GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Aug 2018, 15:38

Close

GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Is |a-b| < |a| +|b| ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 120
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
Is |a-b| < |a| +|b| ?  [#permalink]

Show Tags

New post 03 Aug 2017, 09:35
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (01:05) correct 39% (01:25) wrong based on 158 sessions

HideShow timer Statistics

Is |a-b| < |a| +|b| ?

Statement 1: \(\frac{a}{b}\)<0
Statement 2: \(a^2b\)<0
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4665
Re: Is |a-b| < |a| +|b| ?  [#permalink]

Show Tags

New post 03 Aug 2017, 10:52
1
DH99 wrote:
Is |a-b| < |a| +|b| ?

Statement 1: \(\frac{a}{b}\)<0
Statement 2: \(a^2b\)<0

Dear DH99,

I'm happy to respond. :-)

This is a very clever question. Let's think about the prompt.

If a & b have the same sign, then subtracting produces a difference of a smaller absolute value.
\(5 - 3 = 2
(-5) - (-3) = -2\)
These are examples of choices that would produce "yes" answers for the prompt question.

If a & b have opposite signs, the subtracting produces a difference that has the same absolute value as the sum of the absolute values of a & b separately.
\(5 - (-3) = 8\) and \(|8| = 8 = |5| + |-3|\)
\((-5) - 3 = -8\) and \(|-8| = 8 = |-5| + |3|\)
These are examples of choices that would produce "no" answers for the prompt question.

So really, the prompt question is: do a and b have the same sign?

Statement #1: \(\frac{a}{b}\)<0
When is a fraction negative? It's negative when the numerator and denominator have opposite signs. Thus, a & b have opposite signs. We can give a definitive "no" to the prompt question. Because we can give a definitive answer, we know that Statement #1, alone and by itself, must be sufficient.

Statement #2: \(a^2b\)<0
I assume that this was entered correctly, and that DH99 meant \(a^2b\) and not \(a^{2b}\).

Taking this statement at face value, we know \(a^2\) is always positive, regardless of the sign of a, so we know that b just be negative. Thus, we know the sign of b, but the sign of a could be anything. We are not able to give a definitive answer to the prompt. Thus, we know that Statement #2, alone and by itself, must be insufficient.

OA = (A)

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 120
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
Re: Is |a-b| < |a| +|b| ?  [#permalink]

Show Tags

New post 03 Aug 2017, 10:59
1
mikemcgarry wrote:
DH99 wrote:
Is |a-b| < |a| +|b| ?

Statement 1: \(\frac{a}{b}\)<0
Statement 2: \(a^2b\)<0

Dear DH99,

I'm happy to respond. :-)

This is a very clever question. Let's think about the prompt.

If a & b have the same sign, then subtracting produces a difference of a smaller absolute value.
\(5 - 3 = 2
(-5) - (-3) = -2\)
These are examples of choices that would produce "yes" answers for the prompt question.



If a & b have opposite signs, the subtracting produces a difference that has the same absolute value as the sum of the absolute values of a & b separately.
\(5 - (-3) = 8\) and \(|8| = 8 = |5| + |-3|\)
\((-5) - 3 = -8\) and \(|-8| = 8 = |-5| + |3|\)
These are examples of choices that would produce "no" answers for the prompt question.

So really, the prompt question is: do a and b have the same sign?

Statement #1: \(\frac{a}{b}\)<0
When is a fraction negative? It's negative when the numerator and denominator have opposite signs. Thus, a & b have opposite signs. We can give a definitive "no" to the prompt question. Because we can give a definitive answer, we know that Statement #1, alone and by itself, must be sufficient.

Statement #2: \(a^2b\)<0
I assume that this was entered correctly, and that DH99 meant \(a^2b\) and not \(a^{2b}\).

Taking this statement at face value, we know \(a^2\) is always positive, regardless of the sign of a, so we know that b just be negative. Thus, we know the sign of b, but the sign of a could be anything. We are not able to give a definitive answer to the prompt. Thus, we know that Statement #2, alone and by itself, must be insufficient.

OA = (A)

Does all this make sense?
Mike :-)


Yes,thanks mike
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 493
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Is |a-b| < |a| +|b| ?  [#permalink]

Show Tags

New post 24 Aug 2017, 11:03
1
Clearly from A we are getting definite NO.
See the attached pic.
Attachments

IMG_2982.JPG
IMG_2982.JPG [ 905.22 KiB | Viewed 1036 times ]


_________________

Give Kudos for correct answer and/or if you like the solution.

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1201
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Is |a-b| < |a| +|b| ?  [#permalink]

Show Tags

New post 24 Aug 2017, 12:06
1
DH99 wrote:
Is |a-b| < |a| +|b| ?

Statement 1: \(\frac{a}{b}\)<0
Statement 2: \(a^2b\)<0


Statement 1: implies that either \(a<0\) or \(b<0\)
Putting the values of \(a\) & \(b\) in the inequality as per the scenario
if \(a<0\), then \(|a-b| = |-a-b| = |a+b| = |a| +|b|\). so we get a \(NO\) for the question stem
if \(b<0\), then \(|a-b| = |a-(-b)| = |a+b| = |a| + |b|\). so we get a \(NO\) for the question stem
Hence \(Sufficient\)

[b]Statement 2:/b] implies that \(b<0\) but \(a<0\) or \(a>0\)
Putting the values of \(a\) & \(b\) in the inequality as per the scenario
if both \(a<0\) and \(b<0\), then \(|a-b| = |-a-(-b)| = |-a+b|<|a| + |b|\). so we get a \(YES\) for the question stem
but if \(a>0\) and \(b<0\), then \(|a-b| = |a-(-b)| = |a+b| = |a| + |b|\). so we get a \(NO\) for the question stem
Hence \(Insufficient\)

Option \(A\)
Senior Manager
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 484
GMAT 1: 700 Q50 V34
Is |a-b| < |a| +|b| ?  [#permalink]

Show Tags

New post 12 Dec 2017, 13:49
\(|a-b| < |a| + |b|\)?

squaring on both sides, (as LHS > 0, RHS > 0, it is safe to square)
=> \(a^2 + b^2 - 2ab < a^2 + b^2 + 2|a||b|\) ?
=> \(-2ab < 2|a||b|\) ?
=> \(-ab < |ab|\) ?
=> question is reduced to \(ab > 0\) ?
=> \(a\) and \(b\) are of same sign?

Let us attack the statements

Statement 1: \(a/b < 0\) => which means \(a\) and \(b\) are of opposite sign, sufficient to answer the question as "NO"
Statement 2: \(a^2 * b < 0\) => \(b\) is negative, but we don't about the sign of a => InSufficient

Answer (A)
Is |a-b| < |a| +|b| ? &nbs [#permalink] 12 Dec 2017, 13:49
Display posts from previous: Sort by

Is |a-b| < |a| +|b| ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.