BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Exponential Equation Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 253
Joined: Fri Dec 26, 2008 8:39 pm
Thanked: 8 times
Followed by:1 members

Exponential Equation Problem

by BlindVision » Fri Mar 06, 2009 9:51 pm
If u is a positive integer, which of the following could be a negative number?

A) u^7-u^6
B) u^3+u^4+u^5
C) u^-9
D) u^-13+u^13
E) u^3-u^8

OA=E

I would like to believe that I have a good understanding of exponential properties but for some reason, I'm puzzled at how the answer is derived. I reasoned that odd exponents will result in a positive number, and even exponents can result in either a positive/negative number. So if the variable u is positive to begin with, then how come E is the answer and not A? I would appreciate any help. Thank you...
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

Re: Exponential Equation Problem

by Ian Stewart » Fri Mar 06, 2009 10:02 pm
BlindVision wrote:If u is a positive integer, which of the following could be a negative number?

A) u^7-u^6
B) u^3+u^4+u^5
C) u^-9
D) u^-13+u^13
E) u^3-u^8

OA=E

I would like to believe that I have a good understanding of exponential properties but for some reason, I'm puzzled at how the answer is derived. I reasoned that odd exponents will result in a positive number, and even exponents can result in either a positive/negative number. So if the variable u is positive to begin with, then how come E is the answer and not A? I would appreciate any help. Thank you...
If u is a positive integer (or any positive number - it doesn't need to be an integer), then u^x will be positive no matter what x is. It's only if u is negative that there is a possibility for u^x to be negative. If u is negative, and x is an integer, then u^x will be negative if x is odd, and positive if x is even.

Now if u > 1, it will always be true that u^x > u^y if x > y. So if u > 1, u^8 > u^3, and u^3 - u^8 < 0.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 253
Joined: Fri Dec 26, 2008 8:39 pm
Thanked: 8 times
Followed by:1 members

Re: Exponential Equation Problem

by BlindVision » Fri Mar 06, 2009 10:20 pm
Ian Stewart wrote:If u is negative, and x is an integer, then u^x will be negative if x is odd, and positive if x is even.
Thanks Ian. Now I have a question about the above quote. Can you please explain a little further of why that happens? Maybe some more examples will make me understand this better. Your help is appreciated.
Last edited by BlindVision on Fri Mar 06, 2009 10:25 pm, edited 1 time in total.
Top
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pm
Thanked: 331 times
Followed by:11 members

by cramya » Fri Mar 06, 2009 10:25 pm
Excellent explanation Ian!

If u is negative, and x is an integer, then u^x will be negative if x is odd, and positive if x is even

Let u = -2

(-2)^ odd exponent will always be negative

i.e (-2)^3= - 8 ; (-2)^5 = -32 etc....

(-2)^ even exponent will always be positive

i.e (-2)^2= 4 ; (-2)^4 = 16 etc....



Hope this helps!

Regards,
CR
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 253
Joined: Fri Dec 26, 2008 8:39 pm
Thanked: 8 times
Followed by:1 members

by BlindVision » Fri Mar 06, 2009 10:27 pm
You guys are too awesome! I got it now! Thanks Cramya!
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Fri Mar 06, 2009 10:53 pm
I'd just add two things:

-at least for this question, you could plug in u = 2 to see that E can be negative. Of course, on a different question, with more awkward exponents, that might not be practical;

-I've always found algebraic rules easier to remember when I understand why they're true, and a great way to begin to understand algebraic rules is to see what happens when you plug in simple numbers. That's what cramya did above, and it's a quick and useful thing to do when you're learning, say, any of the exponent rules.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Post new topic Post Reply
• Page 1 of 1