CAT (QA) PYQs

Let $S$ be the set of all points $(x, y)$ in the x-y plane such that $|x|+|y| \le 2$ and $|x| \ge 1$. Then, the area, in square units, of the region represented by $S$ equals:

In how many ways can a pair of integers $(x, a)$ be chosen such that $x^2 - 2 | x | + | a - 2 | = 0$?

If $3x + 2|y|+ y = 7$ and $x + |x|+ 3y = 1$, then $x + 2y$ is