<p>If n and m are non-zero, positive integers, which of the following must also be an integer?</p>
<p>I n^2 - 1 / n + 1 </p>
<p>II m/n+1 </p>
<p>III (m)(n)</p>
<pre><code> a I only
b II only
c III only
d I and III only
e I, II and III
</code></pre>
<p>I chose C as my answer because obviously II does not work since it'll be a fraction, I would not work because if n = 1, then it equals 0, which is zero, and the problem states, non-zero. So obviously, my answer is C.</p>
<p>The correct answer though is A: "If n and m are integers, then obviously (n)(m) is an integer. And n2 -1 factors into (n + 1)(n - 1), so number I just is n - 1, which is obviously an integer. But there is no reason to expect m/(n + 1) to be an integer. Just try n = 3, m = 1 as a counter-example."</p>
<p>Shouldnt the answer be C?</p>
<p>The answer should be D</p>
<p>That’s what I was thinking, and I couldn’t find the question with ACT to confirm the method… But yes, it should be D. Both n-1 (which is I simplified) and mn are integers.</p>
<p>The answer is D, unless the OP typed the question in here wrong.</p>
<p>Oh I’m sorry I dont know why i typed A, but yeah the answer is D according to the website. But my question is why? If you plug in n=1 for n^2-1/n+1 you get 0…</p>
<p>D, integers are whole numbers. This includes positive, negative, and 0. Think of a number line.</p>
<p>Sent from my DROIDX using CC App</p>
<p>Oh! I understand my mistake now. I thought it said the integer (answer after m and n are plugged in) must not be a non-zero. </p>
<p>ahh lol stupid mistakes smh smh. thanks</p>
<p>Why does choice II not work?</p>
<p>^Use 3 and 4 for m and n as a counterexample. In fact, the majority of selections for m and n will not satisfy II.</p>
<p>@Practical: to sum it up, a majority of the numbers you choose will give you a fraction, which is not an integer.</p>