# GRE Math : How to evaluate algebraic expressions

## Example Questions

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### Example Question #401 : Algebra

Compare Quantity A and Quantity B and determine which is larger.

Quantity A:

Quantity B:

For when

Explanation:

For this problem, the limitation given to us is that  must be less than or equal to . Therefore we first attempt to plug in  into both Quantity A and B to determine which is larger.

Quantity A:

Quantity B:

Quantity B is larger.

Plugging in

Quantity A:

Quantity B:

Quantity B is still larger.

Therefore we can conclude for whenever  is positive, Quantity B will be larger.

We notice that because Quantity A is raised to the power of 3 and Quantity B is raised to the power of 1, any time we plug in a negative number, Quantity A and B will be negative.  However, Quantity A will always be more neagtive because it is raised to the power of 3.  Therefore for all negative numbers, Quantity B will be larger.

Therefore, whenever , Quantity B will be larger than Quantity A

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