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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Property of Numbers

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 17
Joined: Fri Jan 22, 2016 11:59 am
by RobertP » Thu Feb 11, 2016 12:23 pm
Hello everyone,

Can some one please help me understand the solution of the problem bellow?

Thank you!

If N = 3^8 - 2^8, which of the following is not a factor of n?

A) 97
B) 65
C) 35
D) 13
E) 5)

Answer: C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members
Location: Boston, MA
Thanked: 1153 times
GMAT Score:770

by DavidG@VeritasPrep » Thu Feb 11, 2016 12:48 pm
RobertP wrote:Hello everyone,

Can some one please help me understand the solution of the problem bellow?

Thank you!

If N = 3^8 - 2^8, which of the following is not a factor of n?

A) 97
B) 65
C) 35
D) 13
E) 5)

Answer: C
3^8 - 2^8 is a difference of squares: it can be rewritten as (3^4)^2 - (2^4)^2.
Because 3^4 = 81 and 2^4 = 16, (3^4)^2 - (2^4)^2 = 81^2 - 16^2.
Because x^2 - y^2 = (x+y)(x-y), 81^2 - 16^2 = (81 + 16)(81 - 16) = 97 * 65.
So clearly 97 and 65 are factors.
65 = 13*5, so 97*65 = 97*13*5; Therefore13 and 5 are factors.
That leaves us with C
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 11, 2016 12:50 pm
David's solution is perfect.
I just want to add something about the concept of algebraic manipulations without variables:

The GMAT loves to test our algebra skills (like factoring), HOWEVER many students associate algebra with variables only, so they don't see that we can apply algebraic principles to numbers as well (which should make sense, since those variables are, indeed, representing numbers).

So, for example, many students are fine with the following:
- Factoring 6x + 3 to get 3(2x + 1)
- Factoring 6x� + 2x³ + 8x² to get 2x²(3x³ + x + 4)
- Factoring x² + 5x + 6 to get (x + 2)(x + 3)
- Factoring x² - y² to get (x + y)(x - y)

On the GMAT, we need to recognize that we can also factor expressions that have no variables.
So, for example, a GMAT question might ask us to evaluate 54² - 53²
If we recognize that this is a difference of squares in the form x² - y², we can factor it to get:
54² - 53² = (54 + 53)(54 - 53) = (107)(1) = 107

Likewise, the expression 2¹�� - 2�� is no different from x¹�� - x��
x¹�� - x�� = x��(x� - 1) in the exact same way that 2¹�� - 2�� = 2��(2� - 1)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members
Thanked: 1443 times

by ceilidh.erickson » Thu Feb 11, 2016 4:40 pm
Here's a guessing strategy that you could have used, if you didn't realize that the question was testing a difference of squares:

Since the problem asks which of the following is NOT a factor of n, we can infer that the other 4 answer choices will be factors of n.

If this is the case, the answer can't possibly be E. 5 can't be the number that's not a factor, if 35 and 65 both are factors. So, eliminate E.

We can eliminate D using the same logic - 13 can't be the one non-factor if that leaves 65 (which contains a factor of 13). So, eliminate D.

If we've logically eliminated D and E, that means that 5 and 13 must be factors of n, and thus 65 must also be a factor of n. So, eliminate B.

You now have it narrowed down to a 50-50 choice between A and C. If you have to guess, that's better than guessing blindly!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1