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 a=−b?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
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] » Fri Apr 06, 2018 4:24 pm
Hi VJesus12,

We're asked if A = (-B). This is a YES/NO question and can be solved by TESTing VALUES and/or with Number Properties. This question essentially asks if A and B are exact opposites of one another (for example 3 and -3).

1) (A)(B) > B^2

With the inequality in Fact 1, we know that B cannot equal 0.
IF....
B = Positive, then B^2 = positive and A would have to be GREATER than B for the inequality to 'work.' In this case, A and B could NEVER be opposites, so answer to the question is ALWAYS NO.
B = Negative, then B^2 = positive and A would have to be NEGATIVE. In this case, A and B could NEVER be opposites, so the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

(2) A^2 = B^2

IF...
A=1 and B=1, then the answer to the question is NO
A=1 and B= -1, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Final Answer: A

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

by Brent@GMATPrepNow » Sun Apr 08, 2018 6:35 am
VJesus12 wrote:Is a = −b?

(1) ab > b²

(2) a² = b²
Target question: Is a = −b?

This is a good candidate for rephrasing the target question.

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Take the equation a = −b and add b to both sides to get: a + b= 0

So, we get....
REPHRASED target question: Is a + b= 0?

Statement 1: ab > b²
When it comes to inequalities, we must be careful when we multiply or divide both sides by a variable. If that variable has a POSITIVE value, the direction of the inequality DOES NOT CHANGE. If that variable has a NEGATIVE, value the direction of the inequality REVERSES.
Since we don't know whether b is positive or negative, we must examine both cases:

Case a: b is positive. Take ab > b² and divide both sides by b to get: a > b
IMPORTANT: if b is positive, then a must also be positive (since a > b).
If a and b are BOTH positive, then the sum a + b must be positive.
In this case, the answer to the REPHRASED target question is NO, a+b does NOT equal 0

Case b: b is negative. Take ab > b² and divide both sides by b to get: a < b (notice that we reversed the inequality symbol)
IMPORTANT: if b is negative, then a must also be negative (since a < b).
If a and b are BOTH negative, then the sum a + b must be negative.
In this case, the answer to the REPHRASED target question is NO, a+b does NOT equal 0

Notice that both cases yielded the same answer to the REPHRASED target question.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a² = b²
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 0 and b = 0, in which case a + b = 0 + 0 = 0. In this case, the answer to the REPHRASED target question is YES, a+b DOES equal 0
Case b: a = 1 and b = 1, in which case a + b = 1 + 1 = 2. In this case, the answer to the REPHRASED target question is NO, a+b does NOT equal 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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: 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 Sep 17, 2019 7:59 am
VJesus12 wrote:Is a=−b?

(1) a·b > b^2

(2) a^2 = b^2

The OA is A.

Why is the first statement sufficient? May someone helps me? Thanks in advanced.
Target question: What is the value of x?

Given: x³ < x²
If we do a little bit of work, we'll see that this given information tells us A LOT about x
x² must be POSITIVE here (since we can see that x ≠ 0, otherwise we can't have x³ < x²). So, we can safely divide both sides of the inequality by x² to get: x < 1
So, x < 1 AND x ≠ 0

Statement 1: -2< x < 2
There are several values of x that satisfy statement 1 (and the given information). Here are two:
Case a: x = -1
Case b: x = 0.5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is an integer greater than -2
So, x is an INTEGER that's less than 1, but greater than -2 AND x ≠ 0
There's only one x-value (x = -1) that satisfies these conditions. So, x must equal -1
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
Post new topic Post Reply
• Page 1 of 1