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 →

30^20 – 20^20 is divisible by all

Expert replies
Post new topic Post Reply
Previous Topic Next Topic

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 » Mon Jun 04, 2018 5:10 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

30^20 - 20^20 is divisible by all of the following values, EXCEPT:

A) 10
B) 25
C) 40
D) 60
E) 64

Answer: D
Difficulty level: 600 - 650
Source: www.gmatprepnow.com
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

multiple

by GMATGuruNY » Mon Jun 04, 2018 6:15 am
Brent@GMATPrepNow wrote:30^20 - 20^20 is divisible by all of the following values, EXCEPT:

A) 10
B) 25
C) 40
D) 60
E) 64
Rule:
(MULTIPLE OF X) ± (MULTIPLE OF X) = MULTIPLE OF X
(MULTIPLE OF X) ± (NON-MULTIPLE OF X) = NON-MULTIPLE OF X.

3²� - 2²� = (multiple of 3) - (non-multiple of 3) = non-multiple of 3.
Since 3²� - 2²� is not divisible by 3, it cannot be divisible by a multiple of 3 such as 60.

The correct answer is D.
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
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 » Tue Jun 05, 2018 8:58 am
Brent@GMATPrepNow wrote:30^20 - 20^20 is divisible by all of the following values, EXCEPT:

A) 10
B) 25
C) 40
D) 60
E) 64

Answer: D
Difficulty level: 600 - 650
Source: www.gmatprepnow.com
Here are some useful divisibility rules:
1. If integers A and B are each divisible by integer k, then (A + B) is divisible by k
2. If integers A and B are each divisible by integer k, then (A - B) is divisible by k
3. If integer A is divisible by integer k, BUT integer B is NOT divisible by integer k, then (A + B) is NOT divisible by k
4. If integer A is divisible by integer k, BUT integer B is NOT divisible by integer k, then (A - B) is NOT divisible by k

Now let's check the answer choices....

A) 10
30^20 = (10^20)(3^20) = (10)(10^19)(3^20), so 30^20 is divisible by 10
20^20 = (10^20)(2^20) = (10)(10^19)(2^20), so 20^20 is divisible by 10
So, by rule #2, 30^20 - 20^20 MUST be divisible by 10
ELIMINATE A

B) 25
30^20 = (5^20)(6^20) = (5^2)(5^18)(6^20) = (25)(5^18)(6^20), so 30^20 is divisible by 25
20^20 = (5^20)(4^20) = (5^2)(5^18)(4^20) = (25)(5^18)(4^20), so 20^20 is divisible by 25
So, by rule #2, 30^20 - 20^20 MUST be divisible by 25
ELIMINATE B


C) 40
30^20 = (10^20)(4^20) = (10)(10^19)(4)(4^19) = (40)(10^19)(4^19), so 30^20 is divisible by 40
20^20 = (10^20)(2^20) = (10)(10^19)(2^2)(2^18) = (40)(10^19)(2^18), so 20^20 is divisible by 40
So, by rule #2, 30^20 - 20^20 MUST be divisible by 40
ELIMINATE C

D) 60
30^20 = (30^1)(30^19) = (30^1)(2^19)(15^19) = (30)(2)(2^18)(15^19) = (60)(2^18)(15^19), so 30^20 is divisible by 60
20^20 = (5^20)(4^20) = (5^20)(2^20)(2^20). This tells us that the prime factorization of 20^20 does not have any 3's, which means 20^20 is NOT divisible by 3. And, if 20^20 is not divisible by 3, then 20^20 is NOT divisible by 60
So, by rule #4, 30^20 - 20^20 IS NOT divisible by 60

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1