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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
Vote for Target Test Prep, Newsweek Readers’ Choice Awards 2026
NEWSWEEK READERS’ CHOICE 2026

BIG NEWS! Target Test Prep has been nominated, and they’d love your vote!

TTP has worked incredibly hard to build the best test prep experience possible, and winning Newsweek’s 2026 Readers’ Choice Award for Best Test Prep would mean a lot to them. If TTP has helped you, they’d be incredibly grateful for your vote. You can vote once each day through September 9.

Vote for TTP
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

What is the sum of all solutions to the

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 » Tue Feb 28, 2017 8:33 am
What is the sum of all solutions to the equation 3x^(2/3) = 54 + 9x^(1/3)
A) 63
B) 189
C) 216
D) 243
E) 567

Answer: B

Source: GMAT Prep Now
Difficulty level: ≈700
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

by regor60 » Tue Feb 28, 2017 9:17 am
Rearrange the equation:

3x(2/3)-9x^(1/3)-54 = 0

Let Y = X(1/3) to simplify things

3Y^2-9Y-54 = 0 >divide through by 3

Y^2-3Y-18=0

Factor: (Y-6)*(y+3) = 0 > Y=6 or Y=-3

X=Y^3, therefore X= 216 or -27

Adding solutions together 216-27=189, B
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 » Wed Mar 01, 2017 5:49 am
Brent@GMATPrepNow wrote:What is the sum of all solutions to the equation 3x^(2/3) = 54 + 9x^(1/3)
A) 63
B) 189
C) 216
D) 243
E) 567
We should start by recognizing that this is a QUADRATIC EQUATION in disguise.

Notice that x^(2/3) = [x^(1/3)]²

So let's let x^(1/3) = k, and replace x^(1/3) with k to get: 3k² = 54 + 9k
Rearrange to get: 3k² - 9k - 54 = 0
Factor: 3(k² - 3k - 18) = 0
Factor more: 3(k - 6)(k + 3) = 0
So, the solutions are k = 6 and k = -3

Since k = x^(1/3), we can write: x^(1/3) = 6 and x^(1/3) = -3
If x^(1/3) = 6, then x = 6³ = 216
If x^(1/3) = -3, then x = (-3)³ = -27

So, the sum of all solutions = 216 + (-27) = 189

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Wed Mar 01, 2017 3:05 pm
I don't think the GMAT would ask this, though, because it can be solved with a simple formula from Algebra II, Viète's Formula. (It isn't really their style to ask questions that have trivial solutions if you know slightly higher math than they expect of you.)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Wed Mar 01, 2017 3:08 pm
With that in mind, let me propose an alternative solution anyway.

Let z equal the cube root of x. With that, we can express the original equation as

3z² - 9z - 54 = 0

z² - 3z - 18 = 0

(z + 3) * (z - 6) = 0

So our solutions are z = -3 and z = 6. z is the cube root of x, so our x's are -3³ and 6³, and their sum = 189.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1