1. (sqroot(9 + sqroot(80)) + sqroot(9 - sqroot(80)))^2 = ?
2. What is the greatest prime factor of 4^17 - 2^28?
Thank you
2 gmat prep 2 questions
This topic has expert replies
-
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Sun Jul 20, 2008 6:19 pm
guys,
Can you please post the solution, will be much appreciated.
Thanks,
karthik
Can you please post the solution, will be much appreciated.
Thanks,
karthik
- VP_RedSoxFan
- GMAT Instructor
- Posts: 85
- Joined: Thu May 01, 2008 12:56 pm
- Location: Salt Lake City, UT
- Thanked: 24 times
- GMAT Score:750+
Here's my unsolicited help on number 2 since I think it is such a classic GMAT problem. Since no one asked for help, feel free to tell me to shut up .
4^17 - 2^28 = (2^2)^17 - 2^28 = 2^34 - 2^28 from here, factor out a 2^28 leaving you with:
2^28 * (2^6 - 1)
Since we know the 2^28 portion just really represents 28 factors of 2, we know that those are not the highest prime factors of this product. If we solve for 2^6 - 1, we get 63 whose prime factors are 3, 3, 7.
7 is therefore the greatest prime factor of this number (the other prime factors are 3, 3, and 28 2's).
4^17 - 2^28 = (2^2)^17 - 2^28 = 2^34 - 2^28 from here, factor out a 2^28 leaving you with:
2^28 * (2^6 - 1)
Since we know the 2^28 portion just really represents 28 factors of 2, we know that those are not the highest prime factors of this product. If we solve for 2^6 - 1, we get 63 whose prime factors are 3, 3, 7.
7 is therefore the greatest prime factor of this number (the other prime factors are 3, 3, and 28 2's).
Ryan S.
| GMAT Instructor |
Elite GMAT Preparation and Admissions Consulting
www.VeritasPrep.com
Learn more about me
| GMAT Instructor |
Elite GMAT Preparation and Admissions Consulting
www.VeritasPrep.com
Learn more about me
If you search there are really good explanations of this question but I will try to help you.
4^17 = (2^2)^17 = 2^34
2^34 - 2^28 = Factor from here!
2^28 * (2^6 - 1) (If you were to multiply this out it goes right back to the form above)
Does this help?
4^17 = (2^2)^17 = 2^34
2^34 - 2^28 = Factor from here!
2^28 * (2^6 - 1) (If you were to multiply this out it goes right back to the form above)
Does this help?
LSU I sent you a PM with a few more examples and steps in it.
nyparis- there are some really good examples of that problem being solved in other threads. The answer can get quite long if all steps are written out so my advce is to do a search for '(sqroot(9 + sqroot(80))' or something similar.
EDIT: Here is one of those threads: https://www.beatthegmat.com/sq-roots-t12808.html
nyparis- there are some really good examples of that problem being solved in other threads. The answer can get quite long if all steps are written out so my advce is to do a search for '(sqroot(9 + sqroot(80))' or something similar.
EDIT: Here is one of those threads: https://www.beatthegmat.com/sq-roots-t12808.html
-
- Senior | Next Rank: 100 Posts
- Posts: 79
- Joined: Sat May 24, 2008 8:57 pm
- Location: O-Town FL
- Thanked: 1 times