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Which of the following numbers is greater than 49, is a multiple of both two and 10, but not a multiple of their product, 20?
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40, 50, 60, or 200.
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This problem gives us some number facts and we need to find out which of the numbers that we’re given matches them.
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The first fact that’s mentioned is that we need to find a number that’s greater than 49.
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The numbers that we’re given to choose from are 40, 50, 60, and 200.
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And out of these numbers, we can see that one of them is not greater than 49.
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The number 40 is less than 49.
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So we know that this number is not the answer we’re looking for.
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Let’s put a cross by it.
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So now we’re left with 50, 60, or 200.
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The next fact about the number that we’re looking for is that we need to find a number that’s a multiple of both two and 10.
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We know that multiples of two are always even.
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That’s what makes them a multiple of two.
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They’re even numbers.
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And we also know that multiples of 10 always end in a zero.
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Now the first thing that we can see about our three remaining numbers is that they all end in zero.
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So they’re all multiples of 10.
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But are they multiples of two?
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Yes they are.
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Any number that ends in a zero is an even number.
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So any multiple of 10 is also a multiple of two.
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So we can’t narrow down our numbers.
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It could still be 50, 60, or 200 that we’re thinking of.
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The final clue that we’re given is that we’re looking for a number that’s not a multiple of their product 20.
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When we say “their product,” we’re talking about the numbers two and 10 that we’ve just talked about.
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When we multiply these together, we make 20.
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But only one of our remaining numbers is not a multiple of 20.
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Which one is it?
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Well, a quick one to cross off our list is 200.
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10 times 20 is 200.
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So we know that this is a multiple of 20.
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So which out of the remaining numbers 50 or 60 is not a multiple of 20?
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Let’s count in 20s to find out.
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20, 40, 60.
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60 is a multiple of 20.
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So the number that we’re looking for that is not a multiple of 20 is 50.
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50 is greater than 49.
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It’s one more than 49 actually.
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It’s a multiple of both two and 10.
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In other words, it’s an even number.
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It ends in zero.
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And it’s not a multiple of 20.
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Out of the four possible numbers, the answer is 50.