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## Comment on

Is this fraction less than 1?## Can't we take -1/2 if the

## 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,

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!

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!!

Perfect!!

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

## 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,

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

## 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