Number Theory on the SAT?

Test Preparation SAT Preparation
1

<p>Recently, I encountered this question during practice:</p>

<p>The integer n is equal to k^2 for some integer k. If n is divisible by 24 and 10, what is the possible smallest value of n?</p>

<p>I know the answer and the steps now, but does this involve number theory? I notice that number theory questions are usually some of the hardest on the SAT (consider the fact that the above question was the last math question of its section). Where can I get info on the number theory needed for the SAT and SAT problems that have to do with number theory?</p>

2

<p>I am still awaiting replies.</p>

3

<p>? Just plug in numbers bro. Simple math</p>

4

<p>Although plugging in numbers is sufficient for most problems, I find that it takes too long for certain problems. Again, I’m referring to the one I typed in the original post. The answer to that question is 3600, by the way; plugging in numbers until I hit 3600 would take quite a while, even if not incrementing by a factor of 1.</p>

<p>That is the reason I want to know what kind of number-theory type techniques I can/should use for certain SAT problems.</p>

5

<p>Using the simplest techniques is the best way to go for SAT 1 Math. Whereas if you go in with a bunch of formulas you’ll just end up confused and miserable. You really only need to know math up to eight grade. I took the SAT the beginning of freshman year and got an 800 in the math section solely be figuring stuff out as I went.</p>

6

<p>Was it a free response?</p>

<p>Otherwise you would have 5 answer choices that would make your life easier.</p>

<p>Again, these are simple concepts.
LCM and Perfect Squares.</p>

7

<p>That question was actually the last free response question of a section.</p>

<p>I don’t see how formulas would apply in this situation; that’s not really what I’m asking for.</p>

<p>The concepts used were simple, yes, but it was not obvious that those specific concepts had to be used. I just didn’t think about how the LCM of two numbers includes the two numbers’ prime factors at first when I did this problem.</p>

<p>What other number theory facts do I need to keep in mind?</p>

8

<p>Least Common Multiple
Greatest Common Factors
Parity - Even/Odd #s
Prime #s
Positivity - Positive Negative Numbers
Reoccurring patterns (eg. 2.417529417529417529…)
Perfect Squares</p>

<p>And usually the harder questions that involve these themes will not directly ask for them much like the above question.</p>

9

<p>For the specific question you asked, the key “number theory concept” is that when you find the prime factorization of a perfect square, you see that the prime factors come in pairs. Similarly, for perfect cubes, the prime factors come in trios. This somewhat obscure idea has in fact been tested on the SAT a couple of times over the years. Not critical though…</p>