If a triangle $PQR$ is constructed such that All sides are integers ; and , $PQ= 37 , QR= M$ , and $M <37$ , then the possible values of $PR$ : If a triangle $PQR$ is constructed such that All sides are integers ; and , $PQ= 37  , QR= M$  , and  $M &lt;37$ , then the possible values of $PR$  :

A) $2M-2$

B)$2M-1$

C)$2M$

D)$2M+1$

I tried to apply triangle inequality 

$37-M &lt;PR &lt;M+37$
$1 &lt;PR &lt;2M+1$         since Max (m)=$36$

But i can't reject except  $D$  ; what should I do?
Your question is confused, but from $PR&lt;M+37$ you can't conclude $PR&lt;2M+1$, you can only say $PR&lt;max(M)+37$
Your question is confused, but from $PR&lt;M+37$ you can't conclude $PR&lt;2M+1$, you can only say $PR&lt;max(M)+37$