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Relation between x, y^2 and z^4 [#permalink ]
19 Apr 2009, 00:21
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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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(c)

if x, y & z are positive (I) is true

if x, y & z are negative (III) is true

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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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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

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Last edited by

dabral on 24 May 2011, 19:12, edited 2 times in total.

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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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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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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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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 ]
29 Oct 2009, 13:38

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 ]
29 Oct 2009, 14:06

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: Relation between x, y^2 and z^4 [#permalink ]
29 Oct 2009, 15:26
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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 .

KUDOS it you find it helpful

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IF x>y^2>z^4

then which of hte following is true?

x>y>z

z>y>x

x>z>y

OA is

Could somebody provide an explanation that for the 3rd one to be correct?