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 →

If the product of X and Y is a positive number, is the sum

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

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 Oct 09, 2018 5:13 am
If the product of x and y is a positive number, is the sum of x and y a negative number?
(1) x > y^5
(2) x > y^6
IMPORTANT CONCEPTS:
An ODD power preserves the sign of the base.
For example, (-5)^3 = -125 and 2^5 = 32
An EVEN power always yields a positive number (as long as the base ≠ 0
For example, (-5)^4 = 625 and 2^6 = 64


Target question: Is the sum of x and y negative?

Given: the product xy is positive
This tells us that EITHER x and y are both positive, OR x and y are both negative

Also, if the product xy is positive, we know that x ≠ 0 and y ≠ 0

Statement 1: x > y^5
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = -1 and y = -2, in which case the sum of x and y IS negative
Case b: x = 10 and y = 1, in which case the sum of x and y is NOT negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y^6
Since y ≠ 0 we know that y^6 must be positive [since we have an EVEN exponent]
If x > y^6, then we know that x MUST BE POSITIVE
So, there are only 2 possible scenarios to consider:
Scenario #1: x is positive and y is positive
Scenario #2: x is positive and y is negative
HOWEVER, scenario #2 CANNOT OCCUR because it is given that the product xy is positive, and the product cannot be positive in scenario #2.
So, scenario #1 is the only possible scenario, which means x is positive and y is positive, which means the sum of x and y is definitely NOT negative
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

If the product of X and Y is a positive number, is the sum

by fskilnik@GMATH » Tue Oct 09, 2018 10:33 am
subh2273 wrote:If the product of X and Y is a positive number, is the sum of X and Y a negative number?

(1) X > Y^5
(2) X > Y^6
\[xy > 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( * \right)\,\,\,\,\left\{ \begin{gathered}
\,\,x > 0\,\,{\text{and}}\,\,y > 0\,\,\,\,\left( {{\text{scenario}}\,\,{\text{I}}} \right) \hfill \\
\,\,\,\,OR\,\,\, \hfill \\
\,\,x < 0\,\,{\text{and}}\,\,y < 0\,\,\,\,\left( {{\text{scenario}}\,\,{\text{II}}} \right) \hfill \\
\end{gathered} \right.\]
\[x + y\,\,\mathop < \limits^? \,\,\,0\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\boxed{\,\,\,?\,\,\,:\,\,\,{\text{scenario}}\,{\text{II}}\,\,}\]
\[\left( 1 \right)\,\,\,x > {y^5}\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( {2,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,\left( {x,y} \right) = \left( { - 1, - 2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,x > {y^6}\,\, \geqslant 0\,\,\,\, \Rightarrow \,\,\,\,x > 0\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\]

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sun Oct 07, 2018 2:38 pm

by happyatharvard » Tue Oct 09, 2018 4:10 pm
in the first case x >y^5 can be satisfied when x, y both are negative or positive. But we want that both should be negative.
in the second case x>y^6 is possible only when both are positive. So we now know that x+y can't be negative. sufficient.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1