The number of n satisfying

The number of n satisfying -n+2≥0 and 2n≤5 is
A. 0
B. 1
C. 2
D. 3
E. None of the above.

The OA is E.

Can any expert illustrate this PS question with an example please?

Hi LUANDATO ,
Let's take a look at your question.

$$-n+2\ge0$$
$$-n\ge-2$$
the inequality is reversed when it is multiplied by a negative number. Therefore,
$$n\le2$$

The next inequality given in the question is,
$$2n\le5$$
$$n\le\frac{5}{2}$$
$$n\le2.5$$

Therefore, n should be restricted to:
$$n\le2$$ and $$n\le2.5$$

By combining both of these inequalities, the values of n should be less than or equal to 2.
It means that n has all the values less than or equal to 2 i.e. n has unlimited number of values.
Therefore, Option E is correct.

Hope this helps.
I am available if you'd like any follow up.