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

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Intern
Joined: 23 Sep 2008
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If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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19 Apr 2009, 01:21
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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. 1 and III only
D. II and III only
E. I, II and II

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-2-z-4-which-of-the-following-statements-could-be-100465.html
[Reveal] Spoiler: OA
Manager
Joined: 12 Apr 2009
Posts: 208
Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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19 Apr 2009, 09:24
(c)

if x, y & z are positive (I) is true

if x, y & z are negative (III) is true
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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20 Apr 2009, 10:14
Can anybody give an example of option 2. Also is there any formula to pick numbers so that the question can be slolved within 2 mins.
Director
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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21 Apr 2009, 20:31
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http://www.gmatquantum.com/shared-posts ... blem5.html

Dabral

mavesum wrote:
If x > y^2 > z^4, Which of the following 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 III

Last edited by dabral on 24 May 2011, 20:12, edited 2 times in total.
Manager
Joined: 14 Dec 2008
Posts: 164
Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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20 Aug 2009, 04:38
case 1 x=10 y=(+/-)3 z=(+/-)1
case 2 x=10 y=(+/-)1/2 z=(+/-)1/4

work out it will give you I and III true hence ans=c
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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20 Aug 2009, 08:31
1
KUDOS
use examples:

x=100
y= 2
z=1

then I is correct

x=0.1
y=0.2
z=0.3

then II is correct

x=0.5
y=0.2
z=0.3
then III is correct

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

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21 Aug 2009, 00:15
1
KUDOS
mavesum wrote:
If $$x > y^2 > z^4$$, Which of the following 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 III

E for me.
I. x > y > z
If x = 0.3, y can be 0.03 & z can be 0.003 and still satisfy $$x > y^2 > z^4$$.

II. z > y > x
If x = 0.4, y can be 0.45 & z can be 0.5 and still satisfy $$x > y^2 > z^4$$.

III. x > z > y
If x = 3, z can be 1, y can be -3 and still satisfy $$x > y^2 > z^4$$.

Hope this makes sense.
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Manager
Joined: 10 Jul 2009
Posts: 126
Location: Ukraine, Kyiv
Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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16 Sep 2009, 09:52
E. Question asks what could be true, not what must be.
in second choice the only way is to pick fractions.
a very good explanation dabral gives on the link, he gave in the post above. kudos for you.
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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29 Oct 2009, 14:38
Hi guys,

Came across this problem in GMAT prep. Could not understand why my answer was incorrect.

Given that x>y^2>z^4. Which of the following 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 III

Pls explain.
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Location: Oklahoma City
Schools: Hard Knocks
Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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29 Oct 2009, 15:06
I think the answer is E and I don't have much time to explain, so what I'll say is think of fractions.

Hi guys,

Came across this problem in GMAT prep. Could not understand why my answer was incorrect.

Given that x>y^2>z^4. Which of the following 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 III

Pls explain.

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Intern
Joined: 25 Oct 2009
Posts: 24
Schools: Wharton, HBS, Stanford
Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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29 Oct 2009, 16:26
1
KUDOS
All you have to do is to pick numbers. Let's test...

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

I.$$x>y>z$$: pick $$x=9$$, $$y=2$$, $$z=1$$. Check $$9>4>1$$. So, it could be true.

II. $$z>y>x$$: pick $$z=8/10$$, $$y=7/10$$ and $$x=6/10$$. Check $$\frac{6}{10}>\frac{49}{100}>\frac{4,096}{10,000}$$. So, it also could be true.

III. $$x>z>y$$: pick $$x=1$$, $$z=8/10$$ and $$y=7/10$$. Checking... $$1>\frac{49}{100}>\frac{4,096}{10,000}$$. And this one could be true.

Hint: Solving this question, you should remember that $$x^2<x^1$$, for all $$0<x<1$$.

Therefore, the answer should be E.

KUDOS it you find it helpful
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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15 Jun 2010, 12:25
IF x>y^2>z^4

then which of hte following is true?

x>y>z
z>y>x
x>z>y

OA is
[Reveal] Spoiler:
all three

Could somebody provide an explanation that for the 3rd one to be correct?
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Posts: 15984
Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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16 Oct 2016, 11:33
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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16 Oct 2016, 12:55
mavesum 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. 1 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-y-2-z-4-which-of-the-following-statements-could-be-100465.html
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Re: If x > y^2 > z^4, which of the following statements could be true?   [#permalink] 16 Oct 2016, 12:55
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