# Question: Big Exponents

## Comment on Big Exponents

### I don't understand what this

I don't understand what this question is asking? ### Are you familiar with Data

Are you familiar with Data Sufficiency question? If not, watch this video: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1095

The question is asking "Is x positive?"

Our goal is to determine whether we can use either of the given statements to definitively answer the question ("Is x positive?")

### If I consider x=0 both the

If I consider x=0 both the cases will be I sufficient. Why x=0 is not considered for the first case ### Keep in mind that 0^15 = 0,

Keep in mind that 0^15 = 0, and 0^16 = 0.

So, x = 0 does not satisfy the conditions in either statement.

For example, for statement 1, 0^15 is NOT greater than 0.
Likewise, for statement 2, 0^16 is NOT greater than 0.

For example, if I use x=-2, x=2
isn't the answer as follows for statement 1:
for x=-2, -2^15>0, then -2^15 will be negative number based on the exponent taking the sign of the base? Wouldn't this make it insufficient because ->0 is wrong? Thank you! ### Statement 1 tells us that x

Statement 1 tells us that x^15 > 0

This means that x CANNOT equal -2, since (-2)^15 equals a negative value.

In fact, if x^15 > 0 then we can be certain that x is positive.

### Still very confusing.. If X

Still very confusing.. If X can be literally any value (we're trying to determine the sufficiency of the statement, if we make X a negative number, it'll have to be a negative value with odd power making it LESS than 0. Thus making the statement insufficient. ### "x can be literally any value

"x can be literally any value..."
This is true. However, the target question doesn't ask us to find the value of x; the target question asks us to determine whether or not x is POSITIVE

"...if we make X a negative number, it'll have to be a negative value with odd power making it LESS than 0"
Also true.
However, statement 1 tells us that x^15 is POSITIVE
In other words, Statement 1 tells us that x^ODD = POSITIVE
This means x must be POSITIVE
So, x CANNOT be negative.

"Wouldn't that make statement 1 insufficient if the number selected is a negative number will automatically make it a negative outcome making the statement false?"
KEY POINT: In a data sufficiency question, the statements are always TRUE.
So, when statement 1 tells us that x^15 is POSITIVE, we can be 100% certain that x^15 is POSITIVE.
If we accept this statement as true, what can we conclude about x?
It tells us that x must be positive (otherwise, that would contradict statement 1, which is 100% true).

ASIDE: Pretty much everyone struggles with DS with Data Sufficiency questions at first. You might want to spend some time reviewing the videos in the Data Sufficiency module (https://www.gmatprepnow.com/module/gmat-data-sufficiency) so that you have a solid understanding of this question type.

Cheers,
Brent

nice question...

### In an earlier video in this

In an earlier video in this module, you said that a negative number raised to an even power will be positive outcome and a negative number raised to an odd power will be a negative outcome.. wouldn't that make statement 1 insufficient if the number selected is a negative number will automatically make it a negative outcome making the statement false? Cheers,
Brent

Oh boy , this had my head spinning. But i think the confirmation that the statements are always true and the analysis of statement 1 and 2 makes sense. Data sufficiency questions are so annoyingly interesting ### I agree!

I agree!
Everybody struggles with DS questions at first, but with practice, they can become easier than Problem Solving questions.

### Hi Brent, as you mentioned in

Hi Brent, as you mentioned in the above that statement 1 is positive irrespective of the sign of x since it is given that x^15>0. Similarly, wouldn't statement 2 be considered positive too since it has already been given that x^16>0?
In other words, why is statement 2 insufficient? ### Key Properties:

Key Properties:
1) An odd exponent preserves the sign of the base.
For example, if x is positive, then x^7 must be positive.
Similarly, if x is negative, then x^11 must be negative.

2) And even exponent always yields a positive result
For example, if x is positive, then x^6 must be positive.
Likewise, if x is negative, then x^4 must also be positive.

So, for statement 1, we have an odd exponent (15), which means the sign of the base will be preserved.
Since we're told x^15 is positive, we know that the base (x) must be positive.

For statement 2, we have an even exponent (16), which means the the value of the power will always be positive, regardless of whether the base (x) is positive or negative.
For example, it could be the case that x = 1 (since 1^16 = 1, and 1 > 0), in which case x is positive.
Conversely, it could also be the case that x = -1 (since (-1)^16 = 1, and 1 > 0), in which case x is negative.
Since x can be either positive or negative, statement 2 is not sufficient.

Does that help?

### got this correct in 30s, this

got this correct in 30s, this one shouldn't be over 500 i guess ### That's right; it's probably

That's right; it's probably in the 300 to 400 range.