ShmoopTube

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Here’s your shmoop du jour...

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Garfield, Odie and Jon have a tray of lasagna they want to divide evenly.

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Well… Garfield wants the whole thing to himself, but Jon is putting his foot down.

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The lasagna is cut evenly into portions such

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that the three people-slash-animals sharing it fairly will have no leftovers.

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If two of Jon’s friends were to come over and five people were to share it,

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two pieces would be left over… …and if nine people were to share it,

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three pieces would be left over.

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Which of the following could be the number of pieces the lasagna was cut into?

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And here are the potential answers…

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At first, this problem looks really hard.

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We need to find a number that has no remainder when we divide it by three…

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...a remainder of two when we divide it by five,

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and a remainder of three when we divide it by nine.

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Lucky for us, this question is multiple choice…

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…which means all we have to do is test the answer choices, starting with (A).

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If we divide (A) by three, we get twelve divided by three is four, with no remainder.

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Good so far.

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Twelve divided by five is two, with a remainder of two.

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That’s also what we want, so this looks promising.

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Twelve divided by nine is one, with a remainder of three.

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Great! This is our answer. And lucky us, we got it on the first try.

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It’s usually a good idea to make sure though,

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so let’s check out the other answers and try to see why they’re wrong.

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The problem with (B) is that twenty-one divided by five is four with a remainder of one, not two.

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With (C), thirty divided by five leaves a remainder of zero,

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which also isn’t what we’re looking for.

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We get a similar problem with (D): thirty-nine divided by five has a remainder of four.

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Looks like our answer is (A).

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As in, “All gone.”

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