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

Question

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:

JeffTargetTestPrep · Accepted Answer

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

EMPOWERgmatRichC · Answer

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,
Rich

Bunuel · Answer

|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

mvrravikanth · Answer

Thanks alot Bunuel.
Is it possible to solve this question by substituting the answer options in the given equation ?

ENGRTOMBA2018 · Answer

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.

mvrravikanth · Answer

Thanks Engr12 and EmpowerGmat!

kanusha · Answer

|z| = w
|z| is always non-negative 
z = w
 (-z)^{2} = (-w)^{2} 
C

dave13 · Answer

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 ?

Bunuel · Answer

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.

EgmatQuantExpert · Answer

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

Kinshook · Answer

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

IMO C

gagansh1840 · Answer

It s a easy one, C is the ans since it satisfies both conditions

adipisfugat · Answer

Start with the given equation: |z| / w = 1.

Multiply both sides by w to get: |z| = w.

Since an absolute value is always non-negative, w must be a positive real number.

Square both sides of the equation to eliminate the absolute value.

Squaring |z| gives z^2, and squaring w gives w^2.

Therefore, the resulting equation must be z^2 = w^2.

Answer Choice: C. z^2 = w^2

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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