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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