Sample Question #273 (brainteaser)

A geeky quantitative finance society in Manhattan has 500 members. One day the steering committee decides to throw a dance party to welcome the new members. At the party (which only members can attend), new members pay only $14 for tickets whereas long-time members pay $20. As a result, all of the new members attend but only 70% of the old members attend.

How much ticket revenue is collected at the party?

[Source: adapted from

*The Mensa Puzzle Calendar 2008*]
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ANSWER

Were you trying to figure out how many of the 500 members are new?

Surprisingly, you don’t need to figure that out to answer the question! Let N=number of new members, so the total ticket revenue is simply R=14N+20[0.7(500-N)]=14*500=$7,000.

Whenever you see questions like this, it always pays to write down the formula first, then worry about whether you have enough information to solve it.

Of course, the answer to this question relies on the fact that the 14N in the first term and the 0.7*20*(-N)=-14N cancel each other out. That’s why you don’t need to solve for N to calculate the total revenue.

This question is wonderful~~~!!! You try, you make it. If you are not willing to try, and you are a loser.

Clever and easy. Is this all I have to know to become a quant? =)

Typically problems like this has no solution since, at first glance, you have been given too little information (or at least not enough to solve the problem).If the problem is solvable (in the sense that there exists a uniques solution) then there is no other way around it.There is some more information actually given to you that’s "hidden". You then read between the lines. Q.E.D. Yanis