# Pre RMO (PRMO) practice questions, specially selected: PRMO 2018

The following set of problems tinkers, kindles some basic mathematical concepts as well as algebraic manipulations, so I suggest you try them out:

Try to decide by yourself which set of points are defined by these relations:

(a) $|x| = |y|$

(b) $\frac{x}{|x|} = \frac{y}{|y|}$

(c) $|x| + x = |y| + y$

(d) $[x] = [y]$.

Note: The symbol $[x]$ denotes the whole part of the number x, that is, the largest whole number not exceeding x. For example, $[3.5] = 3$, $[5] = 5$, $[-2.5] = -3$.

(e) $x - [x] = y - [y]$

(f) $x - [x] > y - [y]$.

Good luck.

Nalin Pithwa.

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