GMAT Math : Term behavior

Terms such as x², √x are favorites of the GMAT quant section. These behave differently in different numeric intervals and it is critical test takers internalize their characteristics to solve questions rapidly. Here is an example :

Is x < y ?

  1. x² < y
  2. √x < y

Instead of taking numerical examples (and bearing the risk of missing some exception!), the fast way to solve this question is to realize that x always falls between (or on) √x and x² regardless of the interval. On the number line –

if x > 1

1…√x …x……x²

if x < 1


and if x = 0 or 1, then x = x² = √x

Consequently, if we know that x² and √x is less than y, then the value in between (i.e x) should also be less than y. Hence we go with option (C).

We have a coverage of other key term behavior questions in our Hackbook