Last visit was: 01 May 2026, 04:50

It is currently 01 May 2026, 04:50

Toolkit

Practice Tests

Quantitative Questions

Problem Solving (PS)

GMAT Club Daily Prep

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.

Go to My Error Log Learn more

Request Expert Reply

Confirm Cancel

Back to Forum

Create Topic

z^4, which of the following statements could be

1 2

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 01 May 2026

Posts: 109,990

Own Kudos:

812,245

Given Kudos: 105,967

Products:

Expert

Expert reply

Posts: 109,990

Kudos: 812,245

23 Sep 2024, 06:24

Kudos

Bookmarks

sarthak1701

KarishmaB

nutella

VeritasKarishma
Bunuel
Please help me understand where I am going wrong.
If you choose x = 1/3 and y = 1/2 then y>x but y^2<x
So how can we choose the options that include 1 - which is x>y>z. Because that might not be true.
Thank you in advance!!

Stmnt I will be true for some values of x, y and z.
Note that only one of the three statements can be true for a given set of values of x, y and z. The three statements hold for different values of x, y and z as shown in my post above: https://gmatclub.com/forum/if-x-y-2-z-4 ... l#p1032823

Basically, the question should be: Which of the following "could be" true for some values of x, y and z?

I. x > y > z
would be true when
z = 0, y = 1 and x = 2

This is more of a semantic problem than a quant one lol. I took x =1/5, y = 1/3 and z = 1/2

These numbers satisfy the condition: x>y^2>z^4

But since the numbers do not satisfy the 1st condition, I rejected the 4 choices containing that condition and selected the one choice that does not contain the 1st condition but alas I was wrong.

KarishmaB For such questions that say COULD BE true, we only need one set of numbers to satisfy a condition to accept it, and for the questions that say MUST BE true, we only need one set of numbers that DO NOT Satisfy the condition to reject it. Correct?

"MUST BE TRUE" ("ALWAYS TRUE"/"IS TRUE") questions:

These questions ask which statement is always true for every valid set of numbers. If you can find just one valid set of numbers where a statement is not true, it means the statement is not always true and therefore not the correct answer. So, for 'MUST BE TRUE' questions, the plug-in method is good for eliminating an option, but it does not provide a 100% guarantee that an option is always true. For "MUST BE TRUE" questions, when using the plug-in method, if you find that more than one option appears to be correct for a particular number or set of numbers, try using different numbers to double-check. Reevaluate only those options that were previously considered correct.
"COULD BE TRUE" questions:

The questions that ask which of the following statements could be true are different. If you can demonstrate that a statement is true for a specific set of numbers, it implies that the statement could be true and therefore is a correct answer.
You can practice more questions of this type HERE.

Hope it helps.

ManishaPrepMinds

Tutor

Joined: 14 Apr 2020

Last visit: 24 Apr 2026

Posts: 140

Own Kudos:

156

Given Kudos: 13

Location: India

Expert

Expert reply

Posts: 140

Kudos: 156

11 Nov 2024, 06:31

Kudos

Bookmarks

Solution:
We start by inferring from the question stem, which states that X > Y^2 > Z^4. This implies:
• X must be greater than Y^2, and Y^2 must be greater than Z^4, X > 0 , Y^2 > 0
• Since squares and fourth powers of numbers between 0 and 1 are smaller than the original numbers, we should consider values for Y and Z that are between 0 and 1 for some cases to verify each statement.
Checking Each Statement:
1. Statement I: X > Y > Z
values: X = 2, Y = 1, Z = 0
Check X > Y^2 > Z^4:
so 2 > 1 > 0, which satisfies X > Y^2 > Z^4.
Conclusion: Statement I could be true.

2. Statement II: Z > Y > X
Values: X = 1/4, Y = 1/3, Z = 1/2
Check X > Y^2 > Z^4:
Y^2 = (1/3)^2 = 1/9 and Z^4 = (1/2)^4 = 1/16, so 1/4 > 1/9 > 1/16, which satisfies X > Y^2 > Z^4.
Check Z > Y > X:
1/2 > 1/3 > 1/4, which holds.
Conclusion: Statement II could be true.

3. Statement III: X > Z > Y
Values: X = 1, Z = 1/3, Y = 1/4
Check X > Y^2 > Z^4:
Y^2 = (1/4)^2 = 1/16 and Z^4 = (1/3)^4 = 1/81, so 1 > 1/16 > 1/81, which satisfies X > Y^2 > Z^4.
Check X > Z > Y:
1 > 1/3 > 1/4, which holds.
Conclusion: Statement III could be true.
Final Conclusion: Answer: E

Nsp10

Joined: 22 May 2023

Last visit: 30 Mar 2026

Posts: 125

Own Kudos:

Given Kudos: 112

Location: India

Schools: IE Schulich

GPA: 3.0

Products:

Schools: IE Schulich

Posts: 125

Kudos: 91

04 Apr 2025, 00:06

Kudos

Bookmarks

Thank you for very nice explanations:
my doubt is in case 3:
III. x>z>y
in order to make this condition true we are assuming y>y^2,
can we also make the same condition true by assuming y<y^2 ?

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 01 May 2026

Posts: 109,990

Own Kudos:

812,245

[1]

Given Kudos: 105,967

Products:

Expert

Expert reply

Posts: 109,990

Kudos: 812,245

[1]

04 Apr 2025, 00:32

Kudos

Bookmarks

Nsp10

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. 1 and III only
D. II and III only
E. I, II and III

Thank you for very nice explanations:
my doubt is in case 3:
III. x>z>y
in order to make this condition true we are assuming y>y^2,
can we also make the same condition true by assuming y<y^2 ?

y < y^2 would imply 0 < y < 1.

For x > z > y we can have (x = 10) > (z = 1/2) > (y = 1/5)

y > y^2 would imply y < 0 or y > 1

For x > z > y we can have (x = 10) > (z = 1/2) > (y = -1)

Legallyblond

Joined: 14 May 2024

Last visit: 01 May 2026

Posts: 71

Own Kudos:

Given Kudos: 1,367

Location: India

Posts: 71

Kudos: 6

16 Nov 2025, 08:19

Kudos

Bookmarks

for third one we can take negative no also right like 9>1>-2?

Bunuel

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.