<p>When the positive integer n is divided by 6, the remainder is 2. What is the remainder when 24*n* is divided by 36?</p>
<p>if the remainder of n/6 = 2, then n must be 4, right? </p>
<p>so 24(4) is 96. </p>
<p>when 96 is divided by 36, 96/36, the remainder is 24, isn't it? </p>
<p>The answer key says its 12...</p>
<p>n/6 has a remainder of 2 , n would be 14</p>
<p>n can be 8, 14, 20…and in all cases the remainder is 2 when divided by 6 and the remainder is 12 when 24n is divided by 36 for all those cases.</p>
<p>The answer is definitely 12. n=8 because 8/6 is 1 with a remainder of 2. Then multiply 8 by 24 and you get 192. Now to get the answer you would subtract all of the possible answers from 192 until when you divide that number by 36 you get a whole number. Now subtract 12 from 192 and you get 180. Divide that by 36 and you get 5, which is a whole number. Thus the answer is 12.</p>
<p>Bizarre way to do it Virginia. All you have to do once you realize n=8 is multiply it by 24=192, divide 192 by 36 and see the remainder is 12.</p>
<p>Oh shoot, sorry I got the divider/dividend messed up, I think.</p>
<p>In fact, if you choose n=2, you can do the entire calculation in your head.</p>
<p>Yes, the answer must be 12 and in similar case, you should choose the smallest n that suit the first equation.</p>