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Senior Manager  P
Joined: 04 Sep 2017
Posts: 318
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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3 00:00

Difficulty:   5% (low)

Question Stats: 89% (00:51) correct 11% (01:26) wrong based on 151 sessions

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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

Originally posted by gmatt1476 on 20 Apr 2020, 10:21.
Last edited by carcass on 01 May 2020, 10:18, edited 1 time in total.
Updated
GMAT Tutor B
Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
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Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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1
gmatt1476 wrote:
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

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

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

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

=> $$w = 1 - z^2$$

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##### General Discussion
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4949
GMAT 1: 770 Q49 V46
Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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Top Contributor
gmatt1476 wrote:
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

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

Cheers,
Brent
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Intern  Joined: 05 May 2020
Posts: 2
If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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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
Intern  B
Joined: 30 May 2020
Posts: 19
Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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

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

1 - z^2 = w

Option C

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http://www.perfectreview.co.in Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =   [#permalink] 30 May 2020, 05:12

# If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  