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Mike and the Bike (Posted on 2003-07-26) Difficulty: 3 of 5
Mike wanted to buy a bike, and he found one he liked at $20, so he bought it. The next day, a friend saw it and offered $30 dollars for it so Mike agreed. He later bought it back for $40. Again someone saw it and offered $50 and again Mike sold it. Mike finally rebought the bike for good for $60. Mike then took it to a bike show where a man told him the bike was worth $40.

Deciding to keep it, did Mike gain or lose money on the transactions? Count the bikes worth in the problem.

See The Solution Submitted by Jon    
Rating: 2.2941 (17 votes)

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Solution solution | Comment 2 of 42 |
Of the five transactions, the first two are paired and the second two are paired. Only the last is unpaired.

In each of the two buy/sell pairs Mike has gained $10 without permanently affecting his non-ownership of the bike, and therefore at that point is $20 ahead (after the two buy/sell pairs).

Finally he buys a bicycle worth $40 but pays $60 for it. So counting the worth of the bicycle as $40, he has overpaid on this one transaction $20.

That exactly offsets the $20 he came out ahead for basically nothing, and therefore Mike is exactly even.
  Posted by Charlie on 2003-07-26 04:50:59
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