Number 26, some blocks are balanced on top of each other as shown. Blocks that are shaded in the same way have the same weight. Bill wants to order the three different types of square blocks from heaviest to lightest. What order should Bill obtain? Pause if you want to try and solve it. Okay, so the key thing to remember here is that if we remove blocks that are of the same type from each side of one of these balances, then the scale will still be balanced, right? So if we remove this block over here, and we remove this block over here, they weigh the same amount, so the scale is still going to be balanced. And same thing if we remove this block over here and this block over here. And so now we can see that these two squared blocks with the holes or the dots in them, weigh the same amount as these three blocks with the x on them. So that means that the blocks with the x are lighter than the blocks with the dots on them. All right, so now that we figured that out, what we can do is look over here at this scale on this side. And the key thing over here. And the thing to remember is that this block over here, right, because it's one of the dotted blocks, weighs more than this block over here, right, because it's one of the x blocks. And so that means that in order to balance this out, because this scale is balanced, this dark block needs to be heavier than this block with the dots, right, because if this one was, if this dark block was lighter than the block with the dots, then the dark block and the blocks with the x would collectively be lighter than these two blocks with the dots. So that means that the dark shaded blocks have to be the heaviest. They have to be heavier than the block with the dots. So now we can look at this and see which answer option that is. And we can see that this ordering is the same as answer option A. So the correct answer for number 26 is option A.

block weights

heaviest to lightest

dark blocks

blocks with dots

blocks with x's