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.
Jan 1610:00 AM EST
-12:00 PM EST
The Target Test Prep team is proud to introduce GMAT OnDemand, a video course created by Scott Woodbury-Stewart, founder and CEO, designed to provide you with everything you need to master the GMAT and achieve your score goals.
Jan 1610:00 AM PST
-11:00 AM PST
Meet Kseniia, a former Public Relations Head at Google in Russia, whose inspiring journey defied the odds and landed her admissions to Wharton, Chicago Booth, and Yale SOM.- Jan 15
07:30 AM PST
-08:30 AM PST
Studying for the GMAT can feel like a long journey, but having the right plan can keep you on track. In this live session, Julia, who scored a perfect 805, will share her step-by-step study plan for 2025. Join for help with key strategies and tips... - Jan 17
10:00 AM PST
-11:00 AM PST
Keshav who scored 99 percentile with near-perfect quant score shares his strategies and techniques to identify and overcome the weaknesses in his GMAT preparation. Learn the preparation tips and study strategies that worked for him. - Jan 18
10:00 AM PST
-11:00 AM PST
In this video, we talked to Rishi, an ambitious Indian student who successfully secured admission into HEC Paris and ESSEC Business School, two of the top Masters in Management (MiM) programs in Europe. 
Jan 1811:00 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- Jan 19
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
![If z is negative, then [m]\sqrt[4]{(4z-5)^4} + [square_root](3-2z)^2[/](https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If z is negative, then [m]\sqrt[4]{(4z-5)^4} + [square_root](3-2z)^2[/"){kind=icon}
17 Feb 2023, 23:07
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:11) correct
50%
(01:55)
wrong
based on 160
sessions
History
Date
Time
Result
Not Attempted Yet
If z is negative, then \(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|} = ?\)
A. 3z-2
B. z-2
C. -8
D. 8-7z
E. 4z-8
Source: Top One Percent (Sandeep Gupta)
A. 3z-2
B. z-2
C. -8
D. 8-7z
E. 4z-8
Source: Top One Percent (Sandeep Gupta)
Updated on: 25 Jun 2024, 19:37
Originally posted by BrushMyQuant on 18 Feb 2023, 01:28.
Last edited by BrushMyQuant on 25 Jun 2024, 19:37, edited 1 time in total.
Last edited by BrushMyQuant on 25 Jun 2024, 19:37, edited 1 time in total.
Kudos
Bookmarks
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧
Given that z is negative and we need to find the value of \(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|}\)
Let z = -k (where k is positive) (k = -z)
=> \(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|}\) = \(\sqrt[4]{(4(-k)-5)^4} + \sqrt{(3-2(-k))^2} + \sqrt{-(-k) |(-k)|}\) = \(\sqrt[4]{(-(4k+5))^4} + \sqrt{(3+2k)^2} + \sqrt{k*k}\)
( As modulus of |-k| = k for k > 0 and modulus of any number is the non-negative value of that number)
Watch this video to know the Basics of Absolute value
=> \((4k+5)^{\frac{4}{4}} + 3+2k + k\)
=> 4k+5 + 3 + 3k = 7k + 8 = 7*(-z) + 8 = 8 - 7z
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Roots
Given that z is negative and we need to find the value of \(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|}\)
Let z = -k (where k is positive) (k = -z)
=> \(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|}\) = \(\sqrt[4]{(4(-k)-5)^4} + \sqrt{(3-2(-k))^2} + \sqrt{-(-k) |(-k)|}\) = \(\sqrt[4]{(-(4k+5))^4} + \sqrt{(3+2k)^2} + \sqrt{k*k}\)
( As modulus of |-k| = k for k > 0 and modulus of any number is the non-negative value of that number)
Watch this video to know the Basics of Absolute value
=> \((4k+5)^{\frac{4}{4}} + 3+2k + k\)
=> 4k+5 + 3 + 3k = 7k + 8 = 7*(-z) + 8 = 8 - 7z
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Roots
18 Feb 2023, 07:40
Kudos
Bookmarks
Kushchokhani
If z is negative, then \(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|} = ?\)
A. 3z-2
B. z-2
C. -8
D. 8-7z
E. 4z-8
Source: Top One Percent (Sandeep Gupta)
A. 3z-2
B. z-2
C. -8
D. 8-7z
E. 4z-8
Source: Top One Percent (Sandeep Gupta)
Concept Tested :
- \(\sqrt{x^2} = |x|\)
- |x| = x , when \(x \geq 0\)
- |x| = -x , when \(x < 0\)
\(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|}\)
As z is negative, |z| = -z
\(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z (-z)}\)
\(\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{z^2}\)
\(|4z-5| + |3-2z| + |z|\)
We know that z < 0
⇒ 4z - 5 < 0, hence |4z-5| = -(4z-5) = 5 - 4z
⇒ 3-2z > 0, hence |3-2z| = 3-2z
⇒ |z| = -z
Substitute the values
\(|4z-5| + |3-2z| + |z|\) = \(5 - 4z + 3 - 2z - z\)
= \(8 - 7z\)
Option D
