Brain Teasers
Mental Money
If I lost 50% of all my money and then regained 50% but am now $50 off my old total, what was my old total?
Answer
$200Since you don't know if you end up $50 more or $50 less than your old total, you have to try each of two equations:
1) 0.5*X + 0.5*(0.5*X) = X - 50
2) 0.5*X + 0.5*0.5*X = X + 50
Where X is the original amount.
The answer to (1) is X = 200 and the answer to (2) is X = -200. Obviously he couldn't have started with -$200, so the answer must be $200.
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Comments
Seems reasonable to me. If you lost 50% and
then regained 50% of the new amount, you now have
(.5)(1.5) = (.75) of the old amount. This will
always be less than what you started with, assuming
that you start with a positive amount.
then regained 50% of the new amount, you now have
(.5)(1.5) = (.75) of the old amount. This will
always be less than what you started with, assuming
that you start with a positive amount.
I thought this to be a straight forward somewhat simple mathematical problem.Using elementary algebra it can
be solved quickly and easily.
be solved quickly and easily.
I liked this teaser. Reminds me of my fun math days. Makes you think but not that much.
i didnt want to think of the answer but i knew how to do it
This is not an algebra problem. Took a couple of seconds.
If you lose then gain the same proportion, the net difference is the square of the proportion. This is easy to see since the difference will be the proportion of the proportion.
Thus, $50 is 50% of 50% = 25% of the total which must be 4 x $50 = $200.
If you lose then gain the same proportion, the net difference is the square of the proportion. This is easy to see since the difference will be the proportion of the proportion.
Thus, $50 is 50% of 50% = 25% of the total which must be 4 x $50 = $200.
Easy trial problem. Say I have $100 I lose $50 then I gain $25 leaving me down $25 which is half of what I need so I must have double $100 = $200.
I am not smart enough for this...
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