<p>I have never understood these problems and miss them about 50% of the time. Usually anything involving remainders puzzles me - manipulation of an equation and then predicting the new remainder, etc.</p>
<p>Anyone have any good tips on how to tackle these problems?</p>
<p>What do you mean? Could you give an example</p>
<p>Any particular example?</p>
<p>Here's one way I look at them. For example what is the remainder when 53 is divided by 3. So divide 53 by 3 which equals 17.66. So you know it goes into 53 seventeen times. Multiply 3 by 17 to get 51 so you know the remainder is 2.</p>
<p>That seems like a lot of work to do but it literally takes 7 seconds, and once you become more better at them you don't need to do all the work out.</p>
<p>actually here is an example:</p>
<p>A number "x" is divided by 5 and has a remainder of 3. What is the remainder of 20x when divided by 8</p>
<p>To do this you know 5 goes into 5 and then just simply add the remainder which is 3. So "x" is 8. 20x= 20 times 8 which is 160 and divided by 8 is 20 with no remainder so the answer is 0 since there is no remainder.</p>
<p>Hope that helps.</p>
<p>Thanks quicksand, that makes sense.</p>
<p>A "dummy it down" strategy can help with problems like these. I.e., pick a number that works, and find the answer using numbers.</p>
<p>For example, in the problem above, pick an easy number that leaves a remainder of 3 when divided by 5 ... let's use 8. Then, 20*8=160, and 160/8=20 with remainder 0. You could also have used 13, but 8 was easiest.</p>
<p>Here's another for practice:</p>
<p>A positive integer n is divided by 9 with remainder 8.</p>
<p>What is the remainder when n+3 is divided by 9?</p>
<p>Oops, actually, that 20x problem doesn't have a unique answer for all x, namely, the remainder of 20x divided by 8 will be either 0 or 4 depending on what x is.</p>
<p>Actually on these kind of problems you can only use the first appropriate number. In the case above, the only number you can use is 8.</p>
<p>what's the answer to fignewton's practice problem?</p>
<p>Every problem (including remainder problems) on the SAT will have one unique correct answer (on the mult. choice), with possibly two or three correct answers for the grid-in problems. There's only one correct answer for that n+3 problem.</p>
<p>n = 17.
17+3 = 20
20/9 = answer?</p>
<p>if x divided by y equals z with remainder R,</p>
<p>this is the same as finding x divided by y, getting the answer z + R/y</p>
<p>So if n divided by 9 has remainder 8, that means the answer here is z + 8/9, or:</p>
<p>n/9 = z + 8/9
Therefore:
(n+3)/9 = (z + 11/9)
And since here R>y, we transfer 9/9's to z:
(n+3)/9 = ((z+9/9) + 2/9)</p>
<p>In this case, R=2, remainder=2</p>
<p>That way of doing it is more of a generalized form for solving other types of problems, but intuitively you can also think that if you have a remainder of 8 when dividing n by 9, that means if you increased n by 1, you'd have no remainder. Therefore, since you're looking for the remainder under n+3, that means you're going +2 over the "no remainder" barrier, meaning a remainder of 2.</p>
<p>
[QUOTE]
A positive integer n is divided by 9 with remainder 8.</p>
<p>What is the remainder when n+3 is divided by 9?
[/QUOTE]
</p>
<p>Wouldn't it just be 2?</p>
<p>If n/9 has a remainder of 8, then you know that (n+1)/9 has a remainder of 0 (n+1 is a multiple of 9). So (n+3)/9 has a remainder of 2.</p>
<p>It's kinda hard to explain, but it's quite straight forward. You don't need to substitute it with any numbers.</p>
<p>EDIT: Dang, legendofmax, you beat me to it!</p>
<p>oops. my bad. i didn't solve for the remainer. 20/9 has a remainder of 2. lol; So technically I had it. I thought of the numbers instead of stupid abstract variables.</p>
<p>Ex. "So if n divided by 9 has remainder 8. What is n?"</p>
<p>It's actually really easy. Just add 9+8 and n = 17.</p>
<p>If it asks, "So if n divided by 9 has remainder 8. What is the remainder when n is divided by 8?"</p>
<p>Just do 8+9=17 then 17/8 = 2 R. 1 So the remainder and answer is 1.</p>
<p>question asks n + 3 dvided by 9. n = 17</p>
<p>17+3 = 20
20/9 = 2 R 2</p>
<p>Jumpngo, the example question I posted is different from the one you are talking about. I just made up mine lol.</p>
<p>k thought so. =]. dude. its tmr. wow.wiawj;eofi</p>