If x > y^2 > z^4, which of the following statements could be : GMAT Problem Solving (PS) - Page 2
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 05:24

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x > y^2 > z^4, which of the following statements could be

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Oct 2012
Posts: 74
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 91 [0], given: 52

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

08 Sep 2013, 07:58
Bunuel wrote:
chetan86 wrote:
Restrictions are not provided on the variables so I planned to check different values I and used x=y=z=1/2.
As if I take 1/2 for each variables, its given condition would be satisfied and it will become 1/2>1/4>1/8.

So according to me none of the conditions are satisfied.
Am I doing anything wrong here?

Notice that the question asks "which of the following statements could be true" NOT "which of the following statements must be true"

Thanks Bunuel for identifying my mistake.
Intern
Joined: 19 Oct 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 6

Re: x > y^2 > z^4 [#permalink]

### Show Tags

07 Nov 2013, 01:10
Bunuel wrote:
Orange08 wrote:
If x > y^2 > z^4, which of the following statements could be true?

I. x>y>z
II. z>y>x
III. x>z>y

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and II

As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.

Given: $$x > y^2 > z^4$$.

1. $$x>y>z$$ --> the easiest one: if $$x=100$$, $$y=2$$ and $$z=1$$ --> this set satisfies $$x > y^2 > z^4$$ as well as given statement $$x>y>z$$. So 1 COULD be true.

2. $$z>y>x$$ --> we have reverse order than in stem ($$x > y^2 > z^4$$), so let's try fractions: if $$x=\frac{1}{5}$$, $$y=\frac{1}{4}$$ and $$z=\frac{1}{3}$$ then again the stem and this statement hold true. So 2 also COULD be true.

3. $$x>z>y$$ --> let's make $$x$$ some big number, let's say 1,000. Next, let's try the fractions for $$z$$ and $$y$$ for the same reason as above (reverse order of $$y$$ and $$z$$): $$y=\frac{1}{3}$$ and $$z=\frac{1}{2}$$. The stem and this statement hold true for this set of numbers. So 3 also COULD be true.

Isn't it stated in the exam that assume all numbers are integers? We can't try fractions unless they say they are not integers.
Math Expert
Joined: 02 Sep 2009
Posts: 36509
Followers: 7063

Kudos [?]: 92871 [1] , given: 10528

Re: x > y^2 > z^4 [#permalink]

### Show Tags

07 Nov 2013, 01:19
1
KUDOS
Expert's post
SaramiR wrote:
Bunuel wrote:
Orange08 wrote:
If x > y^2 > z^4, which of the following statements could be true?

I. x>y>z
II. z>y>x
III. x>z>y

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and II

As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.

Given: $$x > y^2 > z^4$$.

1. $$x>y>z$$ --> the easiest one: if $$x=100$$, $$y=2$$ and $$z=1$$ --> this set satisfies $$x > y^2 > z^4$$ as well as given statement $$x>y>z$$. So 1 COULD be true.

2. $$z>y>x$$ --> we have reverse order than in stem ($$x > y^2 > z^4$$), so let's try fractions: if $$x=\frac{1}{5}$$, $$y=\frac{1}{4}$$ and $$z=\frac{1}{3}$$ then again the stem and this statement hold true. So 2 also COULD be true.

3. $$x>z>y$$ --> let's make $$x$$ some big number, let's say 1,000. Next, let's try the fractions for $$z$$ and $$y$$ for the same reason as above (reverse order of $$y$$ and $$z$$): $$y=\frac{1}{3}$$ and $$z=\frac{1}{2}$$. The stem and this statement hold true for this set of numbers. So 3 also COULD be true.

Isn't it stated in the exam that assume all numbers are integers? We can't try fractions unless they say they are not integers.

