M06-28
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25 Apr 2021, 13:03
Here's my method of solving it, which is a bit different but maybe easier to understand.
I looked at the first few odd numbers to look at the pattern.
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
... + 9 = 25
I already knew that in the typical addition formula, you would do n(n+1)/2. But here, how do you know what to multiply/divide by? I quickly noticed that (1 + 5) * 1.5 = 9. (1 + 7) * 2 = 16. (1 + 9) * 2.5 = 25. Therefore, you multiply the sum of the first and last term by the (last term + 1) / 4. This actually makes sense, because you're still dividing by 2, but here, you divide by 2 AGAIN due to the fact that it's only odd integers.
Second thing I realized was, if the ending odd integer was 3 or 7, then the sum was even. Otherwise, it's odd. This eliminates 3 answer choices, leaving 41 and 29. Plug in 29 which is easier. (1 + 29) * (29 + 1)/4 --> 30 * 7.5 = 210 + 15 = 225. Thus, the answer is 41.