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

It is currently 28 Aug 2014, 01:47

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

M27#12

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 28 Nov 2011
Posts: 20
Location: United States
GMAT 1: 640 Q42 V35
GMAT 2: 710 Q47 V40
GPA: 2.99
Followers: 0

Kudos [?]: 9 [0], given: 6

M27#12 [#permalink] New post 13 Sep 2012, 17:04
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

63% (02:11) correct 38% (00:46) wrong based on 8 sessions
Is xy≤1/2?

(1) x^2+y^2=1
(2) x^2−y^2=0

OFFICIAL EXPLANATION
(1) x^2+y^2=1. Recall that (x−y)2≥0 (square of any number is more than or equal to zero). Expand: x^2−2xy+y^2≥0 and since x2+y2=1 then: 1−2xy≥0. So, xy≤1/2. Sufficient.
(2) x^2−y^2=0. Re-arrange and take the square root from both sides: |x|=|y|. Clearly insufficient.

I am fine with (2). I have trouble with (1).

What if, instead of using x^2-2xy+y^2≥0, I decided to use x^2+2xy+y^2≥0 (note the positive). That would result in xy≥-1/2 instead of the xy≤1/2 that is sufficient. In the end, I would have to use x^2-2xy+y^2≥0?

Anyone care to elaborate on this please? :)
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3407

Kudos [?]: 24900 [0], given: 2697

Re: M27#12 [#permalink] New post 14 Sep 2012, 03:15
Expert's post
lesliehh wrote:
Is xy≤1/2?

(1) x^2+y^2=1
(2) x^2−y^2=0

OFFICIAL EXPLANATION
(1) x^2+y^2=1. Recall that (x−y)2≥0 (square of any number is more than or equal to zero). Expand: x^2−2xy+y^2≥0 and since x2+y2=1 then: 1−2xy≥0. So, xy≤1/2. Sufficient.
(2) x^2−y^2=0. Re-arrange and take the square root from both sides: |x|=|y|. Clearly insufficient.

I am fine with (2). I have trouble with (1).

What if, instead of using x^2-2xy+y^2≥0, I decided to use x^2+2xy+y^2≥0 (note the positive). That would result in xy≥-1/2 instead of the xy≤1/2 that is sufficient. In the end, I would have to use x^2-2xy+y^2≥0?

Anyone care to elaborate on this please? :)


Yes, to solve this question you should use (x−y)^2≥0 not (x+y)^2≥0.
_________________

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

Intern
Intern
User avatar
Joined: 30 May 2011
Posts: 18
Followers: 0

Kudos [?]: 5 [0], given: 4

GMAT ToolKit User
Re: M27#12 [#permalink] New post 18 Feb 2013, 14:38
Because square of any number is more than or equal to zero). so x2−2xy+y2≥0 is used instead of x2+2xy+y2≥0?????????????????????????????

Bunuel wrote:
lesliehh wrote:
Is xy≤1/2?

(1) x^2+y^2=1
(2) x^2−y^2=0

OFFICIAL EXPLANATION
(1) x^2+y^2=1. Recall that (x−y)2≥0 (square of any number is more than or equal to zero). Expand: x^2−2xy+y^2≥0 and since x2+y2=1 then: 1−2xy≥0. So, xy≤1/2. Sufficient.
(2) x^2−y^2=0. Re-arrange and take the square root from both sides: |x|=|y|. Clearly insufficient.

I am fine with (2). I have trouble with (1).

What if, instead of using x^2-2xy+y^2≥0, I decided to use x^2+2xy+y^2≥0 (note the positive). That would result in xy≥-1/2 instead of the xy≤1/2 that is sufficient. In the end, I would have to use x^2-2xy+y^2≥0?

Anyone care to elaborate on this please? :)


Yes, to solve this question you should use (x−y)^2≥0 not (x+y)^2≥0.
Senior Manager
Senior Manager
avatar
Joined: 22 Nov 2010
Posts: 293
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 25 [0], given: 75

Re: M27#12 [#permalink] New post 21 Mar 2013, 02:03
Bunuel,

I am not able to understand this explanation. What triggered you to choose this method to find the solution?

OFFICIAL EXPLANATION
(1) x^2+y^2=1. Recall that (x−y)2≥0 (square of any number is more than or equal to zero). Expand: x^2−2xy+y^2≥0 and since x2+y2=1 then: 1−2xy≥0. So, xy≤1/2. Sufficient.
_________________

YOU CAN, IF YOU THINK YOU CAN

Re: M27#12   [#permalink] 21 Mar 2013, 02:03
Display posts from previous: Sort by

M27#12

  Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: Bunuel, WoundedTiger



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®.