GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Jan 2020, 13:01 ### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60646
If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags 00:00

Difficulty:   5% (low)

Question Stats: 88% (00:43) correct 12% (01:10) wrong based on 305 sessions

### HideShow timer Statistics

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

_________________
Senior Manager  P
Joined: 13 Feb 2018
Posts: 494
GMAT 1: 640 Q48 V28
If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

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

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
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5734
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

Bunuel wrote:
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

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
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4228
Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

1
Top Contributor
Bunuel wrote:
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

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

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9143
Location: United States (CA)
Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

Bunuel wrote:
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

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15985
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

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

GMAT assassins aren't born, they're made,
Rich
_________________
Manager  B
Joined: 25 Sep 2018
Posts: 66
Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

Bunuel wrote:
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

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

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

Posted from my mobile device
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3230
Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?  [#permalink]

### Show Tags

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.

_________________ Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?   [#permalink] 14 May 2019, 23:26
Display posts from previous: Sort by

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