Question

If Sm is the sum of m consecutive natural numbers, what is the probability that Sm is a multiple of 21. (Given that m is less than or equal to 100.)

Answer 1

Sm = m(m+1)/2, so to be divisible by 21, either m is a multiple of 21 or (m+1) is a multiply of 21

Answer 2

idk @matricked

Answer 3

@sourwing, the sequence does not have to start with 1.

Answer 4

m = 21, 42, 63, 84,

m + 1 = 21
m = 20
so, 20, 41, 62, 83,

Answer 5

@eliassaab, since 0 isn't universal agreed that it is a natural number, I defined 0 to be not a natural number in this case.

Answer 6

BUt the sequence can be 4, 5, 6

Answer 7

P = 8/100

Answer 8

Am I missing something?

Answer 9

ah I see what you meant now. The sum starts at some number m. If this is the case, wouldn't this be not enough information?

Answer 10

So I assume m starts at 1.

Answer 11

But it does not say that in the problem. One cannot add assumptions about a question.

Answer 12

well, true. Then I would say not enough information. We need know what m starts at, so we can eliminate the sum that starts at 1 and up to m.

Answer 13

wrong questionah?

Answer 14

not wrong, just not enough info. Unless you left something out.

Answer 15

k

Answer 16

or m starts at 1 but the question did not explicitly stated so

Answer 17

So I would say P = 8/100 = 4/25 anyway.

Answer 18

idk whether it is correct or not

Answer 19

Ten small boxes namely A, B, C.............J and each box can keep one ball only. Five big boxes X, Y, Z, W, U and each big box can keep ten balls maximum. A person is trying to transfer balls from small boxes to big boxes and at least 5 balls should be transferred. Find the number of ways of transfer.

Answer 20

Please do not mix problems. Ask your problem in a new post.
Returning the first problem. It has to specify the starting point. Suppose
m=3, then we can get an infinite sequence of 3 consecutive numbers,
like
{1,23}
{2,3,4}

....

{100,101,102}

{k,k+1,k+2}