Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Oct 2014, 07:32

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a b and |a-b| = b-a, which of the following statements

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 25 Mar 2013
Posts: 3
Location: Italy
WE: General Management (Other)
Followers: 0

Kudos [?]: 9 [1] , given: 6

If a b and |a-b| = b-a, which of the following statements [#permalink] New post 26 Mar 2013, 08:07
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

65% (01:56) correct 35% (01:01) wrong based on 264 sessions
If a ≠ b and |a-b| = b-a, which of the following statements must be true ?

I. a < 0
II. a + b < 0
III. a < b

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

[Reveal] Spoiler:
Thank's in advance for helping to solve the problem, the OA should be ( C ) , but I'm not sure 100% about it; a friend gave to me several GMAT exercises for training.
[Reveal] Spoiler: OA

_________________

Labor omnia vincit

Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23397
Followers: 3610

Kudos [?]: 28830 [4] , given: 2853

Re: If a ≠ b and |a-b| = b-a, which of the following statements [#permalink] New post 27 Mar 2013, 04:06
4
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
If a ≠ b and |a-b| = b-a, which of the following statements must be true ?

I. a < 0
II. a + b < 0
III. a < b


(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

Absolute value properties:

When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}. For example: |-5|=5=-(-5);

When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|={some \ expression}. For example: |5|=5;


Thus, according to the above, since |a-b| = b-a=-(a-b), then a-b\leq{0} --> a\leq{b}. Since we also know that a\neq{b}, then we have that a<b. So, III is always true.

As for the other options:
I. a < 0 --> not necessarily true, consider a=1 and b=2.
II. a + b < 0 --> not necessarily true, consider a=-2 and b=-1.

Answer: C.

For more check here: math-absolute-value-modulus-86462.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

2 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 113

Kudos [?]: 1193 [2] , given: 219

GMAT ToolKit User
Re: If a ≠ b and |a-b| = b-a, which of the following statements [#permalink] New post 26 Mar 2013, 08:32
2
This post received
KUDOS
I think the best way here is using real numbers

I) a < 0
a=1, b=5
|1-5|=5-1
4=4, so I is not always true

II) a + b < 0
a=3,b=4
|3-4|=4-3
1=1, so II is not always true

III) a < b
|a-b| = b-a
if a>b then |a-b| = a-b and doesn't equal b-a
if b>a then |a-b| = -(a-b) = -a+b = b-a so III is true
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

1 KUDOS received
Intern
Intern
avatar
Joined: 22 Jan 2010
Posts: 25
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Followers: 0

Kudos [?]: 12 [1] , given: 3

Re: If a ≠ b and |a-b| = b-a, which of the following statements [#permalink] New post 26 Mar 2013, 23:26
1
This post received
KUDOS
The given conditions are :
i) a is not equal to b ,i,e a-b is non zero.
ii) |a -b | = b-a ,i,e -(a-b).
So ,considering the above conditions,
a - b < 0 => a < b.
_________________

Please press +1 KUDOS if you like my post.

1 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 113

Kudos [?]: 1193 [1] , given: 219

GMAT ToolKit User
Re: If a b and |a-b| = b-a, which of the following statements [#permalink] New post 15 Jun 2013, 10:27
1
This post received
KUDOS
WholeLottaLove wrote:
Because |a-b| = b-a, could we say that b-a is positive (because it is equal to an abs. val.) and therefore, b must be greater than a?

Also, I first tired to solve this problems by:

|a-b| = b-a so:

a-b = b-a
2a = 2b
a=b
(which isn't true as the stem tells us it isn't)

OR

-a+b=b-a
0=0

But I'm not sure how to interpret that result. Is that a valid way to solve the problem?


The second result tells you that whatever value a and b have, that equation will always be true: 0=0 always.

