Hi fambrini,
I'm going to give you a few hints so that you can retry this question on your own:
[spoiler]Notice how Fact 1 does not tell you anything about variable "A" and Fact 2 doesn't tell you anything about variable "C"... it's pretty obvious that each of those Facts is insufficient on its own. When combining Facts, try TESTing VALUES. What values would be easy to TEST? Hint: choose the same value for all 3 variables. Once you've done that, what else could you TEST (and what would the result be?)? After TESTing 3 different sets of numbers, what do you notice about the results? Are they consistent or not?[/spoiler]
GMAT assassins aren't born, they're made,
Rich
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
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
Trouble with this absolute value problem
Source: Beat The GMAT — Data Sufficiency |
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Location: Palo Alto, CA
- Thanked: 2867 times
- GMAT Score:800
Thanks Rich. I've tried this one again after practicing a lot of other absolute value questions and I got it.
The most important concept for me was that |b - c| can be interpreted as the distance between b and c.
Also, I've tried using values like you've mentioned and it worked. Thanks for that too!
Just to verify, my resolution was:
1) In order for the distance between b and c to be equal to |b| - |c|, b and c are greater than 0. No info on a though. Not sufficient.
2) no info on signal of b or any clue about b. Not sufficient.
1 and 2) I know that b and c are greater than 0. With this and statement 2 it is possible to conclude that a > 0. Therefore a(b + c) > 0.
Answer: C
The most important concept for me was that |b - c| can be interpreted as the distance between b and c.
Also, I've tried using values like you've mentioned and it worked. Thanks for that too!
Just to verify, my resolution was:
1) In order for the distance between b and c to be equal to |b| - |c|, b and c are greater than 0. No info on a though. Not sufficient.
2) no info on signal of b or any clue about b. Not sufficient.
1 and 2) I know that b and c are greater than 0. With this and statement 2 it is possible to conclude that a > 0. Therefore a(b + c) > 0.
Answer: C
-
Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Location: New York, NY
- Thanked: 39 times
We need to determine whether a(b + c) > 0.fambrini wrote:If a ≠0, b ≠0, c ≠0, is a(b + c) > 0?
1) |b - c| = |b| - |c|
2) |a + b| = |a| + |b|
OA: C
Statement One Alone:
|b - c| = |b| - |c|
In analyzing statement one, we can use the following rule: When we are given the absolute value equation |b - c| = |b| - |c|, we know that
1) The values of b and c have the same sign.
2) |b| > |c|
However, because we do not know the sign of the value of a, statement one is not enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
|a + b| = |a| + |b|
In analyzing statement two we can use the following rule:when we are given the absolute value equation |a + b| = |a| + |b|, we know that
1) The values of a and b have the same sign.
However, because we do not know the sign of the value of c, statement two is not enough information to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two, we know the following:
The values of b and c have the same sign and the values of a and b have the same sign. Thus, we know that the values of a, b, and c all have the same sign. With that information we can determine that a(b + c) > 0.
Answer: C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Location: New York, NY
- Thanked: 13060 times
- GMAT Score:790
Question stem, rephrased:fambrini wrote:If a ≠0, b ≠0, c ≠0, is a(b + c) > 0?
1) |b - c| = |b| - |c|
2) |a + b| = |a| + |b|
Do a and b+c have the SAME SIGN?
Statement 1:
No information about a.
INSUFFICIENT.
Statement 2:
No information about c.
INSUFFICIENT.
Statements combined:
|b - c| = |b| - |c|
|b - c|² = (|b| - |c|)²
b² + c² - 2bc = b² + c² - 2|b||c|
-2bc = -2|b||c|
bc = |b||c|.
bc = (positive)(positive) = positive.
Implication:
b and c have the SAME SIGN.
|a + b| = |a| + |b|
|a + b|² = (|a| + |b|)²
a² + b² + 2ab = a² + b² + 2|a||b|
2ab = 2|a||b|
ab = |a||b|.
ab = (positive)(positive) = positive.
Implication:
a and b have the SAME SIGN.
Since a and b have the same sign, and b and c have the same sign, all three variables -- a, b and c -- have the same sign.
Thus, a and b+c must have the same sign.
SUFFICIENT.
The correct answer is C.
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
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
