GMAT Question of the Day – Data Sufficiency – Exponents/Number Properties
If x and y are non-zero integers is x^(xy) > y^(xy)?
1) x^y > 0
2) x > y
GMAT Question of the Day Solution
You might say that this GMAT question is just an exponents question but you’ll be better served thinking of it in terms of number properties. Whenever working on a data sufficiency question consider number properties. Consider special numbers: 1, 0, positive numbers, negative numbers, integers, and decimals. This question of the day presents an expression which may seem quite foreign but if you frame the expression in terms of positive numbers/negative numbers the solution becomes clear. A negative number raised to an even power becomes a positive number. The greater the negative the more positive it becomes. This question is built around that idea. Understand the idea and the solution is obvious. Every GMAT question is built around an idea. It’s your job to uncover the idea.
Statement (1) This tells is that either x is positive or that y is even. Insufficient.
Statement (2) Just because x is greater than y does not mean that x^(xy) > y^(xy). If both numbers are negative and one of them is even the relationships is flipped. For example: (-4)^20 < (-5)^20 even though -5 < -4. Insufficient.
Putting the statements together nothing changes because we can’t eliminate anything.