Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

Re: If x > y^2 >z^4 [#permalink]
28 Jun 2011, 12:17

1

This post received KUDOS

Baten80 wrote:

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

I. x > y > z

x=10000 y=10; y^2=100 z=1; z^4=1 x>y^2>z^4

II. z > y > x z=0.5; z^4=0.0625 y=0.4; y^2=0.16 x=0.3 x>y^2>z^4

III. x > z > y x=0.5 z=0.2; z^4=0.0016 y=0.1; y^2=0.01 x>y^2>z^4

a. I only b. I and II only c. I and III only d. II and III only e. I, II and III

We just need to remember that 1. the number decreases in value with increment in the power of the number if 0< number< 1; if x=0.1; x>x^2>x^3>x^(100) because x is between 0 and 1.

2. the number increases in value with increment in the power of the number if number>1 if x=2; x<x^2<x^(100) because x is more than 1.

A) I Only B) I and II Only C) I and III Only D) II and III Only E) I, II and III

I think the actual question is: Which of the following could be true?

Plugging in numbers work best for such questions. The only thing to keep in mind is that you should plug in the right numbers. How do you know the right numbers? When I see \(x > y^2 > z^4\), I think that \(y^2\) and \(z^4\) are non negative. Since \(y^2 > z^4\), \(y^2\) cannot be 0. Only z can be 0. x has to be positive. Also, I have to take into account two ranges: 0 to 1 and 1 to infinity. The powers behave differently in these two ranges. I will consider negative numbers only if I have to since with powers, they get confusing to deal with.

The question says: "Which of the following could be true?" We have to find examples where each relation holds.

I. x > y > z This is the most intuitive of course. z = 0, y = 1 and x = 2 \(2 > 1^2 > 0^4\)

II. z > y > x Let me consider the 0 to 1 range here. Say z = 1/2, y = 1/3 and x = 1/4 \(1/4 > 1/9 > 1/16\)

III. x > z > y Let's stick to 0 to 1 range. z > y as in case II above but x has to be greater than both of them. Say z = 1/2, y = 1/3 and x = 1 \(1>1/9 > 1/16\)

So all three statements could be true. _________________

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
15 Feb 2012, 11:11

I agree with E. Last one was tricky but once you realize that y and z could be fractions it becomes clear. took less than a minute but still a good question to make sure your reasoning is solid

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
28 Feb 2012, 01:31

Hi Bunuel/Karishma, Thanks for the earlier response.. I think, I am very weak in Inequalities.. Could you please post how to go about this question in algebraic way.. ...also if you could let me know how do you make sure about the "Range of the values", that will also work.. Thanks H _________________

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
28 Feb 2012, 01:46

3

This post received KUDOS

Expert's post

imhimanshu wrote:

Hi Bunuel/Karishma, Thanks for the earlier response.. I think, I am very weak in Inequalities.. Could you please post how to go about this question in algebraic way.. ...also if you could let me know how do you make sure about the "Range of the values", that will also work.. Thanks H

Plug-in method is really the best way to handle such kind of questions. No need to look for some kind of textbook or algebraic ways.

Notice that there are are certain GMAT questions which are pretty much only solvable with plug-in or trial and error methods (well at leas in 2-3 minutes). Many difficult inequality problems will often require some sort of plug-ins, as part of your technique or else you'll spend too much time solving them with algebra. Which means that you MUST make plug-in methods part of your arsenal if you want to get a decent score.

P.S. I'm not sure understood the following part of your post: "how do you make sure about the "Range of the values", that will also work.. " _________________

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
28 Feb 2012, 03:01

Thanks Bunuel for your response.. This is what I mean when I said range - Red Part in Karishma's response"

VeritasPrepKarishma wrote:

arps wrote:

1) x > y2 > z4

which of the following is 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

I think the actual question is: Which of the following could be true?

Plugging in numbers work best for such questions. The only thing to keep in mind is that you should plug in the right numbers. How do you know the right numbers? When I see \(x > y^2 > z^4\), I think that \(y^2\) and \(z^4\) are non negative. Since \(y^2 > z^4\), \(y^2\) cannot be 0. Only z can be 0. x has to be positive. Also, I have to take into account two ranges: 0 to 1 and 1 to infinity. The powers behave differently in these two ranges. I will consider negative numbers only if I have to since with powers, they get confusing to deal with.

The question says: "Which of the following could be true?" We have to find examples where each relation holds.

