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Directions: Each question of this type consists of two quantities, one in Column A and one in Column B. Compare the two quantities and indicate:

* A if the quantity in Column A is greater
* B if the quantity in Column B is greater
* C if the quantities are equal
* D if the relationship cannot be determined from the information given

In some questions, additional information pertaining to one or both of the quantities to be compared is centered above the two columns.

Any symbol appearing in both columns represents the same thing in one column as in the other.

All numbers used are real numbers.

Question

x is a positive number.
Column A: x^2
Column B: x^3

Correct Answer
Choice D. The relationship cannot be determined from the information given.

Explanatory Answer
The question states that the given number is a positive number. Positive numbers are numbers that are greater than 0.
Column A is x^2 and Column B is x^3.

If x > 1, then x^2 < x^3.
If x = 1, then x^2 = x^3.
If x < 1 and is positive, then x^2 > x^3.

As we do not know which of these 3 situations apply, as all are likely, we cannot determine which of the two quantities is greater.

The trick in this question is that most of us will assume a positive number to be a positive integer and might not consider the case that x = 1.

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