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A gym that sold only individual and family memberships

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A gym that sold only individual and family memberships

by BTGmoderatorDC » Sun Jul 29, 2018 12:44 am

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A gym that sold only individual and family memberships charged $500 for an individual membership. If the gym's total revenue from memberships was $450,000, what was the charge for a family membership?

(1) The revenue from individual memberships was $150,000 less than the revenue from family memberships.
(2) The total revenue generated by family memberships was twice that generated by individual memberships.
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Source: — Data Sufficiency |
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by deloitte247 » Sat Aug 18, 2018 12:55 pm

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Let the total revenue from individual members = m
Let the total revenue from family members = f
It is given that m + f = $450,000
Question: What is the charge for a family membership?

Statement 1 : The revenue from individual memberships was $150,000 less than the revenue from family memberships
m + $150,000 = f
Substituting this with the equation from the question above
m + f = $450,000
Where, f = m + $150,000
m + m = $150,000 = $450,000
2m = 450,000 - 150,000
$$m\ =\ \frac{\left(300,000\right)}{2}=\ \text{$150,000}$$

m = $150,00
f = $ 300,000
But there is no sufficient information on total No. of families.
Hence, statement 1 is NOT SUFFICIENT enough to find the charge for a family membership.

Statement 2 : The total revenue generated by family memberships was twice generated by individual memberships.
f = 2m: m + 2m = 450,000, m = $150,000 which is the same thing as statement 1.
Hence, statement 2 is NOT SUFFICIENT.
Combining statement 1 and 2 together,
both statement does not provide information about total number of families.
Therefore, both statement together is NOT SUFFICIENT.
Option E is CORRECT.
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