Hey this is Presh Talwalkar. I received this problem by email because it’s going viral on Facebook with thousands of people arguing about the correct answer. How smart are you? A guy walks into a store and steals a hundred-dollar bill from the register without the owner’s knowledge. He then buys seventy dollars worth of good using the hundred-dollar bill and the owner gives thirty dollars in change. How much money did the owner lose? Was it $30, $70, $100, $130, $170, or $200? Can you figure it out? Give this problem a try and when you’re ready keep watching the video for the correct answer. In some math problems, and in this story, it helps to break the problem down into different parts so at first we’ll only consider the first part of the story. A guy walks into a store and steals a hundred-dollar bill from the register without the owner’s knowledge. At this point how much does the owner lose? Everyone agrees the owner loses a hundred dollars. The owner is at minus 100 from the initial part of the story. So now let’s separately consider just the second part of the story. Imagine someone buys seventy dollars worth of goods using a hundred-dollar bill and the owner gives thirty dollars in change. How much would you say the owner has lost in just this part of the story? Well if someone buys seventy dollars worth of good using a hundred-dollar bill you would expect the owner to give thirty dollars in change. In fact the owner is overseeing this transaction. So the owner here is not losing any money. The owner is you could say zero in this transaction. So now we put these two stories together the total loss will be the sum of these two parts of the story so we can add -100 and 0 to get the total loss is $100 the owner is negative one hundred dollars from before the story started the correct answer is the owner lost $100. Now there’s one technicality if you want to really overthink this problem and go into the accounting details. Now when someone buys seventy dollars worth of goods in a store it’s not because the goods are worth seventy dollars to the owner. What happens here is the owner is getting a hundred-dollar bill and gives back thirty dollars in change but the goods have some value V. This is usually going to be less than seventy dollars so you could say the owner’s actually losing the value of the goods but then getting a net seventy dollars because it’s a hundred-dollar bill minus thirty dollars in change but here the owner loses V minus 70 or you could say the owner is 70 minus V in terms of the cash position so if you were to take these two stories now you add up the result the owner ultimately loses thirty dollars plus the value V of the goods so if we assume the value V is seventy dollars which you say seventy dollars worth of goods then you would say the owner lost a hundred dollars. So you can still arrive at the same answer of a hundred dollars but this is a little more accurate in terms of pure accounting. So why are so many people getting this problem wrong? Well one of the common answers is there is a two-hundred-dollar loss to the owner. Many people think this is because in the first part of the story the owner loses a hundred dollars that’s stolen and then in the second part of the story the owner loses another hundred dollars because the owner is giving up seventy dollars worth of goods and thirty dollars in change. So the mistake here is that it’s not taking into account the owner is also getting a hundred-dollar bill so when you take that other part of the story where you get the hundred-dollar bill that will adjust the total by +100 and when you do that, that means the owner ultimately lost a hundred dollars in total. Another common answer is that the owner had a $130 loss. This is from the stolen hundred-dollar bill and the thirty dollars in change. Well the problem with this answer is it’s not taking into account that the owner also gave up seventy dollars in goods but also got a hundred-dollar bill so when you take into account these transactions the net result would be the owner losing $100 which is negative 100. So to summarize most of the incorrect responses either didn’t add or subtract numbers correctly or they didn’t take into account every transaction. It seems the fact that in the second half of the story that person used the stolen dollar bill somehow people don’t treat that as a genuine hundred-dollar bill. That is a hundred dollars that the owner’s getting back. So when you take into account every single transaction and you treated correctly as either a loss or gain for the owner you end up that the owner lost a hundred dollars. Did you figure it out? 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