GRE Quantitative Reasoning: Quantitative Comparison Questions
The Quantitative Comparison questions ask you to compare two quantities – Quantity A and Quantity B – and choose one of four answers:

Quantity A is greater

Quantity B is greater

The two quantities are equal

The relationship cannot be determined from the information given.
The quantity A and B are given in two different columns. Sometimes, additional information about the quantities or variables referenced in the two quantities is also provided with the question. Quantitative comparison questions can be easily solved using elimination techniques.
Tips and Tricks for Quantitative Comparison:

Remember that every Quantitative Comparison question has the same four answer choices. Become familiar with these four.

For simple algebraic questions (i.e. x^{2} and x^{4}), plug in different numbers and see how the answers compare. Try positive and negative numbers, large and small numbers, and decimals and fractions. If Quantity A is not always larger, smaller, or equal to Quantity B, then choose “the relationship cannot be determined from the information given.”

Remember that figures are not drawn to scale. Redraw the figure, keeping the features that are determined by the description constant but changing those features that are not determined.
Example:
Q1.
y > 1
Quantity A 
Quantity B 
y^{8} 
(y^{4})^{2} 
Quantity A is greater. 

Quantity B is greater. 

The two quantities are equal. 

The relationship cannot be determined from the information given. 
Answer: C
Solution:
Remember the exponent rules? One of them states that, when you raise a number with a power to a power, the exponent of the resulting number is the product of the two powers e.g.:
C is the correct answer.