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

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

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New post 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

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

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New post 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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New post 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.

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

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New post 21 Apr 2009, 20:31
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Please see my video solution.

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.

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

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New post 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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New post 20 Aug 2009, 08:31
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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

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

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New post 21 Aug 2009, 00:15
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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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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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

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New post 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.

kalpeshchopada7 wrote:
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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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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New post 29 Oct 2009, 16:26
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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.

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

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

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

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New post 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.

Answer: E.

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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