values.

When combined, we can deduce the exact charge for a family membership.

Hence C

Originally posted by omegacube on 18 Dec 2014, 22:13.
Last edited by omegacube on 19 Dec 2014, 19:07, edited 1 time in total.
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Re: A swim club that sold only individual and family memberships charged $ [#permalink] New post   18 Dec 2014, 08:21
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1. Since we dont know total individual membership we cant determine revenue from family membership from this condition. Insufficient.

2. say x is total no.of individual memberships; and y is total family memberships
from the statement we have y=1.5x
and from the question we have x+y=480000
2 equations and 2 variables are enough to solve teh equations . Solve for y. sufficeint

Ans B
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Re: A swim club that sold only individual and family memberships charged $ [#permalink] New post   25 Jun 2022, 23:04
Bunuel wrote:

Tough and Tricky questions: Word Problems.



A swim club that sold only individual and family memberships charged $300 for an individual membership. If the club’s total revenue from memberships was $480,000, what was the charge for a family membership ?

(1) The revenue from individual memberships was 1/4 of the total revenue from memberships.
(2) The club sold 1.5 times as many family member- ships as individual memberships.

Kudos for a correct solution.


The answer is C. Solution is in the attached picture
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Re: A swim club that sold only individual and family memberships charged $ [#permalink] New post   03 Jul 2023, 04:24
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Re: A swim club that sold only individual and family memberships charged $ [#permalink]
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