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

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Re: x > y^2 > z^4 [#permalink] New post 19 Nov 2013, 10:52
Bunuel wrote:
Orange08 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 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.



Hi Bunuel,

Can we not use negative integers.
For e.g.: x =5, y=-2,z=-1 then the first inequality would be 5>(-2)^2>(-1)^4. In this case x>z>y and y is not greater than z.

Am i missing something?
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Re: x > y^2 > z^4 [#permalink] New post 19 Nov 2013, 14:21
Expert's post
chitrasekar2k5 wrote:
Bunuel wrote:
Orange08 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 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.



Hi Bunuel,

Can we not use negative integers.
For e.g.: x =5, y=-2,z=-1 then the first inequality would be 5>(-2)^2>(-1)^4. In this case x>z>y and y is not greater than z.

Am i missing something?


The questions asks which of the following COULD be true not MUST be true. As shown above each option COULD be true for certain numbers.
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Re: If x > y^2 > z^4, which of the following statements could be [#permalink] New post 04 Apr 2014, 21:06
I and II are pretty much evident.. However III is no, it is better to split the third option in to two parts and focus just on Z>Y which is quite possible.. So the answer is all three..
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If [m]x > y^2 > z^4[/m], which of the following statements [#permalink] New post 09 Jun 2014, 10:19
If \(x > y^2 > z^4\), which of the following statements could be true?

I. \(x > y > z\)
II. \(z > y > z\)
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

[Reveal] Spoiler:
OA
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Re: If [m]x > y^2 > z^4[/m], which of the following statements [#permalink] New post 09 Jun 2014, 10:23
Expert's post
jayasrivaryani wrote:
If \(x > y^2 > z^4\), which of the following statements could be true?

I. \(x > y > z\)
II. \(z > y > z\)
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

[Reveal] Spoiler:
OA


Merging similar topics. Please refer to the discussion on page 1.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x > y^2 > z^4, which of the following statements could be [#permalink] New post 15 Jul 2015, 09:17
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Re: If x > y^2 > z^4, which of the following statements could be   [#permalink] 15 Jul 2015, 09:17

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