Last visit was: 29 Apr 2026, 13:39 It is currently 29 Apr 2026, 13:39
Home
Messages
Tests
Schools
Events
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 (Easy)|   Algebra|            
User avatar
gmatt1476
User avatar
Joined: 04 Sep 2017
Last visit: 04 Feb 2026
Posts: 556
Own Kudos:
27,387
 [22]
Given Kudos: 72
Posts: 556
Kudos: 27,387
 [22]
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = Updated on: 01 May 2020, 11:18
Originally posted by gmatt1476 on 20 Apr 2020, 11:21.
Last edited by Carcass on 01 May 2020, 11:18, edited 1 time in total.
Updated
4
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

94% (00:52) correct 6% (01:23) wrong based on 1503 sessions

History

Date
Time
Result
Not Attempted Yet
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} =\frac{ w}{z}\), then\( w = \)

A. \(z + 1 \)

B. \(z^2 + 1\)

C. \(-z^2 + 1\)

D. \(-z^2 + z + 1\)

E. \(-2z^2 + 1\)

PS14031.02
ShowHide Answer
Official Answer
C
Solving this question helps. Taking a timed set of similar questions in GMAT Club Forum Quiz → is even better.
Most Helpful Reply
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 26 Apr 2026
Posts: 587
Own Kudos:
1,191
 [2]
Given Kudos: 14
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 740 Q51 V39
Expert
Expert reply
GMAT 1: 740 Q51 V39
Posts: 587
Kudos: 1,191
 [2]
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 20 Apr 2020, 11:28
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
gmatt1476
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} = w/z\), then w =

A. z + 1
B. z^2 + 1
C. -z^2 + 1
D. -z^2 + z + 1
E. -2z^2 + 1

PS14031.02
Show more


\(z + \frac{1 - 2z^2}{z} = w/z\)

=> \(z(z + \frac{1 - 2z^2}{z}) = w\)

=> \(w = z^2 + (1 - 2z^2)\)

=> \(w = 1 - z^2\)

Answer C
General Discussion
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,478
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,478
 [2]
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 28 Apr 2020, 08:38
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
gmatt1476
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} = \frac{w}{z}\), then \(w =\)

A. z + 1
B. z^2 + 1
C. -z^2 + 1
D. -z^2 + z + 1
E. -2z^2 + 1

PS14031.02
Show more

Given: \(z + \frac{1 - 2z^2}{z} = \frac{w}{z}\)

Eliminate the fractions, multiply both sides of the equation by \(z\) to get: \(z^2 + (1 - 2z^2) = w\)

Simplify to get: \(1 - z^2 = w\)

Rewrite as: \(-z^2 + 1= w\)

Answer: C

Cheers,
Brent
avatar
rohitambasta
avatar
Joined: 05 May 2020
Last visit: 06 Sep 2021
Posts: 2
Own Kudos:
1
 [1]
Given Kudos: 4
Posts: 2
Kudos: 1
 [1]
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 29 May 2020, 10:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Assume any value of z
Let z=1
=> w = 0
Now check where w= 0 for z=1 in the option
(a) w=2
(b) w=2
(C) w= 0.
(D) w=1
(e) w= -1

Therefore, (c) is the correct option.

Posted from my mobile device
User avatar
perfectreview
User avatar
Joined: 30 May 2020
Last visit: 07 Apr 2022
Posts: 18
Own Kudos:
17
Given Kudos: 1
Posts: 18
Kudos: 17
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 30 May 2020, 06:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post

(z^2 + 1-2z^2)/z = w/z

z^2 + 1 -2z^2 = w

1 - z^2 = w

Option C

User avatar
BlueRocketAsh
User avatar
Joined: 11 Oct 2019
Last visit: 28 Aug 2020
Posts: 76
Own Kudos:
13
Given Kudos: 2
Posts: 76
Kudos: 13
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 06 Jul 2020, 13:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\(z + \frac{(1 - 2z^2)}{z} = \frac{w}{z}\)
\(w=z^2+1-2z^\)
\(w=1-z^2\)

Answer C
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 28 Apr 2026
Posts: 4,846
Own Kudos:
9,188
 [1]
Given Kudos: 226
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,846
Kudos: 9,188
 [1]
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 11 Feb 2021, 07:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SOLUTION:

z+ (1−2z^2/z) = w/z

=> (z^2 + 1-2z^2 )/z = w/z

Cancel out the "w" in the denominators, add the terms in the numerator of the LHS and arrive at

1- z^2 = w (OPTION C)

Hope this helps :thumbsup:
Devmitra Sen(Math)
User avatar
Neghineh
User avatar
Joined: 20 Nov 2020
Last visit: 24 Nov 2022
Posts: 28
Own Kudos:
2
Given Kudos: 7
Posts: 28
Kudos: 2
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 19 Mar 2021, 12:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sujoykrdatta
gmatt1476
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} = w/z\), then w =

A. z + 1
B. z^2 + 1
C. -z^2 + 1
D. -z^2 + z + 1
E. -2z^2 + 1

PS14031.02


\(z + \frac{1 - 2z^2}{z} = w/z\)

=> \(z(z + \frac{1 - 2z^2}{z}) = w\)

=> \(w = z^2 + (1 - 2z^2)\)

=> \(w = 1 - z^2\)

Answer C
Show more

sujoykrdatta

Could you please break down the following for me: => \(w = z^2 + (1 - 2z^2)\)

=> \(w = 1 - z^2\)

This step is unclear.. Why did the Z^2 disappear?
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 26 Apr 2026
Posts: 587
Own Kudos:
1,191
 [1]
Given Kudos: 14
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 740 Q51 V39
Expert
Expert reply
GMAT 1: 740 Q51 V39
Posts: 587
Kudos: 1,191
 [1]
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 19 Mar 2021, 12:31
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Neghineh
sujoykrdatta
gmatt1476
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} = w/z\), then w =

A. z + 1
B. z^2 + 1
C. -z^2 + 1
D. -z^2 + z + 1
E. -2z^2 + 1

PS14031.02


\(z + \frac{1 - 2z^2}{z} = w/z\)

=> \(z(z + \frac{1 - 2z^2}{z}) = w\)

=> \(w = z^2 + (1 - 2z^2)\)

=> \(w = 1 - z^2\)

Answer C

sujoykrdatta

Could you please break down the following for me: => \(w = z^2 + (1 - 2z^2)\)

=> \(w = 1 - z^2\)

This step is unclear.. Why did the Z^2 disappear?
Show more

You are adding the terms z² and -2z² to get the result -z². The '1' remains as it is.

Posted from my mobile device
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 28 Apr 2026
Posts: 6,979
Own Kudos:
16,934
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,979
Kudos: 16,934
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 15 May 2021, 04:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} =\frac{ w}{z}\), then\( w = \)

A. \(z + 1 \)

B. \(z^2 + 1\)

C. \(-z^2 + 1\)

D. \(-z^2 + z + 1\)

E. \(-2z^2 + 1\)

PS14031.02
Show more

Answer: Option C

Video solution by GMATinsight

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,996
Own Kudos:
1,120
Posts: 38,996
Kudos: 1,120
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w = 05 Nov 2025, 14:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109975 posts
Krunaal
Tuck School Moderator
852 posts