<p>When 15 is divided by the positive integer k, the remainder is 3. For how many values of k is this true?</p>
<p>(A) One
(B) Two
(C) Three
(D) Four
(E) Five</p>
<p>SPOILER* Don't read ahead if you didn't do this test yet! </p>
<p>Can please you explain why the answer is three?</p>
<p>4/15, 6/15, 12/15 all have remainder 3.</p>
<p>Thank You, but can you explain your thought process when doing this question? Like did you have a formulaic way of thinking or did you just divide one by one?</p>
<p>Try the method called “picking numbers.” That’s what I did. Poster #2 kind of has it backwards, but basically correct. Divide 15 by 4 and you get 3 wholes and remainder 3. Divide 15 by 6 and you get 2 wholes and a remainder of 3.</p>
<p>It is 3, and I am pretty sure this EXACT question was on the March SAT. It may have been experimental though.</p>
<p>15 = kn + 3, where k>3 and n is an integer
12 = kn
It follows that k is a factor of 12
4, 6, 12 - answer C.</p>
<p>^Realizing that the divisor has to be a factor of 12 is helpful, but only if you also realize that you don’t need to check any number smaller than 4 – a remainder is always less than the divisor. If you don’t realize that, you might include 2 and 3 since they are both factors of 12. But if you check 2 and 3, you see that they don’t give the desired remainder.</p>
<p>Still, if none of these insights occur to you, you can get the right answer just by carefully checking the divisors from 1 thru 15…doesn’t take that long either way.</p>
<p>(@gcf101 – i see that you specified k>3 – others might miss that!)</p>