Refer to this post: https://www.beatthegmat.com/absolute-ine ... tml#324920

beat_gmat_09 wrote:Thanks for the link Rahul.
I feel the algebraic approach time consuming sometimes, it works for certain problems.
I was look for picking numbers (proper numbers) for this problem to evaluate the question.
I think it works faster for some problems.

Yes algebraic approaches are time consuming sometimes. But picking numbers also has its own limitations. You must have a good idea about which number you should pick which is equivalent to having a good algebraic concept .

For this particular question there is also another method which I feel the most easy and elegant method. But to apply this method you should have a clear concept on graphs of certain standard functions.

As I have mentioned earlier, to solve this question we must find the relations of x with √x and x³. Now if you plot these functions (namely f(x) = x, f(x) = √x and f(x) = x³), we can literally see the regions in which y lies.



Referring to the above figure the analysis becomes pretty easier as you visually can see the whole picture.

According to statement 1, y must lie below the blue line. But we can see that for some region y is above the green line (meaning greater than x) and in some region lies below the green line (less than x). Same for statement 2.

Now consider both the statement together. y must lie below both the blue and red lines. We can clearly see this means y always lies below the green line i.e. less than x.