<p>I ran into this one on a CAT practice test
Compare:</p>
<p>All the prime numbers from 1 to 1000
333</p>
<p>How the heck do you figure that out?</p>
<p>Calculating.</p>
<p>Start by dividing 1000 by 2. Now you know that there are at least 500 non-prime numbers. Then divide 100 by 3 and take half of that amount (because half are also multiples of 2). Keep going if you want, but you can be pretty confident after only doing 2 steps.</p>
<p>Multiples of 2: 500 non-prime numbers
Multiples of 3: somewhere around 130 non-prime numbers
1 is also a non-prime number</p>
<p>You already know that you can’t have more than 370 prime numbers. You have a bunch of 5s in there (some are multiples of 3), multiples of 7s that you haven’t accounted for, etc., so the number is almost definitely less than 333. If you wanted to feel really confident about your answer, you could also count the numbers that end in 5, making sure that you’re not overlapping with your multiples of 3.</p>
<p>Awesome!! Thank you so much</p>