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25 Aug 2025, 14:22
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29 Aug 2025, 18:40
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Are you asking why we can't do (numbers we have)/(sequence of 3 numbers) for the multiple of 3 question? That would in fact give us 2/3, which is the answer!
Having said that, it's important to notice that these approaches rely on some assumptions, such as that we have a complete set of sequences. If it were the numbers from, say, 1 to 100, we would not have an integer # of sequences of 3 numbers, so this wouldn't produce an answer. Same thing if we tried to do the divisible of 4 version for the numbers from 1 to 99. It would get us very close, but not quite there.
Having said that, it's important to notice that these approaches rely on some assumptions, such as that we have a complete set of sequences. If it were the numbers from, say, 1 to 100, we would not have an integer # of sequences of 3 numbers, so this wouldn't produce an answer. Same thing if we tried to do the divisible of 4 version for the numbers from 1 to 99. It would get us very close, but not quite there.
ayushi2320
30 Nov 2025, 23:08
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Another of looking at this:
Denominator = 100 (100 numbers from 1 to 100 inclusive)
No lets get the numerator:
There are 25 multiples of 4 between 1 and 100 inclusive, so 25 numbers are surely going to constitute the numerator.
1,2,3,4,5,6,7,8
Also, you can observe that for every value, n which is a multiple of 4, n-1 *n will also qualify the criteria for our numerator because it will always contain n.
Hence our numerator should have 25 multiples of 4 multiples by 2 giving us 50 numbers for which n*(n+1) will be multiples of 4
So our answer becomes 50/100 = 1/2 (C)
Denominator = 100 (100 numbers from 1 to 100 inclusive)
No lets get the numerator:
There are 25 multiples of 4 between 1 and 100 inclusive, so 25 numbers are surely going to constitute the numerator.
1,2,3,4,5,6,7,8
Also, you can observe that for every value, n which is a multiple of 4, n-1 *n will also qualify the criteria for our numerator because it will always contain n.
Hence our numerator should have 25 multiples of 4 multiples by 2 giving us 50 numbers for which n*(n+1) will be multiples of 4
So our answer becomes 50/100 = 1/2 (C)
