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Relation between x, y^2 and z^4

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Relation between x, y^2 and z^4 [#permalink]

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19 Apr 2009, 01:21
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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
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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: GPrep questn [#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.
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Re: GPrep questn [#permalink]

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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: GPrep questn [#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: GPrep questn [#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

therefore answer is e.
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Re: GPrep questn [#permalink]

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21 Aug 2009, 00:15
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: GPrep questn [#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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Relation between x, y^2 and z^4 [#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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Re: Relation between x, y^2 and z^4 [#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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Re: Relation between x, y^2 and z^4 [#permalink]

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29 Oct 2009, 16:26
1
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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.

KUDOS it you find it helpful
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gmat prep Q [#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?
gmat prep Q   [#permalink] 15 Jun 2010, 12:25
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Relation between x, y^2 and z^4

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