Difference between revisions of "2018 AMC 10B Problems/Problem 11"

Revision as of 14:03, 16 February 2018

Which of the following expressions is never a prime number when $p$ is a prime number?

$\textbf{(A) } p^2+16 \qquad \textbf{(B) } p^2+24 \qquad \textbf{(C) } p^2+26 \qquad \textbf{(D) } p^2+46 \qquad \textbf{(E) } p^2+96$

The only expression is always a multiple of $3$ is $\textbf{(C) } p^2+26$ . This is excluding when $p=3$ , then $p^2+26=35$ which is still composite.

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 Which of the following expressions is never a prime number when <math>p</math> is a prime number?
-<math>\textbf{(A)} p^2+16 \qquad \textbf{(B)} p^2+24 \qquad \textbf{(C)} p^2+26 \qquad \textbf{(D)} p^2+46 \qquad \textbf{(E)} p^2+96</math>
+<math>\textbf{(A) } p^2+16 \qquad \textbf{(B) } p^2+24 \qquad \textbf{(C) } p^2+26 \qquad \textbf{(D) } p^2+46 \qquad \textbf{(E) } p^2+96</math>
+==Solution 1==
+The only expression is always a multiple of <math>3</math> is <math>\textbf{(C) } p^2+26 </math>. This is excluding when <math>p=3</math>, then <math>p^2+26=35</math> which is still composite.