GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
[#permalink]
09 Feb 2020, 15:51
09 Feb 2020, 15:51
Expert Reply
2
Bookmarks
00:00
Question Stats:
86% (01:00) correct
13% (01:37) wrong based on 30 sessions
Hide Show timer Statistics
If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Given Kudos: 0
GPA: 3.72
Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
[#permalink]
10 Feb 2020, 00:53
10 Feb 2020, 00:53
2
Carcass wrote:
If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
The concept to be used: For all \(a\) and \(b\), we have: \(|a| + |b| ≥ |a + b|\)
For example:
#1. \(a = 2, b = 3 : |a| + |b| = |2| + |3| = 2 + 3 = 5\) and \(|a + b| = |2 + 3| = 5\) => \(|a| + |b| = |a + b|\)
#2. \(a = -2, b = -3 : |a| + |b| = |-2| + |-3| = 2 + 3 = 5\) and \(|a + b| = |-2 - 3| = 5\) => \(|a| + |b| = |a + b|\)
#3. \(a = -2, b = 3 : |a| + |b| = |-2| + |3| = 2 + 3 = 5\) and \(|a + b| = |-2 + 3| = 1\) => \(|a| + |b| > |a + b|\)
Note:
# \(|a| + |b| = |a + b|\) if \(a\) and \(b\) are of the same sign
# \(|a| + |b| > |a + b|\) if \(a\) and \(b\) are of opposite signs
We have been given that: \(|a| + |b| = |a + b|\) => \(a\) and \(b\) are of the same sign
Thus, \(a*b > 0\)
Answer B
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1115
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
[#permalink]
23 Dec 2021, 09:58
23 Dec 2021, 09:58
1
Given that |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0 and we need to tell which option choice must be true
Now, |a| + |b| = |a +b|
That means Sum of Modulus of two numbers is equal to modulus of their sum, now this is true only when the two numbers have the same sign
i.e. Either both are positive or both are negative
(Check out this video to know more about Absolute values/Modulus of a number)
=> a and b have the same sign
Now, if both have the same sign then their product will always be > 0
Because POSITIVE * POSITIVE = POSITIVE and NEGATIVE * NEGATIVE = POSITIVE
(Check out this video to know more about basics of Inequalities)
=> ab > 0
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Now, |a| + |b| = |a +b|
That means Sum of Modulus of two numbers is equal to modulus of their sum, now this is true only when the two numbers have the same sign
i.e. Either both are positive or both are negative
(Check out this video to know more about Absolute values/Modulus of a number)
=> a and b have the same sign
Now, if both have the same sign then their product will always be > 0
Because POSITIVE * POSITIVE = POSITIVE and NEGATIVE * NEGATIVE = POSITIVE
(Check out this video to know more about basics of Inequalities)
=> ab > 0
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