0=0 means that that case will always hold, hence that case (b>a) will always be "true"
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

1 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 113

Kudos [?]: 1193 [1] , given: 219

GMAT ToolKit User
Re: If a b and |a-b| = b-a, which of the following statements [#permalink] New post 15 Jun 2013, 22:32
1
This post received
KUDOS
WholeLottaLove wrote:
So, in other words,

I.) |a-b| = b-a
II.) b-a is positive because it is equal to an absolute value
III.) b must be greater than a because b-a is positive
IV.) a-b must be negative
V.) |a-b| = -(a-b)
VI.) a-b ≤ 0
VII.) a ≤ b



Yes, perfect. Just remember that we are told that a\neq{b} so

VII)a<b
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 476
Followers: 1

Kudos [?]: 58 [0], given: 134

Re: If a b and |a-b| = b-a, which of the following statements [#permalink] New post 15 Jun 2013, 10:24
Because |a-b| = b-a, could we say that b-a is positive (because it is equal to an abs. val.) and therefore, b must be greater than a?

Also, I first tired to solve this problems by:

|a-b| = b-a so:

a-b = b-a
2a = 2b
a=b
(which isn't true as the stem tells us it isn't)

OR

-a+b=b-a
0=0

But I'm not sure how to interpret that result. Is that a valid way to solve the problem?
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 476
Followers: 1

Kudos [?]: 58 [0], given: 134

Re: If a b and |a-b| = b-a, which of the following statements [#permalink] New post 15 Jun 2013, 16:58
So, in other words,

I.) |a-b| = b-a
II.) b-a is positive because it is equal to an absolute value
III.) b must be greater than a because b-a is positive
IV.) a-b must be negative
V.) |a-b| = -(a-b)
VI.) a-b ≤ 0
VII.) a ≤ b

Zarrolou wrote:
WholeLottaLove wrote:
Because |a-b| = b-a, could we say that b-a is positive (because it is equal to an abs. val.) and therefore, b must be greater than a?

Also, I first tired to solve this problems by:

|a-b| = b-a so:

a-b = b-a
2a = 2b
a=b
(which isn't true as the stem tells us it isn't)

OR

-a+b=b-a
0=0

But I'm not sure how to interpret that result. Is that a valid way to solve the problem?


The second result tells you that whatever value a and b have, that equation will always be true: 0=0 always.

0=0 means that that case will always hold, hence that case (b>a) will always be "true"
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 476
Followers: 1

Kudos [?]: 58 [0], given: 134

Re: If a b and |a-b| = b-a, which of the following statements [#permalink] New post 16 Jun 2013, 06:58
Ahh - I forgot about that. Thanks!

Zarrolou wrote:
WholeLottaLove wrote:
So, in other words,

I.) |a-b| = b-a
II.) b-a is positive because it is equal to an absolute value
III.) b must be greater than a because b-a is positive
IV.) a-b must be negative
V.) |a-b| = -(a-b)
VI.) a-b ≤ 0
VII.) a ≤ b



Yes, perfect. Just remember that we are told that a\neq{b} so

VII)a<b
Intern
Intern
avatar
Joined: 09 Apr 2013
Posts: 2
GPA: 3.5
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: If a b and |a-b| = b-a, which of the following statements [#permalink] New post 02 Sep 2014, 15:42
Another thing to remember is that, because of the absolute value

|a-b| ≤ b-a

because the absolute value either turns a negative positive or leaves a positive the same..
Re: If a b and |a-b| = b-a, which of the following statements   [#permalink] 02 Sep 2014, 15:42
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If a≠b and a·b≠0, which of the following may be true? goodyear2013 4 05 Aug 2014, 04:14
Experts publish their posts in the topic Is a^b > b^a? fozzzy 3 20 May 2013, 22:31
8 Experts publish their posts in the topic If the quotient a/b positive, which of the following must be Bunuel 9 03 Sep 2012, 04:49
1 Experts publish their posts in the topic If the quotient a/b is positive, which of the following must Bunuel 0 06 May 2012, 05:51
89) If the quotient a/b is positive, which of the following chuckle 4 03 Apr 2006, 05:18
Display posts from previous: Sort by

If a b and |a-b| = b-a, which of the following statements

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.