# 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!!

### X^2n+1 < 1, means the value

x^(2n+1) < 1 means the value of x^(2n+1) can also be in between 0 and 1 (i.e. positive), but as per second statement, for any value for which x < 0 can not bring answer as positive value. Can you pls clarify, whether the question is correct? ### The original question is

The original question is correct/valid.
I have a feeling you may be reading the question the wrong way.
Without any additional information, we don't know whether x^(2n+1) < 1. So, at this point, we can't make any conclusions about the value of x.

All we know is that, IF x < 1, then x^(2n+1) < 1
And IF x > 1, then x^(2n+1) > 1
And IF x = 1, then x^(2n+1) = 1

As such, statement 1 is insufficient, and statement 2 is sufficient

Does that help?

### Hi Brent,

Hi Brent,
I marked statement 1 as sufficient, because in question stem we were given that x is not 0 and statements 1 is says x> -1 ...but I didn’t consider the values fraction values between -1 and 0...

Any advice on how to avoid such assumptions? ### That's a common mistake.

That's a common mistake.
From time to time, you might find it useful to watch the following video on common mistakes: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1105
The video covers the mistake of assuming variables are integers.

### Can we consider X=1/2 as

Can we consider x = 1/2 as proof in statement 2?. Thanks ### We can't use x = 1/2, since

We can't use x = 1/2, since that value breaks statement 2's condition that x < 0