<p>Redoing my October QAS:</p>
<p>How many positive integers less than 1000 are NOT divisible by 3?</p>
<p>Numbers are divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
In every 30 number 9 are divisible from 63. So 990/30=33. 33*21=693.
And in that 10 we left, there are 7 indivisible. So at all 700 integers.</p>
<p>
The range is 1-999</p>
<p>999 is the highest number in the range that is divisible by 3. So divide 999 by 3 to to find out how many positive integers ARE divisible by 3. Then deduct the quotient from 999.</p>
<p>999/3= 333
999-333= 666</p>
<p>Sorry, my miscalculation. My method is still good, but I made one counting mistake.
I’m really sorry.
It should look like this:
</p>
<p>Thank you both!</p>
<p>999/3= 333</p>
<p>999-333= 666</p>
<p>So if the question asked 7 instead of 3</p>
<p>it would be 994/7= 142 since 994 is the biggest number between 1-999 that is divisible by 7</p>
<p>And then finally 999-142= 857</p>
<p>How many positive integers less than 1000 are NOT divisible by 3?</p>
<p>Every three numbers starting from three are divisible by three.</p>
<p>So, since 999 is the last possible number, and 3 is the first, there are 999-3, 996 numbers in between 3 and 999. Divide by three, and you get 332. That means 332 numbers between 3 and 999 are divisible by 3.</p>
<p>332 + 1, because we didn’t count 3, = 333.</p>
<p>999 - 333 = 666 numbers not divisible by three.</p>