<p>Hi, how could I do a problem like this without taking a lot of time. How many positive integers less than 1000 are NOT divisible by 3?</p>
<p>If you have PWN the SAT book, it very well covers this topic on the math section of the SAT :)</p>
<p>The tip is to find what IS divisible by 3 and subtract the remaining amount… </p>
<p>But to solve this:
You are trying to find positive integers that are not divisible by 3 but in the range of 999 (less than 1000)</p>
<p>Divide 999 by 3 to get 333. Therefore, 333 integers are divisible by 3. Now… 999-333 = 666
666 integers less than 1000 are not divisible by 3!</p>
<p>@medicsz Thanks!</p>
<p>Or you could notice that every third number is divisible by 3.</p>
<p>1 2 3 > 4 5 6 > 7 8 9 > 10 11 12 and so on. In a series of 999 numbers, 666 are not divisible. </p>