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Posts Tagged ‘**Maths Olympiad**’

*How many 3-digit numbers are multiple of 21?*

Yes, we can solve this question by counting, but there is another way to solve this type of problem.

First, find the smallest 3-digit number divisible by 21:

- the smallest 3-digit number is 100
- divide 100 by 21 gives 4.76, which
to 5rounds up- so the smallest 3-digit multiple of 21 will be 5 x 21 = 105.
Next, find out the largest 3-digit number divisible by 21:

- the largest 3-digit number is 999
- divide 999 by 21 gives 47.57, which
to 47rounds down- so the largest 3-digit multiple of 21 will be 47 x 21 = 987.

Method 1:The 3-digit multiples of 21 form the arithmetic sequence5 x 21, 6 x 21, …, 46 x 21, 47 x 21

Hence, the number of 3-digit numbers which are multiples of 21 is 47 – 5 + 1 = 43

Method 2:Find out how many intervals by 21 are between these two numbers.(987 – 105) ÷ 21 = 42

Hence, the number of multiples of 21 from 105 to 987 inclusively is 42 + 1 = 43.

Now, let’s try this:

*How many 3-digit numbers are multiple of 23?*

Answer: 39

Power Point: Maths Olympiad-Bases other than Ten

PDF worksheet: MathsOlympiad-Advanced-L19-Bases-other-than-Ten.pdf

### Maths Olympiad Book 6 (Chinese)

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on:Some Maths Olympiad books I found from the web.

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