No that's not true at all. All numbers on the test represent real numbers: Integers, Fractions and Irrational Numbers. You cannot assume a variable is integer if you are not explicitly told so.
_________________
Intern
Joined: 10 Sep 2012
Posts: 3
GMAT Date: 08-27-2013
GPA: 3.5
WE: Investment Banking (Energy and Utilities)
Followers: 0

Kudos [?]: 5 [0], given: 26

Re: x > y^2 > z^4 [#permalink]

### Show Tags

19 Nov 2013, 10:52
Bunuel wrote:
Orange08 wrote:
If x > y^2 > z^4, which of the following statements could be true?

I. x>y>z
II. z>y>x
III. x>z>y

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and II

As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.

Given: $$x > y^2 > z^4$$.

1. $$x>y>z$$ --> the easiest one: if $$x=100$$, $$y=2$$ and $$z=1$$ --> this set satisfies $$x > y^2 > z^4$$ as well as given statement $$x>y>z$$. So 1 COULD be true.

2. $$z>y>x$$ --> we have reverse order than in stem ($$x > y^2 > z^4$$), so let's try fractions: if $$x=\frac{1}{5}$$, $$y=\frac{1}{4}$$ and $$z=\frac{1}{3}$$ then again the stem and this statement hold true. So 2 also COULD be true.

3. $$x>z>y$$ --> let's make $$x$$ some big number, let's say 1,000. Next, let's try the fractions for $$z$$ and $$y$$ for the same reason as above (reverse order of $$y$$ and $$z$$): $$y=\frac{1}{3}$$ and $$z=\frac{1}{2}$$. The stem and this statement hold true for this set of numbers. So 3 also COULD be true.

Hi Bunuel,

Can we not use negative integers.
For e.g.: x =5, y=-2,z=-1 then the first inequality would be 5>(-2)^2>(-1)^4. In this case x>z>y and y is not greater than z.

Am i missing something?
Math Expert
Joined: 02 Sep 2009
Posts: 36509
Followers: 7063

Kudos [?]: 92871 [0], given: 10528

Re: x > y^2 > z^4 [#permalink]

### Show Tags

19 Nov 2013, 14:21
chitrasekar2k5 wrote:
Bunuel wrote:
Orange08 wrote:
If x > y^2 > z^4, which of the following statements could be true?

I. x>y>z
II. z>y>x
III. x>z>y

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and II

As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.

Given: $$x > y^2 > z^4$$.

1. $$x>y>z$$ --> the easiest one: if $$x=100$$, $$y=2$$ and $$z=1$$ --> this set satisfies $$x > y^2 > z^4$$ as well as given statement $$x>y>z$$. So 1 COULD be true.

2. $$z>y>x$$ --> we have reverse order than in stem ($$x > y^2 > z^4$$), so let's try fractions: if $$x=\frac{1}{5}$$, $$y=\frac{1}{4}$$ and $$z=\frac{1}{3}$$ then again the stem and this statement hold true. So 2 also COULD be true.

3. $$x>z>y$$ --> let's make $$x$$ some big number, let's say 1,000. Next, let's try the fractions for $$z$$ and $$y$$ for the same reason as above (reverse order of $$y$$ and $$z$$): $$y=\frac{1}{3}$$ and $$z=\frac{1}{2}$$. The stem and this statement hold true for this set of numbers. So 3 also COULD be true.

Hi Bunuel,

Can we not use negative integers.
For e.g.: x =5, y=-2,z=-1 then the first inequality would be 5>(-2)^2>(-1)^4. In this case x>z>y and y is not greater than z.

Am i missing something?

The questions asks which of the following COULD be true not MUST be true. As shown above each option COULD be true for certain numbers.
_________________
Intern
Joined: 29 Mar 2014
Posts: 14
Location: United States
Concentration: Entrepreneurship, Finance
GMAT 1: 720 Q50 V39
GPA: 3
Followers: 0

Kudos [?]: 25 [0], given: 4

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

04 Apr 2014, 21:06
I and II are pretty much evident.. However III is no, it is better to split the third option in to two parts and focus just on Z>Y which is quite possible.. So the answer is all three..
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13410
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

15 Jul 2015, 09:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 31 Jul 2015
Posts: 3
GMAT 1: 720 Q50 V37
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

07 Aug 2015, 14:45
1
KUDOS
Algebraic solution:

In the question we are given: x>y2>z4, hence from concepts of inequalities we break it into 2 parts: x>y2 and y2>z4.
1. x>y2 means -x(1/2)<y<x(1/2)
2. y2>z4 means -y<z2<y, but a square cannot be negative so 0<z2<y, this implies -y(1/2)<z<y(1/2).

