Showing MAXIMUM CLique is NPO-simple and MAXIMUM GRAPH COLORING is not

Question

Recall the notion of NPO problem. An NPO problem is simple if the following is true:

$\forall k \in \mathbb{N}^*. (\forall x. OPT(x) \leq k) \in P$

In words, given any positive integer $k$, the problem of deciding if for instance $x$ its optimal is less or equal than k is in $P$.

I'm asked to show the MAXIMUM CLIQUE problem is simple and that assuming $P \neq NP$ MINIMUM GRAPH COLORING is not simple.

References

This is problem 3.13 of "Complexity and Approximation" of Ausiello et alii.