If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?

Question

If xyz ≠ 0, what is the value of  \frac{x^4z^2}{z^2y^2}  ?

(1) y^2 = x^4
(2) x = 2 and y = 4

DS41602.01
OG2020 NEW QUESTION

LevanKhukhunashvili · Answer

\frac{x^4*z^2}{z^2*y^2} = \frac{x^4}{y^2}

1 stm:  y^2 = x^4 , divide both sides by  y^2 , 1= \frac{x^4}{y^2} .  suff 
2 stm: two unknowns turn into "knowns".  suff

IMO
Ans:  D

Archit3110 · Answer

given 
 \frac{x^4z^2}{z^2y^2}

can be written as 
 \frac{x^4}{y^2}

#1y^2 = x^4
sufficeint
#2
x = 2 and y = 4
sufficeint
IMO D

BrentGMATPrepNow · Answer

Target question :    What is the value of (x⁴z²)/(z²y²)?  
This is a good candidate for  rephrasing the target question . 
Since z ≠ 0, we know that z² ≠ 0
So, we can safely take  (x⁴z²)/(z²y²)  and divide top and bottom by z² to get:  x⁴/y² 
  REPHRASED target question :    What is the value of x⁴/y²?

Aside: The video below has tips on rephrasing the target question

Statement 1 : y² = x⁴ 
Take:  x⁴/y²  and replace y² with x⁴ to get:  x⁴/x⁴ , which equals 1
So, the answer to the REPHRASED target question is  x⁴/y² = 1 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : x = 2 and y = 4 
So,  x⁴/y² = 2⁴/4² = 16/16 = 1 
Since we can answer the  REPHRASED target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

RELATED VIDEO 
 https://www.youtube.com/watch?v=MyG1K3ee69w

ScottTargetTestPrep · Answer

After canceling z^2, we can simplify the question to read:

What is the value of (x^4)/(y^2) ?

Statement One Alone:

y^2 = x^4

Since y^2 = x^4, we see that (x^4)/(y^2) = 1.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

x = 2 and y = 4

Thus, we see that (x^4)/(y^2) = 16/16 = 1.

Statement two alone is sufficient to answer the question.

Answer: D

EMPOWERgmatRichC · Answer

Hi All,

We're told that If (X)(Y)(Z) ≠ 0. We're asked for the value of (X^4)(Z^2) / (Z^2)(Y^2). This question can be approached in a number of different ways, including Algebra and TESTing VALUES.

To start, it's worth noting that none of the given variables can equal 0 and the term (Z^2) appears in both the numerator and denominator (meaning that it essentially 'cancels out' - and we're ultimately asked for the value of (X^4)/(Y^2).

1) Y^2 = X^4

The information in Fact 1 matches the two 'terms' that we need to have values for to answer the given question. Since these two items are equal, the question can be rewritten as "What is the value of (X^4)/(X^4)?" Since the numerator is divided by itself, the answer to the question is clearly "1." You can also use TEST IT to prove that the answer is always 1...

IF... 
X=2 and Y=4, then the question becomes "What is the value of 16/16?" That fraction simplifies to 1 - and it will always simplify to 1 as long as you choose values that fit the given information. 
Fact 1 is SUFFICIENT

(2) X = 2 and Y = 4

We can 'plug in' the values from Fact 2 - which would give us 16/16 = 1. Even if we didn't cancel out the Z^2 terms, we would have 16(Z^2)/16(Z^2), which is still 1. 
Fact 2 is SUFFICIENT

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

shaonkarim · Answer

Stat. 1 is sufficient:
x^4z^2/z^2x^4  
=1

Stat. 2 is sufficient:
2^4z^2/z^24^2

Answer is D

Posted from my mobile device

EgmatQuantExpert · Answer

Solution

Steps 1 & 2: Understand Question and Draw Inferences  
In this question, we are given
 • The value of xyz ≠ 0

We need to determine
 • The value of the expression  \frac{x^4 z^2}{z^2 y^2}

As the value of xyz ≠ 0, none of x, y and z are individually 0.
Now, simplifying the given expression, we get
 •  \frac{x^4 z^2}{z^2 y^2} = \frac{x^4}{y^2}  (as z ≠ 0)

Hence, we need to know the values of x and y, or the relationship between x4 and y2
With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1  
As per the information given in statement 1,  y^2 = x^4 
 • Therefore,  \frac{x^4}{y^2} = 1

Hence, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2  
As per the information given in statement 2, x = 2 and y = 4.
 • From this statement, we can determine the values of  x^4  and  y^2 , and also their ratio.

Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)  
Since we can determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer choice is option D.

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-Algebra-e1533292163516.png

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=5_r5bALQNNQ

bumpbot · Answer

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.

If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards