Question: Big Exponents

Comment on Big Exponents

I don't understand what this question is asking?
gmat-admin's picture

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 cases will be I sufficient. Why x=0 is not considered for the first case
gmat-admin's picture

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.

I'm confused about x^15>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!
gmat-admin's picture

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 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.
gmat-admin's picture

"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 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?
gmat-admin's picture

Please see my reply to your question above.
If you have any questions, please don't hesitate to ask.

Cheers,
Brent

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