# Question: Is this fraction less than 1?

## Comment on Is this fraction less than 1?

### Can't we take -1/2 if the

Can't we take -1/2 if the first statement, since x>-1? ### Yes, we could have also tried

Yes, we could have also tried x = -1/2
The result would remain the same though (statement 1 is not sufficient) ### Hi Brent,

Hi Brent,

I marked statement 1 as sufficient because I thought that X > -1 will be negative thus x^(2n+1) < 1.

Where am I making a mistake? x > -1 means that x can be -0.9, 0.5, 1 and etc? ### You're correct to say that,

You're correct to say that, if x > -1, then some possible values of x include: -0.9, -0.5, 0.5, 1, 10, etc

This, however, does not necessarily mean that x^(2n+1) will be less than 1.

For example, if x = 10 and n = 1, then x^(2n+1) = 10^2 = 1000, which is GREATER THAN 1.
Conversely, if x = -0.1 and n = 1, then x^(2n+1) = (-0.1)^3 = -0.001, which is LESS THAN 1.

Does that help?

### Hello Brent!

Hello Brent!
Thank you for the these great videos.
What I did was to simplify the equation to see that the numerator has to be positive irrespective of what sign X carries and the denominator will retain whatever sign X carries. So, I rephrased the question to be "is X < 1?" in which case the equation will result into a figure less than 1. Of course statement 1 is not sufficient and statement 2 is. Perfect!!