Math question...

[DentalKitty]

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Hi guys, this one has me completely confused. I eventually picked an integer and somehow guessed correctly, but Kaplan's explanation of how it was done baffles me. Am I missing something easy here? Maybe I've just been at this too long today....😕

If N is any positive integer, how many consecutive
integers following N are need to insure that at least
one of the integers is divisible by another positive
integer m?

A. m - 1
B. m
C. m + 1
D. 2m​

E. m2 (m squared)

 

[Streetwolf]

My vote goes for A (provided that if m divides N, you can use N as your integer... otherwise I'd go with B).

If you want to find a number divisible by m, you only have to look m-1 numbers ahead of where you are at - at least one of them will divide by m evenly (including N itself).

I won't give a formal proof, but the idea is that if you take N+m and divide by m, you get N/m + 1. So somewhere inbetween N/m and N/m + 1 is a whole number. But of course you don't need to go m numbers above N since if m divides N+m, it will divide N also. So you just have to go m-1 numbers above it.

 

[DentalKitty]

Yep, it's A. I think I get it now, I was just having trouble conceptualizing what they wanted. Thanks for the help!