ShmoopTube

00:03

Here’s your shmoop du jour, brought to you by positive integers.

00:06

Sometimes they’re so upbeat you just want to strangle them.

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When a certain positive integer, n, is divided by 11, the remainder is 1.

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What is the remainder when n + 10 is divided by 11?

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And here are the potential answers…

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All right, so we’ve got some mystery number, and we know the remainder is 1 when you divide it by 11.

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Now we want to tack on 10 more and do the same… and we need to determine the new remainder.

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We need a quotient… we’ll call that k.

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Let’s work in reverse. But be safe – check the rear view mirror first.

00:41

Multiplying both sides by 11 and then adding back the remainder gives us n = 11k + 1.

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So now we’re looking for the remainder when n + 10 is divided by 11.

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Adding 10 to both sides, n + 10 = 11k + 11.

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Factoring out the 11, so n + 10 = 11(k + 1).

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We want to figure out what the remainder is of (n + 10) divided by 11...

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…so dividing both sides of the equation by 11 makes the left side exactly what we’re

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looking for. When n + 10 is divided by 11 the quotient

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is k + 1 and the remainder is 0. Looks like out answer is (A).

01:22

As in, “Auto repair.”

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