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

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Intern
Joined: 10 Sep 2012
Posts: 3
GMAT Date: 08-27-2013
GPA: 3.5
WE: Investment Banking (Energy and Utilities)
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Kudos [?]: 5 [0], given: 26

Re: x > y^2 > z^4 [#permalink]  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: 28784
Followers: 4606

Kudos [?]: 47695 [0], given: 7130

Re: x > y^2 > z^4 [#permalink]  19 Nov 2013, 14:21
Expert's post
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 [?]: 12 [0], given: 4

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]  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..
Intern
Joined: 10 Apr 2014
Posts: 7
Location: United States
Concentration: General Management, Technology
GMAT 1: 700 Q48 V37
GPA: 3.95
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 37

If [m]x > y^2 > z^4[/m], which of the following statements [#permalink]  09 Jun 2014, 10:19
If $$x > y^2 > z^4$$, which of the following statements could be true?

I. $$x > y > z$$
II. $$z > y > z$$
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

[Reveal] Spoiler:
OA
Math Expert
Joined: 02 Sep 2009
Posts: 28784
Followers: 4606

Kudos [?]: 47695 [0], given: 7130

Re: If [m]x > y^2 > z^4[/m], which of the following statements [#permalink]  09 Jun 2014, 10:23
Expert's post
jayasrivaryani wrote:
If $$x > y^2 > z^4$$, which of the following statements could be true?

I. $$x > y > z$$
II. $$z > y > z$$
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

[Reveal] Spoiler:
OA

Merging similar topics. Please refer to the discussion on page 1.
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Posts: 5736
Followers: 325

Kudos [?]: 64 [0], given: 0

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]  15 Jul 2015, 09:17
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Re: If x > y^2 > z^4, which of the following statements could be   [#permalink] 15 Jul 2015, 09:17

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