<p>Please help!</p>
<p>17.If the integer m is divided by 6, the remainder is 5. What is the remainder if 4m is divided by 6</p>
<p>(A) 0
(B) 1
(C) 2
(D) 4
(E) 5</p>
<p>I got C.</p>
<p>10 char</p>
<p>Please Explain.</p>
<p>m/6 = x + 5</p>
<p>4m/6 = 4x + 5(4) = 4x + 20</p>
<p>However, 20 is also divisible by 6 so you get 20/6 = a remainder of 2.</p>
<p>Okay. Got it. Thanks! :)</p>
<p>Let’s choose a positive integer whose remainder is 5 when it is divided by 6. A simple way to find such an m is to add 6 and 5. So let m = 11. It follows that 4m = 44. 6 goes into 44 seven times with a remainder of 2, choice (C). </p>
<p>Important: To find a remainder you must perform division by hand. Dividing in your calculator does not give you a remainder!</p>
<p>Note: A slightly simpler choice for m is m = 5. Indeed, when 5 is divided by 6 we get 0 with 5 left over. Since this choice for m sometimes confuses students I decided to use 6 + 5 = 11 which is the next simplest choice. Note that in general we can get a value for m by starting with any multiple of 6 and adding 5. So m = 6n + 5 for some integer n.</p>
<ul>
<li>Quickest solution: Let m = 5. It follows that 4m = 20. 6 goes into 20 three times with a remainder of 2, choice (C). </li>
</ul>
<p>Remark: The answer to this problem is independent of our choice for m (assuming that m satisfies the given condition, of course). The method just described does not show this. It is not necessary to do so.</p>
<p>For the advanced student: Here is a complete algebraic solution that actually demonstrates the independence of choice for m. The given condition means that we can write m as m = 6n + 5 for some integer n. Then 4m = 4(6n + 5) = 24n + 20 = (24n + 18) + 2 = 6(4n + 3) + 2 = 6z + 2 where z is the integer 4n + 3. This shows that when 4m is divided by 6 the remainder is 2, choice (C).</p>