Is y^3 < |y|?

Have a quick query. It doesn't state that y is an integer.

So for y < 0.
If we take y = \(-\frac{1}{2}\) then \(y^3\) would be greater than |y|, but if we take y = -2 then \(y^3\) would be less than |y|.

Anything I'm missing here?

Hi

If you take y= -1/2 then y^3 = -1/8, which is negative but |y| = 1/2, which is positive. So y^3 < |y|

Solution:

Statement 1: y<1
Case 1: y=0. We get a "No"scenario.
Case 2: y=-ve, we get a "Yes" Scenario.

Therefore this statement is insufficient.

Statement 2: For any negative value whether integer or fraction this statement holds good.

Therefore the answer is Option B.

\(y^3 < |y|\)

(1) \(y < 1\)

Consider \(y = \frac{1}{2}\)

\({\frac{1}{2}}^3 < {|\frac{1}{2}|}\)

\({\frac{1}{8}} < {\frac{1}{2}}\) ==> TRUE

Lets check for ZERO as well

\({0}^3 ≤ |0| = 0 = 0\) ==> FALSE

Now, lets check for Negative values as well, as we know that mod/absolute function will always give us positive values and cube of negative will always give us negative values, our L.H.S. Should always be < R.H.S. Lets test

\({\frac{-1}{2}}^3 < {|\frac{-1}{2}|}\)

\({\frac{-1}{8}} < {\frac{1}{2}}\) ==> TRUE

As we are getting both true and false

Hence, Eq. (1) is NOT SUFFICIENT

2) \(y < 0\)

As y is negative, we know for Negative values as well, as we know that mod/absolute function will always give us positive values and cube of negative will always give us negative values, our L.H.S. Should always be < R.H.S. Lets test

\({\frac{-1}{2}}^3 < {|\frac{-1}{2}|}\)

\({\frac{-1}{8}} < {\frac{1}{2}}\) ==> TRUE

Hence, Eq. (2) is SUFFICIENT

Answer is B

Did you like it? 1 Kudos Please

Hi Bunuel - You seems to have merged two different questions, could you please segregate these questions again?

Question you had <= while the one which I posted had only < sign. Hence, both have different answers too.

________________________________________
Done.

Statement 1: as \(y<1\), so \(y=0\) is a possibility. at \(y =0\), \(y^3 = |y|\), So we get a No but at \(y = -1\), \(y^3=-1\) and \(|y|=1\), so we get a Yes. Hence insufficient

Statement 2: implies that\("y"\) is negative, so \(y^3\) will be negative but \(|y|\) will always be positive.
therefore \(y^3 < |y|\) will always be true. Hence Sufficient

Hence B