Video: Using Multiples to Identify a Certain Number given a Range

Which of the following numbers is greater than 49, is a multiple of both 2 and 10 but not a multiple of their product 20? [A] 40 [B] 50 [C] 60 [D] 200

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Video Transcript

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? 40, 50, 60, or 200.

This problem gives us some number facts and we need to find out which of the numbers that we’re given matches them. The first fact that’s mentioned is that we need to find a number that’s greater than 49. The numbers that we’re given to choose from are 40, 50, 60, and 200. And out of these numbers, we can see that one of them is not greater than 49. The number 40 is less than 49. So we know that this number is not the answer we’re looking for. Let’s put a cross by it. So now we’re left with 50, 60, or 200.

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. We know that multiples of two are always even. That’s what makes them a multiple of two. They’re even numbers. And we also know that multiples of 10 always end in a zero.

Now the first thing that we can see about our three remaining numbers is that they all end in zero. So they’re all multiples of 10. But are they multiples of two? Yes they are. Any number that ends in a zero is an even number. So any multiple of 10 is also a multiple of two. So we can’t narrow down our numbers. It could still be 50, 60, or 200 that we’re thinking of.

The final clue that we’re given is that we’re looking for a number that’s not a multiple of their product 20. When we say “their product,” we’re talking about the numbers two and 10 that we’ve just talked about. When we multiply these together, we make 20. But only one of our remaining numbers is not a multiple of 20. Which one is it?

Well, a quick one to cross off our list is 200. 10 times 20 is 200. So we know that this is a multiple of 20. So which out of the remaining numbers 50 or 60 is not a multiple of 20? Let’s count in 20s to find out. 20, 40, 60. 60 is a multiple of 20. So the number that we’re looking for that is not a multiple of 20 is 50.

50 is greater than 49. It’s one more than 49 actually. It’s a multiple of both two and 10. In other words, it’s an even number. It ends in zero. And it’s not a multiple of 20. Out of the four possible numbers, the answer is 50.

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