19. There were 20 apples and 20 pears in a box. Carl randomly took 20 pieces of fruit from the box and Luca took the rest. Which of the following statements is always true? What we can try and do is we can eliminate answers by providing counterexamples. We'll start with A. Carl got at least one pear. What if Carl gets 20 apples and 0 pears? That's clearly a counterexample. In that case, Luca would have 0 apples and 20 pears. This counterexample holds for a lot of situations. What about Carl got as many apples as pears? Nope, that's not necessary either. Carl could have 20 apples and 0 pears. Luca could have the same thing as he had before. Nope, that doesn't hold up. What about C? Carl got as many apples as Luca? Nope, not the case here. Carl has 20 apples and Luca has 0. This counterexample is really going well for us. In E, Carl got as many pears as Luca. Nope, Carl has 0 pears. Luca has 20. This counterexample has already eliminated four of our answers. Let's now take a look at answer choice D and see if that is always holding to be true. If Carl has X apples, he takes out X apples, then since he took 20 pieces of fruit, 20 minus X have to be pears. Now, if X apples are no longer in the box, Luca can only have 20 minus X apples and Luca can only have 20 minus 20 minus X pears. This is all that's remaining for Luca. Now, if we simplify this, however, we get that Carl has X apples, 20 minus X pears. Luca has 20 minus X apples and X pears. So we see that Carl always has as many apples as Luca has pears. Carl always has as many pears as Luca has apples. And that is what D says, so the answer is D.

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Luca

apples

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distribution