Thiftico is a subscription-only store with three membership

Question

Thiftico is a subscription-only store with three membership tiers: individual, premium, and executive. The annual membership fees are €85 for individual, €100 for premium, and €200 for executive. The average annual membership fee across all members is €110, and there are 55,000 more executive members than premium members. If two-thirds of the members are individual members, what is the total number of members of Thiftico?

A) 550,000
B) 660,000
C) 750,000
D) 825,000
E) 990,000

Show Answer

Official Answer

D

A) 550,000
B) 660,000
C) 750,000
D) 825,000
E) 990,000

niks_1412 · Answer

let number of individual, premium and executive memberships be i, p and e respectively.
total memberships = i + p + e
it is given that, 55000 + p = e and i = 2(i + e + p)/3

average fee = 110
=> 110 = (85i + 100p + 200e)/(i + p + e)

solving all 3 equations, we get total number of memberships as 825,000 (D)

pal26 · Answer

I solved it the traditional way and it took a lot of time. Definitely would have messed up time wise during the actual exam . Pls suggest if there are smarter ways to solve this question.

kevincan · Answer

If you’re really adept at weighted averages, you can make quick work of this question

saitama2024 · Answer

Would suggest practicing would reduce your solving time. There aren't many shortcuts here

kevincan1 · Answer

If 2/3 of the members are individual , there are twice as many individual as non-individual members . If individual members pay $25 less than than $110 , the others must pay on average $50 more than $110.

How can we proceed ?

How can we proceed ?

VibhuAnurag · Answer

Let the total # of members = x ; Average Fee = 110
--> Total Fee = 110x
Category-wise:
Individual = 85 * 2x/3
Premium = 100p
Executive = 200(p + 55,000)

--> (170x/3) + 100p + 200p + 11,000,000 = 110x
--> (170x + 300p + 600p + 33,000,000)/3 = 110x
--> 170x + 900p + 33,000,000 = 330x
--> -160x + 900p + 33,000,000 = 0

We also know that since Individual = 2x/3
--> p + e = x - (2x/3)
--> p + (p + 55,000) = x/3
--> 2p + 55,000 = x/3
--> 6p + 165,000 = x

Substituting:
-160(6p + 165,000) + 900p + 33,000,000 = 0
--> -960p - 26,400,000 + 900p + 33,000,000 = 0
--> 6,600,000 = 60p
--> p = 110,000

x = 6(110,000) + 165,000 = 660,000 + 165,000 = 825,000

The answer is D.

Ikemen · Answer

Such an interesting question, and you can def call the answer within 40 sec.

Assume total members=y, and let no. of Premium members = x, we have Executive members=55k+x.

We also know that no. of Individual members = 2/3y, therefore, Premium + Executive members is 1/3y.

From here we can set up the equation: 55k+x + x=1/3y --> 55k+2x=1/3y --> 165k+6x = y. 
This essentially tells us that y is a multiple of 6 after subtracting 165k from it.

Now we look at the answer choice before doing any further calculations.

The answer choices give you a clear hint that 5 and 0 is critical here. Only Choice D satisfy the condition.

If you are not sure about the 5 and 0 hint, you'd still be left with plenty of time to run subtraction from A to E to see for yourself.

Hope this helps

Thiftico is a subscription-only store with three membership

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