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[BrownieDDD]

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if N is any positive integer, how many consecutive integers following N are needed to insure @ least one of the integers is divisible by another positive integer M?

a) m-1
b) m
c) m+ 1
d) 2m
e) m^2

answer: a
kaplans' explanation: out of every m consecutive integers is divisble by the integer m. the wording is difficult so you might have thought the quetion was asking yout o count N itself to get the correct answer, but it wasn't so m-1 consecutive after N plus N itself are required to ensure that oen fo the integers, including N, is a multiple of m.

i dont' understand kaplan's explanation

nor can i pick numbers to try to find an explanatio nfor myself....

 

[crax]

So if you think about what numbers are divisible by M, they are M, 2M, 3M, 4M, etc...
The number you are looking for is a multiple of M. So assuming you start from 0, you must add M digits to have a number divisible by M, which is M/M = 1
Now assume you start from "a positive number" (N), you want to get at least to a value of M, or a multiple of it. Since youre starting with a positive number, the farthest possible distance you can be from a multiple of M is "M-1".

Real example: M=45 N=1
You need to travel from N (1) to the closest multible of M (45) which is M-N = (M-1)

Real example: M=45 N=50
You need to travel from N (50) to the closest multiple of M (90). This is so 90/M = a whole integer.
90-50 = 40. 40 is less than (M-1).

(M-2) would miss out on the M-1 possible multiple, and M Itself is a multiple. Hopefully this ranting makes sense.