Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Dec 0610:00 AM PST
-11:00 AM PST
In this video, we uncover the top errors applicants unknowingly make during MBA interviews and provide actionable tips to avoid them. Watch it carefully to avoid the common mistakes committed by applicants in delivering interviews.
Dec 0711:00 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- Dec 08
11:00 AM IST
-01:00 PM IST
Attend this session to evaluate your current skill level, learn process skills, and solve through tough Arithmetic questions.
niteshwaghray
GMAT 1: 700 Q45 V40
Posts: 59
Updated on: 26 Aug 2019, 02:23
Originally posted by niteshwaghray on 31 May 2017, 23:14.
Last edited by Bunuel on 26 Aug 2019, 02:23, edited 3 times in total.
Last edited by Bunuel on 26 Aug 2019, 02:23, edited 3 times in total.
Renamed the topic and edited the question.
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (01:57) correct
48%
(01:57)
wrong
based on 360
sessions
History
Date
Time
Result
Not Attempted Yet
If \(z^2=\sqrt{2+{\sqrt{2+\sqrt{2+\sqrt{2+...}}}}}\), where the given expression extends till infinity, which of the following statements must be true ?
I. Two values are possible for z
II. 4 - z^2 = 2
III. z^8 = 16
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above
I. Two values are possible for z
II. 4 - z^2 = 2
III. z^8 = 16
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above
31 May 2017, 23:33
Kudos
Bookmarks
niteshwaghray
If \(z^2=\sqrt{2+{\sqrt{2+\sqrt{2+\sqrt{2+...}}}}}\), where the given expression extends till infinity, which of the following statements must be true ?
I. Two values are possible for z
II. 4 - z^2 = 2
III. z^8 = 16
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above
I. Two values are possible for z
II. 4 - z^2 = 2
III. z^8 = 16
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above
\(z^2=\sqrt{2+{\sqrt{2+\sqrt{2+\sqrt{2+...}}}}}\);
\(z^2=\sqrt{2+({\sqrt{2+\sqrt{2+\sqrt{2+...}})}}}\), as the expression under square root extends infinitely then expression in brackets would equal to z^2 itself so we can rewrite given expression as \(z^2=\sqrt{2+z^2}\). Square both sides \(z^4=2+z^2\) --> \(z=\sqrt{2}\) or \(z=-\sqrt{2}\).
We have two possible values, so I is true. Also, both of them satisfy II and III.
Answer: D.
31 May 2017, 23:34
Kudos
Bookmarks
Bunuel
niteshwaghray
If \(z^2=\sqrt{2+{\sqrt{2+\sqrt{2+\sqrt{2+...}}}}}\), where the given expression extends till infinity, which of the following statements must be true ?
I. Two values are possible for z
II. 4 - z^2 = 2
III. z^8 = 16
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above
I. Two values are possible for z
II. 4 - z^2 = 2
III. z^8 = 16
A. I only
B. II only
C. III only
D. I, II and III
E. None of the above
\(z^2=\sqrt{2+{\sqrt{2+\sqrt{2+\sqrt{2+...}}}}}\);
\(z^2=\sqrt{2+({\sqrt{2+\sqrt{2+\sqrt{2+...}})}}}\), as the expression under square root extends infinitely then expression in brackets would equal to z^2 itself so we can rewrite given expression as \(z^2=\sqrt{2+z^2}\). Square both sides \(z^4=2+z^2\) --> \(z=\sqrt{2}\) or \(z=-\sqrt{2}\).
We have two possible values, so I is true. Also, both of them satisfy II and III.
Answer: D.
Similar questions to practice:
https://gmatclub.com/forum/tough-and-tri ... l#p1029228
https://gmatclub.com/forum/find-the-valu ... 38049.html
https://gmatclub.com/forum/find-the-valu ... 75403.html
https://gmatclub.com/forum/if-the-expre ... 32547.html
https://gmatclub.com/forum/if-the-expre ... 98647.html
Hope it helps.
