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if x > y^2 > Z^4,

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vrajesh.dave
 Post subject: if x > y^2 > Z^4,
 Post Posted: Mon Aug 24, 2009 7:35 am 
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Course Students


Posts: 31
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. I and III only
d. II and III only
e. I, II, and III

OA: E

we can know for sure that X has to be positive for it be to greater than Y^2 and Z ^4.
and similarly |y| > |z| since Y^2 > Z^4

So I is definitely true.

But I do not understand how II and III could be true.

Please explain.

again, when they say could be true, do we have to take same values for that satisfy all 3 conditions or can we change the values of x,y and z for each statement.
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nimish.tiwari
 Post subject: Re: if x > y^2 > Z^4,
 Post Posted: Mon Aug 24, 2009 2:06 pm 
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Students


Posts: 13
vrajesh.dave 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. I and III only
d. II and III only
e. I, II, and III

OA: E

we can know for sure that X has to be positive for it be to greater than Y^2 and Z ^4.
and similarly |y| > |z| since Y^2 > Z^4

So I is definitely true.

But I do not understand how II and III could be true.

Please explain.

again, when they say could be true, do we have to take same values for that satisfy all 3 conditions or can we change the values of x,y and z for each statement.


In the given primary inequality: x > y^2 > z^4, all the terms would be positive (since we have even powers of y & z).

for this to hold true, x can be any +ve number (may be fraction as well) and y & z have to be necessarily fractions. Hence, I holds true.

For II. z > y > x. Consider, x=1/4, y=1/3, z=1/2. This satisfies given primary inequality. Hence, II also holds true.

For III. Consider x=1, y=1/3,z=1/2. This satisfies given primary inequality. Hence, III also holds true.

Hence, E.
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anoo.anand
 Post subject: Re: if x > y^2 > Z^4,
 Post Posted: Sat Sep 19, 2009 1:55 pm 
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Students


Posts: 73
is there any criteria on which we have to choose numbers for solving these kind of problems...?
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RonPurewal
 Post subject: Re: if x > y^2 > Z^4,
 Post Posted: Sat Sep 26, 2009 2:44 am 
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ManhattanGMAT Staff


Posts: 7146
anoo.anand wrote:
is there any criteria on which we have to choose numbers for solving these kind of problems...?


as a takeaway from this problem, you should absorb the association between COMPARING POWERS and FRACTIONS.

basically, the idea is that fractions (i.e., numbers between 0 and 1) "act funky" when they're raised to powers.
so do negatives.
therefore, when you pick numbers, you MUST consider these sorts of numbers!
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