<p>Sorry, I didnt mean to insult you. It’s just that most people cant imagine this kind of questions, while some do. Unfortunately, it’s practically impossible to learn, you can only practise some types of questions.</p>
<p>btw Imagination was a wrong word. I meant more like a “math imagination”.</p>
<p>It’s alright, I understand and I know what you mean.</p>
<p>I can imagine most of the SAT questions, at least in the way you mean, especially those who deal with concepts I still use in school (IB Maths HL) but I haven’t dealt with whether a number is divisible by x in a while.</p>
<p>Functions, however, I love.
I can see them just by looking at their equations, no matter how complex they may be.
(unless they’re like, cosmology-level math stuff lol)</p>
<p>thanks again</p>
<p>OK, it seems I uderestimated you. I was judging you based on my experience from our school, you guys in US are probably a bit different :-D</p>
<p>On divisibility, here is a general algorithm. </p>
<p>If I want to find the number of integers divisible by k less than m, then I set up the inequality kx < m. Dividing by k, I get x < m/k, then find the nearest integer to that value, I find how many integers satisfy that equation. </p>
<p>Example: </p>
<p>How many positive integers less than 1000 are not divisible by 3? </p>
<p>3x < 1000
x < 1000/3, which means x is at most the integral part of 1000/3, which is 333. This means that there are 333 positive integers that satisfy this condition. Realizing that there are 998+ = 999 integers between 1 and 999 and that there are 333 integers that satisfy the negative of our condition, we need only see 999-333 = 666 positive integers are not divisible by 3 and below 1000.</p>
<p>I have imagination enough to generalize it ;)</p>
<p>Your solution is perfect, congratz! :-D</p>
<p>Don’t generalize. I know many Americans may take seconds at this problem while others may take minutes.</p>
<p>Who CARES?!</p>