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.
Sep 1712:30 AM EDT
-01:30 AM EDT
Thought your job leaves no time for GMAT prep? After multiple GMAT attempts and a demanding consulting job, Kshitij improved to 695 in under 2 months. Learn the mindset shifts, study strategy, and execution changes that made the breakthrough possible.
Sep 1801:30 AM EDT
-02:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Sep 1808:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
25 Jul 2010, 18:51
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:26) correct
67%
(02:19)
wrong
based on 337
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are integers such that (x+1)^2 less than equal to 36 and (y-1)^2 less than 64. What is the largest possible and minimum possible value of xy.
A. 40 and -30, respectively
B. 40 and -56, respectively
C. 42 and -30, respectively
D. 42 and -56, respectively
E. 49 and -56, respectively
A. 40 and -30, respectively
B. 40 and -56, respectively
C. 42 and -30, respectively
D. 42 and -56, respectively
E. 49 and -56, respectively
In equalities how to handle an expression which is squared
Does the above equation
(x+1)^2 <= 36 mean |x+1| < (+6 or -6)
I then get 4 equations.. and I am am not able to proceed. Can you someone please explain how such questions are to be handled.
Does the above equation
(x+1)^2 <= 36 mean |x+1| < (+6 or -6)
I then get 4 equations.. and I am am not able to proceed. Can you someone please explain how such questions are to be handled.
12 Aug 2010, 13:01
Kudos
Bookmarks
gmatrant
If x and y are integers such that (x+1)^2 less than equal to 36 and (y-1)^2 less than 64. What is the largest possible and minimum possible value of xy.
\((x+1)^2\leq{36}\) --> \({-\sqrt{36}}\leq{x+1}\leq{\sqrt{36}}\) --> \({-6}\leq{x+1}\leq{6}\) --> \({-7}\leq{x}\leq{5}\).
\((y-1)^2<{64}\) --> \({-\sqrt{64}}<{y-1}<{\sqrt{64}}\) --> \({-8}<{y-1}<{8}\) --> \({-7}<{y}<{9}\), as \(y\) is an integer we can rewrite this inequality as \({-6}\leq{y}\leq{8}\).
We should try extreme values of \(x\) and \(y\) to obtain min and max values of \(xy\):
Min possible value of \(xy\) is for \(x=-7\) and \(y=8\) --> \(xy=-56\);
Max possible value of \(xy\) is for \(x=-7\) and \(y=-6\) --> \(xy=42\).
Solving with absolute values gives the same results:
\((x+1)^2\leq{36}\) means \(|x+1|\leq{6}\) --> \({-7}\leq{x}\leq{5}\).
\((y-1)^2<{64}\) means \(|y-1|<{8}\) --> \({-7}<{y}<{9}\).
Hope it's clear.
General Discussion
One thing I notice is that you have to be careful with the exclusivity and inclusivity of ranges. In these questions, you will get it wrong if you thought y = 9 is included in the range.