Now we plot all these points on number line with the intersection of there ranges. But before that we need to understand that we will only be taking x,y,z as positive since if we take y as negative for example(easiest one) the value z(2) becomes negative, whereas a square can never be negative.

hence we plot all of them on the positive x-axis. From above 1 & 2 point we get a general range as such 0<z<y(1/2)<y<x(1/2)<x.
Now, we need to see that we haven't in reality considered various values of x,y,z but have come up with a general idea of how they look on the number line.
Now we define the ranges, since we know about a^x graph varies for values 0<a<1 and a>1, we also take such cases for all three of them.
1. 0<x<1 and x>1
2. 0<y<1 and y>1
3. 0<z<1 and z>1

Hence looking at the combinations we find we have 8 possibilities (2*2*2). taking the 2 general ones:
1. x>1 y>1 z>1. In the general formula we simply put x,y,z and get x>y>z. (Would have figured initially).
2. 0<x<1, 0<y<1 and 0<z<1. In this possibility put x as 1/x, y as 1/y and z as 1/z in general formula we get z>y>x.
3. x>1 0<y<1 and 0<z<1. In this put y as 1/y and z as 1/z. Keep x as x in general formula, we see x>1/y>1/z. since only 1/y>1/z are in reciprocal hence z>y by inequalities. thus x>z>y.

Therefore we can get 8 possibilities and the fact is all of them are correct.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13410
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If x > y^2 >z^4 [#permalink]

### Show Tags

19 Aug 2015, 03:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Current Student
Joined: 21 Nov 2014
Posts: 41
Location: India
Concentration: General Management, Strategy
GMAT 1: 750 Q51 V40
WE: Operations (Energy and Utilities)
Followers: 0

Kudos [?]: 8 [0], given: 35

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

19 Aug 2015, 07:19
For statement 3: x>z>y
Question: x > y^2 > z^4

It translates to, z>y & y^2 > z^4 (x is a big value and feature in both equalities)

This is same as statement 2 now: z>y
Intern
Joined: 16 Apr 2015
Posts: 45
Concentration: Operations, Strategy
Schools: UFlorida '18, UFL '17
Followers: 2

Kudos [?]: 9 [0], given: 73

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

20 Aug 2015, 06:13
VeritasPrepKarishma wrote:
arps wrote:
1) x > y2 > z4

which of the following is true:

I x>y>z
II z>y>x
III x>z>y

A) I Only
B) I and II Only
C) I and III Only
D) II and III Only
E) I, II and III

I think the actual question is: Which of the following could be true?

Plugging in numbers work best for such questions. The only thing to keep in mind is that you should plug in the right numbers. How do you know the right numbers?
When I see $$x > y^2 > z^4$$, I think that $$y^2$$ and $$z^4$$ are non negative. Since $$y^2 > z^4$$, $$y^2$$ cannot be 0. Only z can be 0. x has to be positive. Also, I have to take into account two ranges: 0 to 1 and 1 to infinity. The powers behave differently in these two ranges. I will consider negative numbers only if I have to since with powers, they get confusing to deal with.

The question says: "Which of the following could be true?"
We have to find examples where each relation holds.

I. x > y > z
This is the most intuitive of course.
z = 0, y = 1 and x = 2
$$2 > 1^2 > 0^4$$

II. z > y > x
Let me consider the 0 to 1 range here. Say z = 1/2, y = 1/3 and x = 1/4
$$1/4 > 1/9 > 1/16$$

III. x > z > y
Let's stick to 0 to 1 range. z > y as in case II above but x has to be greater than both of them. Say z = 1/2, y = 1/3 and x = 1
$$1>1/9 > 1/16$$

So all three statements could be true.

