[Math Revolution GMAT math practice question]
What is the sum of the prime factors of 2^8-1?
A. 8
B. 16
C. 19
D. 22
E. 25
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
What is the sum of the prime factors of 2^8-1?
This topic has expert replies
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
-
fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
\[?\,\,:\,\,{\text{prime}}\,\,{\text{factors}}\,\,{\text{sum}}\]Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
What is the sum of the prime factors of 2^8-1?
A. 8
B. 16
C. 19
D. 22
E. 25
\[\begin{gathered}
{{\text{2}}^{\text{8}}} - {\text{1 = }}\left( {{2^4} + 1} \right)\left( {{2^4} - 1} \right) = 17 \cdot \left( {{2^4} - 1} \right) \hfill \\
{2^4} - 1 = \left( {{2^2} + 1} \right)\left( {{2^2} - 1} \right) = 5 \cdot 3 \hfill \\
\end{gathered} \]
\[{2^8} - 1 = 17 \cdot 5 \cdot 3\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 3 + 5 + 17 = 25\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Alternate approach:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
What is the sum of the prime factors of 2^8-1?
A. 8
B. 16
C. 19
D. 22
E. 25
2� - 1 = 256 - 1 = 255 = 5*51 = 5*3*17.
Sum of the prime factors = 5+3+17 = 25.
The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
2^8-1 = (2^4+1)(2^4-1) = (2^4+1)(2^2+1)(2^2-1) = (2^4+1)(2^2+1)(2+1)(2-1) = 17*5*3*1.
Thus, the sum of prime factors of 2^8-1 is 17 + 5 + 3 = 25.
Therefore, the answer is E.
Answer: E
2^8-1 = (2^4+1)(2^4-1) = (2^4+1)(2^2+1)(2^2-1) = (2^4+1)(2^2+1)(2+1)(2-1) = 17*5*3*1.
Thus, the sum of prime factors of 2^8-1 is 17 + 5 + 3 = 25.
Therefore, the answer is E.
Answer: E
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Simplifying we have:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
What is the sum of the prime factors of 2^8-1?
A. 8
B. 16
C. 19
D. 22
E. 25
(2^4 - 1)(2^4 + 1)
15 x 17 = 3 x 5 x 17, so the sum of the prime factors is 3 + 5 + 17 = 25.
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
