It is currently 13 Dec 2017, 09:13

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1

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

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 10 Jul 2013
Posts: 326

Kudos [?]: 430 [0], given: 102

For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1 [#permalink]

Show Tags

New post 20 Aug 2013, 11:37
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:35) correct 26% (01:04) wrong based on 163 sessions

HideShow timer Statistics

For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1. Which of the following must be true?

I. a◊b = b◊a
II. (a◊a)/a = 1◊1
III. ( a◊b)◊c = a◊(b◊c)

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
[Reveal] Spoiler: OA

_________________

Asif vai.....


Last edited by Bunuel on 20 Aug 2013, 11:40, edited 1 time in total.
Edited the question.

Kudos [?]: 430 [0], given: 102

Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 832

Kudos [?]: 1644 [0], given: 197

Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
GMAT ToolKit User
Re: For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1 [#permalink]

Show Tags

New post 20 Aug 2013, 11:43
Asifpirlo wrote:
For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1. Which of the following must be true?
I. a◊b = b◊a
II. (a◊a)/a = 1◊1
III. ( a◊b)◊c = a◊(b◊c)
(A) I only (B) II only (C) III only (D) I and II only (E) I and III only


I. a◊b = b◊a
\(ab-1 = ba-1\)==>correct.

II. (a◊a)/a = 1◊1
\(\frac{(a^2-1)}{a}= 1-1\) ==>not correct

III. ( a◊b)◊c = a◊(b◊c)
\((ab-1)c -1 =(bc-1)a - 1\) not correct.

hence A
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...



GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
: http://www.youtube.com/watch?v=APt9ITygGss

Kudos [?]: 1644 [0], given: 197

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42585

Kudos [?]: 135508 [0], given: 12697

Re: For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1 [#permalink]

Show Tags

New post 20 Aug 2013, 11:45
Asifpirlo wrote:
For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1. Which of the following must be true?

I. a◊b = b◊a
II. (a◊a)/a = 1◊1
III. ( a◊b)◊c = a◊(b◊c)

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


I. a◊b = b◊a --> a◊b=ab-1 and b◊a=ba-1 --> ab-1=ba-1. This option is always true.

II. (a◊a)/a = 1◊1 --> (a◊a)/a=(a^1-1)/a and 1◊1=1-1=0. These 2 expressions are not always equal. Discard.

III. (a◊b)◊c = a◊(b◊c) --> (a◊b)◊c=(ab-1)◊c=(ab-1)c-1 and a◊(b◊c)=a◊(bc-1)=a(bc-1)-1. These 2 expressions are not always equal. Discard.

Answer: A.

Similar question to practice: for-all-real-numbers-a-and-b-where-a-b-0-let-a-b-ab-102228.html

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135508 [0], given: 12697

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14872

Kudos [?]: 287 [0], given: 0

Premium Member
Re: For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1 [#permalink]

Show Tags

New post 28 Oct 2017, 23:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Re: For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1   [#permalink] 28 Oct 2017, 23:16
Display posts from previous: Sort by

For all real numbers a and b, a ⋅ b ≠ 0, let a◊b = ab − 1

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.