ShmoopTube

00:02

And here's an unshmoopy question you may find on an exam somewhere in life...

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When a certain positive number is divided by 5 the remainder is 1.

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When it is divided by 8, the remainder is 4.

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What is the smallest possible value of this number?

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And here are the potential answers...

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The best way to find the answer is to just guess and check, using logic.

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Since we want the smallest possible answer, let's start with the smallest answer choice

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and work our way up until we find the right one.

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We'll first start with Choice A first.

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When divided by 5, 16 does leave a remainder of 1, but 16 is divisible by 8.

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So Choice A gets the axe.

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Time for Choice B's audition.

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21 fits the first criterion, but when divided by 8, it has a remainder of 5.

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Choice C is next. We see right away that 24 is a multiply of 8...

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Now Choice D. 34 has a remainder of 4 when divided by 5

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and a remainder of 2 when divided by 8.

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Nope.

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Now we only have one candidate left.

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36 has a remainder of 1 when divided by 5 and a remainder of 4 when divided by 8.

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Choice E is the correct answer.

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