<p>How would I solve this question:</p>
<p>How many positive integers less than 1,000 are not divisible by 3?</p>
<p>What if the number was changed to not divisible by 5?</p>
<p>I really hate these kind of questions and was wondering if there was a standard way of solving this type of problem quickly.</p>
<p>NOTE: The set [x, y) contains all the numbers between x and y, including x but excluding y.</p>
<hr>
<p>The highest number in the set [1, 1000) that is divisible by 3 is 999.</p>
<p>999/3 = 333</p>
<p>Therefore, there are 333 numbers in the set [1, 999] that are divisible by 3.
Therefore, there are 666 (999-333) numbers in the set [1, 999] that are NOT divisible by 3.
There are 666 numbers in the set [1, 1000) that are NOT divisible by 3.</p>
<hr>
<p>The highest number in the set [1, 1000) that is divisible by 5 is 995.</p>
<p>995/5 = 199</p>
<p>Therefore, there are 199 numbers in the set [1, 995] that are divisible by 5.
Therefore, there are 796 (995-199) numbers in the set [1, 995] that are NOT divisible by 5.
Therefore, there are 800 numbers in the set [1, 999] that are NOT divisible by 5.</p>
<p>Haha, this question was on the Oct SAT last year:P</p>
<p>I would find out all the integers less than 1000 that ARE divisible by 3, then substract that from the total number of integers. The same for the other question. Last year, so many people lost points on this question because they misread and counted 1000 as one of the numbers.</p>
<p>Hence, if I remember correctly, the answer was 666 and NOT 667, because the number 1000 is not included in the set [1, 1000).</p>
<p>omg i rememeber this from the Oct SATs</p>
<p>I put 667 instead of 666
and that was the end of my 800 dreams…</p>
<p>Ah, good times:) did crazybandit just change his answer?</p>
<p>^yea, misread</p>
<p>Yeah I was doing the Oct 2009 QAS lol.</p>
<p>@crazybandit</p>
<p>so lets say it asks for positive integers between 1-999 that aren’t divisible by 7</p>
<p>(1,994) Which would be 994-142= 852</p>
<p>so it would be 852 + 5= 857? Meaning 857 numbers aren’t divisible by 7?</p>
<p>^ bump</p>