Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jun 1312:30 AM EDT
-01:00 AM EDT
Struggling to find the right strategies to score a 99 %ile on GMAT Focus? Riya (GMAT 715) boosted her score by 100-points in just 15 days! Discover how the right mentorship, tailored strategies, and an unwavering mindset can transform your GMAT prep.
Jun 1401:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and....
Jun 1603:00 PM PDT
-04:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
Jun 2207:30 PM EDT
-09:30 PM EDT
Master the GMAT with expert live instruction, a personalized study plan, and real-time support. Includes 40 hours of online classes plus 6 months of access to the TTP GMAT OnDemand video course. Class date: Mon/Wed June 22, 2026 →August 26, 2026
13 Sep 2012, 18:04
Kudos
Bookmarks
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?
(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?
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests
for the latest questions.
Still interested? Check out the "Best Topics" block below for better discussion and related questions.
Thank you for understanding, and happy exploring!
18 Feb 2013, 15:38
Kudos
Bookmarks
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
