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.
Nov 1912:30 PM EST
-01:30 PM EST
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 more
Nov 2001:30 PM EST
-02:30 PM IST
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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
21 Apr 2021, 02:00
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:
36% (03:09) correct
64%
(02:40)
wrong
based on 47
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y belong to the set {2, 4}, and \(x^{ky} = x^{(ly^2−8)}\), is \(kl > 2\)?
(1) \(k = −6\)
(2) \(3l − k = 3\)
(1) \(k = −6\)
(2) \(3l − k = 3\)
21 Apr 2021, 20:42
Kudos
Bookmarks
Bunuel
Since x is either 2 or 4, we can equate the powers in \(x^{ky} = x^{(ly^2−8)}\)
\(ky=ly^2-8.......ly^2-ky-8\)
If the quadratic equation is \(ax^2+bc+c=0\), then
Sum of the roots =\(x_1+x_2=\frac{-b}{a}\)
In \(ly^2-ky-8=0\), it will be \(\frac{k}{l}\)
Product of the roots =\(x_1*x_2=\frac{c}{a}\)
In \(ly^2-ky-8=0\), it will be \(\frac{-8}{l}\)
we know the roots \(x_1 \ \ and \ \ x_2\) can be 2 or 4.
Let us check the values that l can take
\(x_1* x_2\) can be 2*2 or 2*4 or 4*4
a) If it is 2*2, then \(4=\frac{-8}{l}.....l=-2\), so if k<-1, then kl>2.
b) If it is 2*4, then \(8=\frac{-8}{l}.....l=-1\), so if k<-2, then kl>2.
c) If it is 4*4, then \(16=\frac{-8}{l}.....l=-\frac{1}{2}\), so if k<-4, then kl>2.
Thus we can say if k<-4, then the answer is YES for sure.
(1) \(k = −6\)
k<-4, so kl>2
Sufficient
(2) \(3l − k = 3\)
We have 3 possible values of l
a) l=-2, then (3*-2)-k=3 or k=-9......kl=-2*-9=18>2
b) l=-1, then (3*-1)-k=3 or k=-6......kl=-1*-6=6>2
c) l=-\(\frac{1}{2}\), then \(3*\frac{-1}{2}-k=3.....k=\frac{-9}{2}.........kl=\frac{-1}{2}*\frac{-9}{2}=9/4>2\)
So in each case, the answer is yes
Sufficient
D
24 Apr 2021, 13:57
Kudos
Bookmarks
Bunuel
Since x = 2 or 4, which are positive and not 1, we must have equal exponents on both sides. Hence \(ly^2 - 8 - ky = 0\). Since y can only be 2 or 4, we must have \(4l - 2k - 8 = 0\) or \(16l - 4k - 8 = 0\).
Statement 1:
Plugging \(k = -6\) in both equations give \(l = -1\). Hence \(kl = 6 > 2\) in either case. Sufficient.
Statement 2:
We can write this as \(k = 3l - 3\) to plug in. With the first equation, solving gives \(L = -1\) and \(k = -6\). Plugging in the second equation gives the same set of solutions, hence \(kl = 6 > 2\) in either case. Sufficient.
Ans: D
