-1

$m$ is the sum of all multiples of $3$ between $1$ and $100$. $n$ is the sum of all multiples of $3$ between $5$ and $95$. what is $m-n$?

Jamāl
  • 594
Maybeline Lee
  • 153
  • 1
    Any thoughts? What numbers are counted by $m$ but not by $n$? – lulu Mar 16 '20 at 17:46
  • $198$, by inspection. How was I able to see it right away, and how can you formulate that into a proper solution? – Andrew Chin Mar 16 '20 at 17:46
  • No math (or very little) All logic. The multiples of $3$ between $5$ and $95$ are being subtracted for the multiples of $3$ between $1$ and $100$. That leaves just the multiples of $3$ that aren't between $5$ and $95$. – fleablood Mar 16 '20 at 18:23

1 Answers1

0

If $m$ is the sum of all multiples of $3$ between $1$ and $100$, then that is the sum of all multiples between $1$ and $5$, plus all multiples between $5$ and $95$ and all multiples between $95$ and $100$.

Don't read what's below

All multiples between $1$ and $5$ is $3$. The sum of all multiples between $5$ and $95$ is $n$. And the multples between $95$ and $100$ are $96$ and $99$.

Really. Do NOT read what's below!

So $m = 3 + n +96 +99 = n + 198$.

Surely, you don't need to read what's below.

ANd $m -n = (n+198)-n = 198$

And under NO circumstances read what is hidden below!!!

QUIT IT!!!!!!

fleablood
  • 124,253