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 →

Is x^3 > y^2?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times
by Vincen » Wed Jan 03, 2018 11:49 am
Is x^3 > y^2?

(1) y = x^2
(2) x > x^2

The OA is the option C.

How can I use both statements together to solve this DS question? I don't know what should I do. Experts, I'd appreciate your help.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Thu Jan 04, 2018 11:00 am
Hi Vincen,

We're asked if X^3 is greater than Y^2. This is a YES/NO question. We can answer this question by TESTing VALUES.

1) Y = X^2

IF....
X=0 and Y=0, then 0^3 is not greater than 0^2 and the answer to the question is NO.
X = 1/2 and Y = 1/4, then (1/2)^3 is greater than (1/4)^2 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.

2) X > X^2

Fact 2 tells us nothing about the value of Y. It does 'restrict' the value of X to just positive fractions (meaning 0 < X < 1).
Fact 2 is INSUFFICIENT.

Combined, we know:
Y = X^2
0 < X < 1

If we substitute, Y = X^2 into the prompt, then the question becomes....
"Is X^3 greater than (X^2)^2?"
"Is X^3 greater than X^4?"
Since X is a positive fraction, X^3 will ALWAYS be greater than X^4... and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

by Jay@ManhattanReview » Tue Jan 09, 2018 5:30 am
Vincen wrote:Is x^3 > y^2?

(1) y = x^2
(2) x > x^2

The OA is the option C.

How can I use both statements together to solve this DS question? I don't know what should I do. Experts, I'd appreciate your help.
We have to determine whether x^3 > y^2.

(1) y = x^2

Replaing the value of y = x^2 in x^3 > y^2, we get x^3 > y^2 => x^3 ? (x^2)^2 => x^3 ? x^4

Case 1: x is negative

Is x is negative, then x^3 is negative and x^4 is positive, thus x^3 < x^4. The answer is No.

Case 2: 0 < x < 1

Say x = 1/2, then x^3 = (1/2)^3 = 1/8 and x^4 = (1/2)^4 = 1/16. We see that x^3 > x^4. The answer is Yes. No unique answer.

For the sake of understanding, we discuss the third case too.

Case 3: x ≥ 1

Say x = 2, then x^3 = 2^3 = 8 and x^4 = 2^4 = 16. We see that x^3 < x^4. The answer is No. Insufficient.

(2) x > x^2

We do not have any information about y. Insufficient.

(1) and (2) combined

Among the three cases discussed above, only Case 2 is applicable for x > x^2. Thus, the answer is Yes. No unique answer.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New Haven | Doha | Stockholm | Pretoria | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1