<p>I generally get 'remainder' problems wrong on SAT Math, so obviously, had trouble with this:</p>
<p>When the positive integer 'n' is divided by 6, the remainder is 2. What is the remainder when 24n is divided by 36?
A: 10.5</p>
<p>I basically multiplied 2 by 24, since it's now 24 x n, and divided it by 6, since it's now being divided by a number 6 times what it was being divided by before. Which all gives me 8... only 2.5 off, lol.
Anyone know how to actually handle this?</p>
<p>n divided by 6, gives a remainder of 2. RULE: Remainder + Dividend = Divisor. Therefore, 6+2 = 8 = n.
24n = 24 x 8 = 192.
Now let’s divide 192 by 36. Gives us an answer of 5 and 1 over 3. Multiply 3 by 12 to get 36 (which is the dividend), and now multiple 1 by the same number (12) to get the remainder. The remainder should be 12, not 10.5
Typo or is it me who’s doin somethin wrong?</p>
<p>A remainder is a positive integer, so of course 10.5 can’t be the answer. </p>
<p>By the way, in a problem like this you can just let n be the remainder. So let n=2 (when you divide 2 by 6 you get 0 with a remainder of 2). Then 24n=24*2=48. When you divide 48 by 36, the remainder is 48-36=12. So the answer is 12.</p>
<p>Here is a complete algebraic solution for the more advanced students reading this post (I would not recommend doing it this way on the SAT, but it’s good to get a deep mathematical understanding of the problem):</p>
<p>You are given that n=6k+2 for some integer k.</p>
<p>Then 24n = 24(6k+2) = 144k+48 = 144k+36+12 = 36(4k+1)+12. Since 4k+1 is an integer, we have shown that when 24n is divided by 36, the remainder is 12.</p>
<p>Thanks again for the quick and detailed replies (I’m almost certain it’s almost always you guys that answer my math q’s).</p>
<p>And yeah… it was a typo on my part, the answer really is 12, not 10.5. </p>
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<p>God yes, this rule for some reason I can never remember (which makes me sound kinda dumb). Although honestly, now that I look at this question, as long as you understand that rule and know how to convert a decimal into a 3rd grade style remainder, this question isn’t hard at all.</p>