<p>MN + NP = MPN</p>
<p>In the correctly worked addition problem above, each letter represents a different digit. What is the value of MPN + NM?</p>
<p>(A) 109
(B) 190
(C) 200
(D) 201
(E) 218</p>
<p>Thank you!</p>
<p>Clearly, M = 1 (if M was at least 2, either MN or NP would have to be three-digit #).</p>
<p>Hence, we have 1N + NP = 1PN. Note that 1N and 1PN have the same units digits. This means that P = 0.</p>
<p>Now we have 1N + N0 = 10N. Here, N = 9.</p>
<p>Therefore, (M,N,P) = (1,9,0) and MPN + NM = 109 + 91 = 200, C.</p>
<p>That makes much more sense now. Thank you very much!</p>