If x>y^2>z^4, Which of The Following Statements Could Be True? GMAT Data Sufficiency

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

1. x>y>z
2. z>y>x
3. x>z>y

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If x>y^2>z^4, which of the following statements could be true?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2022". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

There is only one way to solve the problem statement.
Since this is a “COULD be TRUE” question, even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.
To solve this, we will have to consider various values for various statements.
Given:
x>y^2>z^4
We will consider each options one by one.

1. Let us proceed with 1, which says: x>y>z

This is the simplest one:
Let us consider that x=100, y=2 and z=1.
This set satisfies x>y^2>z^4 and also x>y>z.
Hence, the statement 1 could be true.

2. Let us proceed with 2, which says: z>y>x

We have reverse order than in the given statement x>y^2>z^4
Since the order is reverse, we will take the value as fractions:
Let x=\(\frac{1}{5}\), y=\(\frac{1}{4}\), z=\(\frac{1}{3}\)
This also verifies that the statement is true. Hence, option 2 also could be the possibility.

3. Let us proceed with 2, which says: 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 statement 3 also COULD be true.
All 3 statements can be true.

Correct Answer: E

Some suggested GMAT Data Sufficiency Questions

• 2x+3y GMAT Data Sufficiency 
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Data Sufficiency 
• If the Vertices of a Triangle have Coordinates (x,1) (5,1) and (5,y) Where x<5 and y>1, What is the Area of the Triangle? GMAT Data Sufficiency 
• Each Term of Set T is Multiple of 5. Is Standard Deviation of T Positive? GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio GMAT Data Sufficiency
• If x and y are positive integers and xy is divisible by prime number. Is p an even number? GMAT Data Sufficiency 
• What is the Product of 6 Consecutive Numbers? GMAT Data Sufficiency 
• If x is an integer is an x/12 integer? GMAT Data Sufficiency 
• Is 7^7 / 7^x an integer?GMAT Data Sufficiency 
• The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC? GMAT Data Sufficiency 
• Is the area of the triangle ABC greater than the area of the triangle DEF? GMAT Data Sufficiency
• There is atleast one viper and atleast one cobra in Pandora’s Box GMAT Data Sufficiency 
• If L not equals to 0, is 18K/L an Integer? GMAT Data Sufficiency 
• If a, b, and c are positive and a^2 + c^2 = 202, what is the value of b – a – c? GMAT Data Sufficiency 
• If x and y are positive integers, is x odd? GMAT Data Sufficiency 
• If 0 < x < 53, what is the value of integer x? GMAT Data Sufficiency 
• What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency 
• If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency 
• If m is a positive integer, is √m>25? GMAT Data Sufficiency 
• If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency