X>Y^2>Z^4

[Raj]

I am not able to find a simple solution to this problem (that I could use to solve in 2 mins), any help appreciated. This is from my first GMAT Prep Exam:

If X>Y^2>Z^4, which of the following statements could be true:

I. X > Y > Z (easy)
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

[Guest]

I am not able to find a simple solution to this problem (that I could use to solve in 2 mins), any help appreciated. This is from my first GMAT Prep Exam:

If X>Y^2>Z^4, which of the following statements could be true:

I. X > Y > Z (easy)
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

Raj - by stating "which of the following statements could be true" we are really looking for one instance where the preceding statements could be true.

you can take 3 cases,
1. When X,Y,Z are positive integers in that case:
I. X > Y> Z holds true

2. When X, Y, Z are fractions:
Z > Y > X
1/2 > 1/3 > 1/4
X>Y^2>Z^4
1/4 > 1/9 > 1/16

3. X > Z > Y (Negative, positive)
20 > -3 > -4
X>Y^2>Z^4
20 > 16 > 9

Therefore answer is E.

Can you please confirm.

Hope this helps !!

[divya]

I am not able to find a simple solution to this problem (that I could use to solve in 2 mins), any help appreciated. This is from my first GMAT Prep Exam:

If X>Y^2>Z^4, which of the following statements could be true:

I. X > Y > Z (easy)
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

Raj - by stating "which of the following statements could be true" we are really looking for one instance where the preceding statements could be true.

you can take 3 cases,
1. When X,Y,Z are positive integers in that case:
I. X > Y> Z holds true

2. When X, Y, Z are fractions:
Z > Y > X
1/2 > 1/3 > 1/4
X>Y^2>Z^4
1/4 > 1/9 > 1/16

In the last one - take z as -1
3. X > Z > Y (Negative, positive)
20 > -1 > -4
X>Y^2>Z^4
20 > 16 > 1

Therefore answer is E.

Can you please confirm.

Hope this helps !!

[Raj]

Divya,

you are right and thanks for the solution. I like the way people plug in numbers.. I am just not that good at it but I guess any other methods would not work in cases like these.

Thanks much,
-Raj.

I am not able to find a simple solution to this problem (that I could use to solve in 2 mins), any help appreciated. This is from my first GMAT Prep Exam:

If X>Y^2>Z^4, which of the following statements could be true:

I. X > Y > Z (easy)
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

Raj - by stating "which of the following statements could be true" we are really looking for one instance where the preceding statements could be true.

you can take 3 cases,
1. When X,Y,Z are positive integers in that case:
I. X > Y> Z holds true

2. When X, Y, Z are fractions:
Z > Y > X
1/2 > 1/3 > 1/4
X>Y^2>Z^4
1/4 > 1/9 > 1/16

In the last one - take z as -1
3. X > Z > Y (Negative, positive)
20 > -1 > -4
X>Y^2>Z^4
20 > 16 > 1

Therefore answer is E.

Can you please confirm.

Hope this helps !!

[RonPurewal]

Divya,

you are right and thanks for the solution. I like the way people plug in numbers.. I am just not that good at it but I guess any other methods would not work in cases like these.

Thanks much,
-Raj.

if you are really, really, really good at conceptualizing the properties of different types of numbers, then there's a chance that you could solve problems like this one simply by thinking about the behavior of different types of numbers (e.g., fractions, negatives, negative fractions, etc.).
however, in the vast majority of cases, it's easier simply to plug in numbers.

note that number plugging is NOT random. whenever you do number plugging in a number properties problem, you have to figure out what types of numbers will have different effects upon the problem. in this case, you're considering both even and odd powers, and you're comparing those powers. therefore, you must consider signs (because there are both even and odd powers) AND fractions (because power comparisons are reversed with fractions). plug numbers accordingly, just as divya did.

there's nothing brilliant about plugging in the right numbers; you just have to ASSOCIATE the content of the problem with the correct types of numbers, and then plug in the appropriate types of numbers.
as long as you don't hesitate and stare at the problem, you'll have plenty of time to do this.