I. x > y > z This is the most intuitive of course. z = 0, y = 1 and x = 2 \(2 > 1^2 > 0^4\)

II. z > y > x Let me consider the 0 to 1 range here. Say z = 1/2, y = 1/3 and x = 1/4 \(1/4 > 1/9 > 1/16\)

III. x > z > y Let's stick to 0 to 1 range. z > y as in case II above but x has to be greater than both of them. Say z = 1/2, y = 1/3 and x = 1 \(1>1/9 > 1/16\)

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
28 Feb 2012, 04:59

Expert's post

2

This post was BOOKMARKED

imhimanshu wrote:

Thanks Bunuel for your response.. This is what I mean when I said range - Red Part in Karishma's response"

VeritasPrepKarishma wrote:

First notice that since x>z^4 (x is greater than some nonnegative value) then x>0.

Now, as Karishma correctly noted, numbers in powers behave differently in the range {0. 1} and {1. +infinity}. For example:

If 0<a<1 then a, a^2 and a^4 will be ordered as follows: 0--(a^4)--(a^2)--(a)--1

If a>1 then a, a^2 and a^4 will be ordered as follows: 1--(a)--(a^2)--(a^4)--

So, we should take the above difference in ordering into account when picking numbers for x, y, and z, since we need to find the values which satisfy 3 different statements.

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
13 Mar 2012, 00:05

So, Karishma, can it be said that any configuration of x, y and z COULD be true? Because we can always find fractions or integers which will satisfy.

6 configurations are possible, x>y>z, x>z>y, y>x>z, y>z>x, z>x>y and z>y>x. The answer choices in the question are the first, second and the last but I think any of these 6 configurations COULD be true. _________________

If you like it, Kudo it!

"There is no alternative to hard work. If you don't do it now, you'll probably have to do it later. If you didn't need it now, you probably did it earlier. But there is no escaping it."

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
13 Mar 2012, 01:14

1

This post received KUDOS

Hi,

Agree its a super tricky problem. I was so focused on the 0-1 range for x,y & z that forgot that for statement 3 you could have larger numbers _________________

Giving +1 kudos is a better way of saying 'Thank You'.

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
20 Jan 2013, 11:48

Sorry to open up a new thread!

Bunuel, I was impressed from your geometric way to solve inequalities. I was trying this one but could not really figure out how? Would you mind giving us a geometric way to solve this problem?

A) I Only B) I and II Only C) I and III Only D) II and III Only E) I, II and III

I think the actual question is: Which of the following could be true?

Plugging in numbers work best for such questions. The only thing to keep in mind is that you should plug in the right numbers. How do you know the right numbers? When I see \(x > y^2 > z^4\), I think that \(y^2\) and \(z^4\) are non negative. Since \(y^2 > z^4\), \(y^2\) cannot be 0. Only z can be 0. x has to be positive. Also, I have to take into account two ranges: 0 to 1 and 1 to infinity. The powers behave differently in these two ranges. I will consider negative numbers only if I have to since with powers, they get confusing to deal with.

The question says: "Which of the following could be true?" We have to find examples where each relation holds.

I. x > y > z This is the most intuitive of course. z = 0, y = 1 and x = 2 \(2 > 1^2 > 0^4\)

II. z > y > x Let me consider the 0 to 1 range here. Say z = 1/2, y = 1/3 and x = 1/4 \(1/4 > 1/9 > 1/16\)

III. x > z > y Let's stick to 0 to 1 range. z > y as in case II above but x has to be greater than both of them. Say z = 1/2, y = 1/3 and x = 1 \(1>1/9 > 1/16\)

So all three statements could be true.

Hey Karishma,

Can you please confirm if this type of solving is justified

As x>y^2>z^4. It can be inferred that x>y^2 and is true for both x>y and x<y (As we don't have any limitations for the three variables) Also, y^2>z^4 which means y>z^2 and the inequality is valid for both y>z and y<z Additionally, x>z^4, similar to prior cases x>z and z<x

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
08 Sep 2013, 06:15

Restrictions are not provided on the variables so I planned to check different values I and used x=y=z=1/2. As if I take 1/2 for each variables, its given condition would be satisfied and it will become 1/2>1/4>1/8.

So according to me none of the conditions are satisfied. Am I doing anything wrong here?

Re: If x > y^2 > z^4, which of the following statements could be [#permalink]
08 Sep 2013, 06:40

Expert's post

chetan86 wrote:

Restrictions are not provided on the variables so I planned to check different values I and used x=y=z=1/2. As if I take 1/2 for each variables, its given condition would be satisfied and it will become 1/2>1/4>1/8.

So according to me none of the conditions are satisfied. Am I doing anything wrong here?

Notice that the question asks "which of the following statements could be true" NOT "which of the following statements must be true" _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

UNC MBA Acceptance Rate Analysis Kenan-Flagler is University of North Carolina’s business school. UNC has five programs including a full-time MBA, various executive MBAs and an online MBA...

To hop from speaker to speaker, to debate, to drink, to dinner, to a show in one night would not be possible in most places, according to MBA blogger...

Most top business schools breed their students for a career in consulting or financial services (which is slowly being displaced by high tech and entrepreneurial opportunities). Entry into...