How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?
15
16
17
18
19
What's the best way to approach the above?
Thanks!
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- JackH825
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- Sage Pearce-Higgins
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Re: Divisibility
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When faced with a pattern, or counting cases, or unusual cases, I strongly recommend that you pick some examples. What's the first number that would give a remainder of 1 when divided by 3? If you haven't thought about that already, then you're probably making things too complicated. The first number is 1, then 4, then 7, and you can probably see a pattern. Actually, the answers show you that the number of cases is small enough that you could probably count them on your fingers or write them all out in less than a minute. The risk of missing a case means that I would probably take that crude approach.
However, more theoretically, every multiple of 3 is followed by a number that gives a remainder of 1 when divided by 3. So how many multiples of 3 are there up to 50? Simply divide by 3: 50/3 = 16. We need to make sure that the last number is still included, so 48 + 1 = 49, that's fine. Also, don't forget that we also need to add 1 as another case, making 17 in total.
When faced with a pattern, or counting cases, or unusual cases, I strongly recommend that you pick some examples. What's the first number that would give a remainder of 1 when divided by 3? If you haven't thought about that already, then you're probably making things too complicated. The first number is 1, then 4, then 7, and you can probably see a pattern. Actually, the answers show you that the number of cases is small enough that you could probably count them on your fingers or write them all out in less than a minute. The risk of missing a case means that I would probably take that crude approach.
However, more theoretically, every multiple of 3 is followed by a number that gives a remainder of 1 when divided by 3. So how many multiples of 3 are there up to 50? Simply divide by 3: 50/3 = 16. We need to make sure that the last number is still included, so 48 + 1 = 49, that's fine. Also, don't forget that we also need to add 1 as another case, making 17 in total.
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