Problem number 10. There are six weights. One kilogram, two kilograms, three kilograms, four kilograms, five kilograms, and six kilograms. Amy puts five of them on the scales and puts one weight aside. The scales balance. Which weight did she put aside? In a problem like this, first it's very helpful to find the total weight because that can help us eliminate some choices. Amy has a weight that's one kilogram, another one that's two kilograms, another one that's three kilograms, one that's four kilograms, one that's five kilograms, and one that's six kilograms. We can put four and six together for a total of ten. Then we can put the two and three together, that's five, and the five, that's another ten, so it's 20, and then the one. So the total weight is 21 kilograms. In order for scales to balance, the weight will be the same on both sides, which means that the total weight of what's actually on the scales has to be an even number. If both of these are even, then they will add up to an even number, and if both of these are odd, they also add up to an even number. Since we know that the total weight of the six weights is 21 kilograms, Amy will have to have set aside one of the odd number weights so that the total that she uses is even. So we know that our choice will either be the one kilogram weight or the three kilogram weight. We know that she used the five kilogram weight. If Amy put aside the one kilogram weight, then the total weight is 20 kilograms. The five kilogram weight is on one side, and the six kilogram weight is on the other side. Since the total would be 20 kilograms, each side would have a weight of ten kilograms. So the side with the six kilogram weight would need a four kilogram weight here to make ten, and that would leave us the weights of two kilograms and three kilograms to put on this side. So the one kilogram weight works. Since one of our answer choices that we can't be sure, let's see if she could have set aside the three kilogram weight. If she sets aside three kilograms, then the total is 21 minus 3, or 18 kilograms. If the total is 18 kilograms, each side would need to total nine kilograms. So the side with the six needs just one weight, and that would be the three kilogram weight. But in this case, that's the way that was set aside. So that's not available. So this one does not work. So our only choice is A, one kilogram.

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