<p>I was browsing through past Sat test discussions on here and came across this problem:</p>
<p>n = p^2 - 100p</p>
<p>N and P have to be two different numbers.</p>
<p>You have to figure out what N is. </p>
<p>Can anyone solve this?</p>
<p>Thanks!</p>
<p>I think you copied this problem wrong. It doesn't seem like something that would be on the SAT I. This equation is true for all real numbers N and P except 0 which breaks the condition that N and P are two different numbers.</p>
<p>For example, 5^2 - 500 = -475
5^2-500+475=0</p>
<p>when p = -3</p>
<p>(-3)^2+300=309</p>
<p>(-3)^2+300-309 = 0</p>
<p>If you do the quadratic formula and expand and combine terms, you end up with n = n and at the end, which means this is basically an identity, and plugging in confirms that.</p>
<p>I think I did copy it down incorrectly or something... because the answer was supposed to be 101 or something.</p>
<p>But thanks for your help!</p>
<p>I think the problem should read 'N and P should have the same value, and be positive numbers'.</p>
<p>In that case, you have p = p^2 - 100p, or p(p-101) = 0
So p = 0 or p=101 . If only positive numbers are allowed, then N=p=101 .</p>