Karishma...In "could be true" scenarios, do we need just a one situation that fits in to answer the question ?
Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 588
Followers: 111

Kudos [?]: 428 [1] , given: 14

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

22 Aug 2015, 22:59
1
KUDOS
Hi vinnisatija,

Yes, if you see a "could be" question, then just one example that satisfies the given condition is sufficient. In case of "must be" questions, the required condition must hold true under all circumstances along with whatever additional constraint is given in the problem.

Dabral
Intern
Joined: 12 Jul 2015
Posts: 43
Location: Singapore
GMAT 1: 730 Q50 V39
WE: Operations (Retail)
Followers: 0

Kudos [?]: 0 [0], given: 36

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

30 Sep 2015, 20:15
Bunuel wrote:
Orange08 wrote:
If x > y^2 > z^4, which of the following statements could be true?

I. x>y>z
II. z>y>x
III. x>z>y

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and II

As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.

Given: $$x > y^2 > z^4$$.

1. $$x>y>z$$ --> the easiest one: if $$x=100$$, $$y=2$$ and $$z=1$$ --> this set satisfies $$x > y^2 > z^4$$ as well as given statement $$x>y>z$$. So 1 COULD be true.

2. $$z>y>x$$ --> we have reverse order than in stem ($$x > y^2 > z^4$$), so let's try fractions: if $$x=\frac{1}{5}$$, $$y=\frac{1}{4}$$ and $$z=\frac{1}{3}$$ then again the stem and this statement hold true. So 2 also COULD be true.

3. $$x>z>y$$ --> let's make $$x$$ some big number, let's say 1,000. Next, let's try the fractions for $$z$$ and $$y$$ for the same reason as above (reverse order of $$y$$ and $$z$$): $$y=\frac{1}{3}$$ and $$z=\frac{1}{2}$$. The stem and this statement hold true for this set of numbers. So 3 also COULD be true.

Bunuel actually for option 3, since the sign stays the same z>y as in option 2, there is no need to reverse the value of z and y from option 2 right?
Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 588
Followers: 111

Kudos [?]: 428 [0], given: 14

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

30 Sep 2015, 23:46
SamuelWitwicky

Yes, there is no need to change the examples that Bunuel used for z and y in II, they work in III as well.

Dabral
Intern
Joined: 12 Jul 2015
Posts: 43
Location: Singapore
GMAT 1: 730 Q50 V39
WE: Operations (Retail)
Followers: 0

Kudos [?]: 0 [0], given: 36

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

01 Oct 2015, 00:02
dabral ok cool thanks. I thought maybe I was missing something
Current Student
Joined: 12 Aug 2015
Posts: 307
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Followers: 5

Kudos [?]: 278 [0], given: 1474

If x > y^2 > z^4, which of the following statements could be [#permalink]

### Show Tags

10 Feb 2016, 21:18
since we have no constraints all the inequalities could be true because we can play with +ve and -ve and integer (tiny and huge) and fractions (proper and improper) in any way to satisfy inequalities. if needed we can assume any number to be a fraction and nothing prevents us from considering this fraction to be as small as possible and maximize other numbers
_________________

KUDO me plenty

If x > y^2 > z^4, which of the following statements could be   [#permalink] 10 Feb 2016, 21:18

Go to page   Previous    1   2   [ 36 posts ]

Similar topics Replies Last post
Similar
Topics:
8 If x^3 > y^2 > z, which of the statements could be true? 5 15 Jul 2015, 02:03
9 If x > 0, which of the following could be true? 7 03 Dec 2014, 07:18
2 If X>Y2>Z4, then which of the following could be true? 1 27 Oct 2014, 23:59
x > y^2 > z^4 7 16 Jul 2009, 19:02
13 If x > y^2 > z^4, which of the following statements could be true? 13 19 Apr 2009, 00:21
Display posts from previous: Sort by