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

Redeem

Question about factoring (should be simple)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 69
Joined: Fri Jul 11, 2008 8:49 am
Thanked: 1 times

Question about factoring (should be simple)

by uncbeers » Sun Aug 24, 2008 12:51 am
I just want to make sure I am understanding this corectly...for some reason factoring these particular scenarios gives me problems.

Anyways-stolen from the GmatPrep stuff:

3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162



Now, to make sure I am understanding these correctly, if it was say:

3^x - 3^x-2 = xxx (this number is a non-issue for me)

Would the two ways to factor become:

1. 3^x (1-(1/9)) = xxx

2. 3^x-2 ((3^2)-1) = xxx

I just want to make sure I am understanding it correctly. I guess, in the same manner, you could take 5^x-1 - 5^x-3 and turn it into:

5^x-3 ((5^2) - 1)

If I am wrong please let me know! Thank you!
Top
Source: — Problem Solving |
Legendary Member
Posts: 829
Joined: Mon Jul 07, 2008 10:09 pm
Location: INDIA
Thanked: 84 times
Followed by:3 members

Re: Question about factoring (should be simple)

by sudhir3127 » Sun Aug 24, 2008 1:16 am
uncbeers wrote:I just want to make sure I am understanding this corectly...for some reason factoring these particular scenarios gives me problems.

Anyways-stolen from the GmatPrep stuff:

3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162



Now, to make sure I am understanding these correctly, if it was say:

3^x - 3^x-2 = xxx (this number is a non-issue for me)

Would the two ways to factor become:

1. 3^x (1-(1/9)) = xxx

2. 3^x-2 ((3^2)-1) = xxx

I just want to make sure I am understanding it correctly. I guess, in the same manner, you could take 5^x-1 - 5^x-3 and turn it into:

5^x-3 ((5^2) - 1)

If I am wrong please let me know! Thank you!
Ur Absolutely right !!!
Top
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Tue Jan 08, 2008 10:30 pm
Thanked: 30 times
Followed by:2 members

by AlaaQasem » Sun Aug 24, 2008 7:33 am
You are right but for the last statement it is going to be like this instead:
5^x-3 ((5^3) - 1)
Top
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 » Sun Aug 24, 2008 7:55 am
Yes, with that one small correction, everything looks perfect.
3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162
I'd just add one thing- you can factor 3^x - 3^x-1 in more than two ways, though most of the ways you might factor won't be helpful. You can factor it any way you like, in fact. You could factor out a 7 if you want to:

3^x - 3^(x-1) = 7[ (3^x/7) - (3^(x-1)/7)]

or you could factor out 3^2:

3^x - 3^(x-1) = (3^2)[3^(x-2) - 3^(x-3)]

The main thing is to recognize what would be most useful to factor out, and in the question

3^x - 3^(x-1) = 162

the most useful factorizations are the two that you suggest: factoring out 3^x, or probably even better, factoring out 3^(x-1).
Top
Senior | Next Rank: 100 Posts
Posts: 69
Joined: Fri Jul 11, 2008 8:49 am
Thanked: 1 times

by uncbeers » Sun Aug 24, 2008 9:42 am
I think the 5^2 was a typo but either way thanks for confirming and correcting.

THank you to Ian as well for the additional info-all is clear and rally helps to look at it and figure that out.
Top
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Tue Jul 20, 2010 7:42 pm
Thanked: 1 times
Followed by:1 members

by rbansal » Mon May 09, 2011 5:39 pm
AlaaQasem wrote:You are right but for the last statement it is going to be like this instead:
5^x-3 ((5^3) - 1)

Why is it a 3 and not a 2?
Top
Post new topic Post Reply
• Page 1 of 1