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

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

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New post 23 Apr 2011, 14:40
00:00
A
B
C
D
E

Difficulty:

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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
[Reveal] Spoiler: OA

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

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New post 24 Apr 2011, 10:42
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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New post 24 Apr 2011, 18:17
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

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

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New post 19 May 2011, 22:26
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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New post 19 May 2011, 22:33
x,y,z with values 1,2,3.
0.1,0.4 and 0.5.

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

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New post 02 Dec 2017, 23:53
Expert's post
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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.

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-y-2-z-4- ... 00465.html
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Re: If x > y^2 > Z ^4, which of the following statements   [#permalink] 02 Dec 2017, 23:53
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If x > y^2 > Z ^4, which of the following statements

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