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# If x > y^2 > Z ^4, which of the following statements

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Senior Manager
Joined: 24 Mar 2011
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If x > y^2 > Z ^4, which of the following statements  [#permalink]

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23 Apr 2011, 15:40
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:37) correct 30% (00:45) wrong based on 20 sessions

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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

1) I only
2) I & II only
3) I & III only
4) II & III only
5) I, II & III

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-y-2-z-4- ... 00465.html

--== Message from the GMAT Club Team ==--

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This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Posts: 1835
Re: If x > y^2 > Z ^4, which of the following statements  [#permalink]

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24 Apr 2011, 11:42
agdimple333 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

1) I only
2) I & II only
3) I & III only
4) II & III only
5) I, II & III

We know between 0 and 1; the higher power of the number is less than lower power of the number.

0.1^4<0.1^2<0.1

Consider 3 numbers between 0 and 1, which are close to one another.
0.1,0.2,0.3

Assign the value as per the option and see whether the stem holds true.

I. x > y > Z
x=0.3
y=0.2; y^2=0.04
z=0.1; z^4=0.0001
x>y^2>z^4
TRUE.

II. z > y > x
z=0.3; z^4=.0081
y=0.2; y^2=0.04
x=0.1
x>y^2>z^4
TRUE.

III. x > z > y
x=0.3
z=0.2; z^4=.0016
y=0.1; y^2=0.01
x>y^2>z^4
TRUE.

Ans: "E"
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Re: If x > y^2 > Z ^4, which of the following statements  [#permalink]

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24 Apr 2011, 19:17
x = 6, y = 2, z = 1 => (I) is true

z = 1/5, y = 1/6, x = 1/7 => (II) is true

x = 3/4, y = 1/3, z = 1/2 => (III) is true

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Senior Manager
Joined: 21 Dec 2010
Posts: 474
Re: If x > y^2 > Z ^4, which of the following statements  [#permalink]

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19 May 2011, 23:26
ans is E, plug positive numbers and fractions and negative numbers and zero and check.
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Re: If x > y^2 > Z ^4, which of the following statements  [#permalink]

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19 May 2011, 23:33
x,y,z with values 1,2,3.
0.1,0.4 and 0.5.

gives E
Math Expert
Joined: 02 Sep 2009
Posts: 50009
Re: If x > y^2 > Z ^4, which of the following statements  [#permalink]

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03 Dec 2017, 00:53
agdimple333 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

1) I only
2) I & II only
3) I & III only
4) II & III only
5) I, II & III

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-y-2-z-4- ... 00465.html

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: http://gmatclub.com/forum/if-x-y-2-z-4- ... 00465.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: If x > y^2 > Z ^4, which of the following statements &nbs [#permalink] 03 Dec 2017, 00:53
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