<p>I need help with this problem as I cannot figure out any solution: When the positive integer S is divided by 12, the remainder is 4. When the positive integer T is divided by 12, the remainder is 5. What is the remainder when the product ST is divided by 6?
I tried using 16 and 17 as S and T then doing this problem, but I get the answer "3", when it should be "2". Can anyone explain?</p>
<p>Your thought process is right, but maybe you made a computation error.</p>
<p>16*17 = 272</p>
<p>When 272 is divided by 6 (using long division), the answer should be 45 with a remainder of 2.</p>
<p>12k + 4 = S
12u + 5 = T</p>
<p>ST = (12k+4)(12u+5)
= 144ku+48u+60k+20</p>
<p>ST/6 = (144ku+48u+60k+20)/6 = 24ku+8u+10k+3; REMAINDER 2</p>
<p>i probably made it more complicated, but yeah the remainder is 2</p>
<p>Kay, thanks a lot. It’s weird, when i use a calculator I get 45.3333 but normal division by hand gives me remainder 2</p>
<p>That’s how it should be though on the calculator. Because a remainder of (2/6)=(1/3)=.333333333. It’s the same thing, but expressed differently. I think that’s right. Am I wrong?</p>
<p>^^^
You are right – it’s the difference between “remainder” and “decimal part” of the answer to a division question. If you are using a calculator, it gives you the decimal part. You can multiply the decimal part by the divisor to get the remainder. So as you say, in this case:</p>
<p>6 x .333… = 2</p>
<p>Personally, I think it’s a lot of easier if you just realize that S could/has to be 8 and T be 7 because the remainders are 4 and 5 respectively. Then 8x7 = 56 and 56/2 = 9 r 2. So much simpler.</p>
<p>You can use any numbers you want that fit. For example, S = 100 and T = 101 (divide by 12 to get remainders of 4 and 5, respectively).</p>
<p>100x101 = 10100. Divide this by 6 to get 1683 and 1/3. Since the remainder is 1/3 of 6 (what you divided by), the remainder is 2.</p>