Brain Teasers
X Likes Cars
X likes to buy and sell cars. For two weeks he bought 5 cars every 12 hours. Then, on June 2nd, he decided to start selling. Every day he would sell 6 cars, then buy 2. But every third day, he would sell 5 cars, and buy 3. X decided that he'll shut down his business when he has no more cars. At this rate, what day will X shut down his business?
Answer
July 12th, 41 days after he started selling.5 cars every 12 hours = 10 cars per day = 140 cars bought in the two weeks. This is the starting point.
Every two out of three days, he nets 4 cars sold (2 bought - 6 sold). The third day, he nets 2 cars sold (3 bought - 5 sold). This means that he nets 4 + 4 + 2 = 10 cars sold every three days.
Since he needs to sell 140 cars, it will take him 14 3-day cycles to do this. 14 * 3 = 42 days. But on day 41 he sells his 6 cars and runs out. He would normally buy two more later that day, but he is already out.
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Comments
Actually he runs out of cars one day earlier.
At the start of that day (the second one of a
three day cycle), he has 6 cars. He sells the
six and is out of cars. He would normally
buy 2 later that day, but he is already out.
If he didn't stop, he would start the next
day with 2 cars, and be unable to sell his
normal 5.
At the start of that day (the second one of a
three day cycle), he has 6 cars. He sells the
six and is out of cars. He would normally
buy 2 later that day, but he is already out.
If he didn't stop, he would start the next
day with 2 cars, and be unable to sell his
normal 5.
'X'?
It often appears from the comments that the answer has been edited. Anyway the teaser is OK. I should have been awake to the old frog in the well trick but on first reading it was not clear whether he bought and sold a different lot of cars on the third day or if it was an additional transaction. It does say every day he sold 6 and bought 2.
Yes, this is just a more interesting, more complicated variation on the old frog in the well teaser as Jimbo says. Also, Jimbo makes a good point that I didn't catch, about whether the 5 and 3 on every third day is additional or a replacement.
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