I love this number.
Find the sum of all the odd numbers between 10 and 550 that are divisible by three.
Answered July 28 by Mike Alexander Studied A-Level Mathematics, Physics & Computer Science
So, the odd numbers in the range go: [he shortens lists for visual reasons]
11 13 15 17 19 21 23 25 27 … 543 545 547 549
Every third number in bold is divisible by 3.
[Remember the math fact: if the sum of the digits in the number equals three, the number is divisible by three. Try it with each one of the boldface numbers.]
So, the sum is
15+21+27+33 … +543+549
Since all terms are divisible by 3, we can write this as:
3(5+7+9+11 … +181+183)
[Because multiplication is the inverse of division. Proof: multiply the last number, 183, by three, and the product is 549.]
Now notice that the series inside the parentheses is almost a full set of consecutive odd numbers - it just lacks 1+3+ at the start. So, it will be 4 less than the series:
I will stop here. If you want the rest of the proof, click https://www.quora.com/How-do-I-do-this-arithmetic-question-Find-the-sum-of-all-the-odd-numbers-between-10-and-550-that-are-divisible-by-3
The final answer is 25,380.
Guess what? The answer is divisible by three.
Find the sum of all the odd numbers between 10 and 550 that are divisible by three.
Answered July 28 by Mike Alexander Studied A-Level Mathematics, Physics & Computer Science
So, the odd numbers in the range go: [he shortens lists for visual reasons]
11 13 15 17 19 21 23 25 27 … 543 545 547 549
Every third number in bold is divisible by 3.
[Remember the math fact: if the sum of the digits in the number equals three, the number is divisible by three. Try it with each one of the boldface numbers.]
So, the sum is
15+21+27+33 … +543+549
Since all terms are divisible by 3, we can write this as:
3(5+7+9+11 … +181+183)
[Because multiplication is the inverse of division. Proof: multiply the last number, 183, by three, and the product is 549.]
Now notice that the series inside the parentheses is almost a full set of consecutive odd numbers - it just lacks 1+3+ at the start. So, it will be 4 less than the series:
I will stop here. If you want the rest of the proof, click https://www.quora.com/How-do-I-do-this-arithmetic-question-Find-the-sum-of-all-the-odd-numbers-between-10-and-550-that-are-divisible-by-3
The final answer is 25,380.
Guess what? The answer is divisible by three.
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