The operation ⊗ is defined for all nonzero numbers a and b

Oldest

Best Reply

Author

Message

TAGS:

Senior Manager

Joined: 28 Aug 2010

Posts: 280

Followers: 3

Kudos [?]: 20 [0], given: 11

The operation ⊗ is defined for all nonzero numbers a and b [#permalink]

18 Dec 2010, 08:46

00:00

Question Stats:

61% (02:49) correct

38% (01:42) wrong

based on 1 sessions

The operation ⊗ is defined for all nonzero numbers a and b by a ⊗ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?

I. x ⊗ xy = x(1 ⊗ y)
II. x ⊗ y = -(y ⊗ x)
III. 1/x ⊗ 1/y = y ⊗ x

A. I only
B. II only
C. III only
D. I and II
E. II and III

[Reveal] Spoiler: OA

_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Last edited by Bunuel on 20 May 2012, 11:29, edited 1 time in total.

Edited the question and added the OA

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11611

Followers: 1801

Kudos [?]: 9597 [1] , given: 829

Re: Symbols problem [#permalink]

18 Dec 2010, 09:02

This post received
KUDOS

ajit257 wrote:

The operation ⊗ is defined for all nonzero numbers a and b by a ⊗ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?
I. x ⊗ xy = x(1 ⊗ y)
II. x ⊗ y = -(y ⊗ x)
III. 1/x ⊗ 1/y = y ⊗ x

A. I only
B. II only
C. III only
D. I and II
E. II and III

Please can someone confirm the ans. I am not sure about the ans

Given: a@b=\frac{a}{b}-\frac{b}{a}, for all nonzero numbers a and b.

I. x@(xy) = x(1@y): LHS=x@(xy)=\frac{x}{xy}-\frac{xy}{x}=\frac{1}{y}-y and RHSx(1@y)=x(\frac{1}{y}-y) as you see LHS doen't equal to RHS;

II. x@y = -(y@x): LHS=x@y=\frac{x}{y}-\frac{y}{x} and RHS=-(y@x)=-(\frac{y}{x}-\frac{x}{y})=\frac{x}{y}-\frac{y}{x} --> LHS=RHS;

III. (\frac{1}{x})@(\frac{1}{y}) = y@x: LHS=(\frac{1}{x})@(\frac{1}{y})=\frac{y}{x}-\frac{x}{y} and RHS=y@x=\frac{y}{x}-\frac{x}{y} --> LHS=RHS.

Answer: E (II and III).

Similar questions:
a-third-problem-solving-question-102358.html
gmat-prep-question-101282.html
just-800-level-question-99064.html
operators-problem-86208.html

Hope it's clear.
_________________

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

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. NEW!!!

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. NEW!!!

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

Find out what's new at GMAT Club - latest features and updates

Re: Symbols problem [#permalink] 18 Dec 2010, 09:02

	Similar topics	Author	Replies	Last post
Similar Topics:	If the operation (#) is defined for all "a" and "b" by the	luve	1	04 Nov 2003, 12:17
	The operation  is defined for all nonzero numbers a	TOUGH GUY	2	10 Oct 2005, 06:38
	The operation @ is defined for all non-zero x and y by the	sideslip	5	16 Mar 2006, 19:07
	The operation delta is defined for all nonzero x and y b x	nfa1rhp	3	29 Jul 2007, 11:56
	If the operation * is defined for all integers a and b by	Ant	5	06 Jan 2008, 16:34

The operation ⊗ is defined for all nonzero numbers a and b

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

The operation ⊗ is defined for all nonzero numbers a and b

The operation ⊗ is defined for all nonzero numbers a and b

Main navigation

GMAT Resources

Partners

MBA Resources