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Remainders, a la Shmoop. Paul Deen, Paula's little brother...

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...is trying to follow in big sis' footsteps. However, every time he tries baking chocolate

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tortes for his dinner guests... ...he ends up with left over dessert after

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divvying the rest out evenly. He made the same number of tortes for each

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of his first three dinner parties... ...and they were eaten by 4, 6 and 8 people

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respectively. Each time, exactly 2 tortes went uneaten.

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Which of the following expressions gives us a number that is evenly divisible by 4, 6

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and 8? Here are the choices:

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To Paul's abject horror, Paula steps in to save the day.

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His sister got all the math smarts in the family, too. Don't you just hate that?

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Paula starts by finding the least common multiple of 4, 6 and 8... which is 24.

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Then she adds the remainder of 2 to get an x value of 26.

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Next, she plugs her x value into each of the expressions until she finds another common

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multiple of 4, 6 and 8.

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"A" doesn't work because 34 isn't divisible by any of our three numbers

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"B" -- Same story... 38 isn't divisible by any of the three.

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"C" doesn't fit the bill either...42's only factor here is 6...

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"D"...Nope - 46 hasn't a single factor either... Answer "E," however, works just perfectly.

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26 plus 22 equals 48... ...and 48 is definitely a common multiple

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of 4, 6 and 8. The Deen family is all about going "big"...

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...so Paul decides to bake 48 tortes for his next dinner party.

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That amount will be perfect for 4, 6 or 8 people...

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...or if Paula opts to gorge herself on them all alone.

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