<p>I always seem to have trouble with problems such as "How many positive integers less than 1000 are not divisible by 3?" They always seem pretty straightforward but I always have trouble with them. What's the best approach? Anyone have some more examples of these?</p>
<p>You just have to understand these types of problems… There is no set formula that you can use…</p>
<p>To answer that question, ask another question to yourself:
how many positive integers less than 10 are not divisible by 3? = 3, 6, and 9</p>
<p>At these point, you might be able to grasp what to do. Either you find a multiple of 3 that is less than, and nearest to 1000, and divide that by 3. 999/3 = 333 OR divide 1000 by 3 and truncate the decimals.</p>
<p>You must first understand what the question is asking you…</p>
<p>How many numbers from 1-30 are divisible by 3? 10 numbers.</p>
<p>And how many 30 numbers are there in 1000? 1000/30 = 33.3</p>
<p>So 33.3 groups of 30 numbers. And each group has 10 numbers. So 33.3 x 10 = 333 numbers </p>
<p>Then again, we have the shortcut of dividing 1000 by 3 = 333, but I just explained the process for more difficult questions like “From 1-1000, how many numbers are divisible by both 2 and 7” and so on.</p>