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If |z|/w=1,which of the following must be true?

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mvrravikanth
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If |z|/w=1,which of the following must be true? [#permalink] New post   Updated on: 23 Aug 2015, 11:17
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If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3

GMAT Prep Exam Pack 1 PS Question:
ShowHide Answer
Official Answer
C

Originally posted by mvrravikanth on 23 Aug 2015, 11:13.
Last edited by Bunuel on 23 Aug 2015, 11:17, edited 1 time in total.
Edited the question, added the OA and moved to PS forum.
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   01 May 2018, 09:58
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mvrravikanth wrote:
If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3


Simplifying, we have |z| = w.

Using a basic property of absolute value, we see that z = w or z = -w.

However, regardless of whether z = w or z = -w, when we square both sides of either equation, we have:

z^2 = w^2

Answer: C
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   23 Aug 2015, 12:23
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Hi mvrravikanth,

This question can be solved by TESTing VALUES (as Engr2012 has pointed out in his post). There are a couple of 'clues' about how you can work through this prompt in the most efficient way possible:

1) The absolute value in the original equation often 'hints' that we should be thinking about NEGATIVE VALUES...
2) The answer choices are written in such a way that if we TEST 1 or -1, we'll end up with multiple 'true' answers, so we should avoid those values...

We're told that |Z|/W = 1. We're asked which of the following MUST be true.

IF....
Z = -2, W = 2
Eliminate Answers B, D and E.

IF...
Z = 2, W = 2
Eliminate Answer A.

GMAT assassins aren't born, they're made,
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   23 Aug 2015, 11:20
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mvrravikanth wrote:
If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3

GMAT Prep Exam Pack 1 PS Question:


|z|/w = 1;

|z| = w. Since |z| is non-negative, then w is non-negative too. This means that we can safely square both sides: z^2 = w^2.

Answer: C.

P.S. Please follow the rules: rules-for-posting-please-read-this-before-posting-133935.html
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   23 Aug 2015, 11:23
Thanks alot Bunuel.
Is it possible to solve this question by substituting the answer options in the given equation ?

Bunuel wrote:
mvrravikanth wrote:
If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3

GMAT Prep Exam Pack 1 PS Question:


|z|/w = 1;

|z| = w. Since |z| is non-negative, then w is non-negative too. This means that we can safely square both sides: z^2 = w^2.

Answer: C.

P.S. Please follow the rules: rules-for-posting-please-read-this-before-posting-133935.html
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   23 Aug 2015, 12:12
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mvrravikanth wrote:
Thanks alot Bunuel.
Is it possible to solve this question by substituting the answer options in the given equation ?


You can use certain values for z and w to eliminate incorrect options and to arrive at the correct answer.

In a must be true question, the correct option MUST satisfy all possible scenarios. The incorrect options will satisfy certain conditions but not all.


Assume, z=w=1, |z| =1=w and |z|/w =1 . Eliminate A. Keep B,C,D,E.

Assume, z=2=w, |z|/w =1. Eliminate D. Keep B,C,E.

Assume, z=-2, |z|=2=w. Eliminate B and E.

The only option remaining = C .

Hence C is the correct answer.
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   24 Aug 2015, 04:35
Thanks Engr12 and EmpowerGmat!
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   03 Jan 2017, 12:29
|z| = w
|z| is always non-negative
z = w
\((-z)^{2} = (-w)^{2}\)
C
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If |z|/w=1,which of the following must be true? [#permalink] New post   19 Jun 2018, 11:07
mvrravikanth wrote:
If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3

GMAT Prep Exam Pack 1 PS Question:



Bunuel can you please clear my confusion regarding B option :)

if \(z = w\) , means if one is positive another value is positive, if one is negative another value is negative...

case 1. both positive ---> say z = 2 ....2/2 = 1 so we get 1

case 2. both negative ---> z =-1 --> -z/-w = 1

so why B is wrong ? :?
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If |z|/w=1,which of the following must be true? [#permalink] New post   19 Jun 2018, 22:00
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dave13 wrote:
mvrravikanth wrote:
If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3

GMAT Prep Exam Pack 1 PS Question:



Bunuel can you please clear my confusion regarding B option :)

if \(z = w\) , means if one is positive another value is positive, if one is negative another value is negative...

case 1. both positive ---> say z = 2 ....2/2 = 1 so we get 1

case 2. both negative ---> z =-1 --> -z/-w = 1
so why B is wrong ? :?


Case 2: if both are negative, say z = w = -1, then \(\frac{|z|}{w} = \frac{|-1|}{-1}=\frac{1}{-1}=-1\), not 1 as given in the stem. So, B is not always true.
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   29 Sep 2019, 06:46
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Solution



Given
• |z|/w = 1

To find
• The option which is true.

Approach and Working out
• |z|/w= 1
• |z| = w
o |z|= Positive. Hence, w has to be positive.
o However, z can be positive or negative.
• So, only z^2 = w^2

Hence, option C is the correct answer.

Correct Answer: Option C
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   29 Sep 2019, 09:23
mvrravikanth wrote:
If |z|/w = 1,which of the following must be true?

A. z = -w
B. z = w
C. z^2 = w^2
D. z^2 = w^3
E. z^3 = w^3

GMAT Prep Exam Pack 1 PS Question:


|z|/w -1 = 0
(|z| - w)/w = 0
|z| = w & w \(\neq\) 0
squaring both sides
\(z^2 = w^2\)

IMO C
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   20 Aug 2020, 11:28
It s a easy one, C is the ans since it satisfies both conditions
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Re: If |z|/w=1,which of the following must be true? [#permalink] New post   25 Jun 2023, 11:46
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Re: If |z|/w=1,which of the following must be true? [#permalink]
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