Lesson: Data Sufficiency Challenging - 11t01

Tough Content: Example 1

If x is an odd integer, is x ^x > x ^-x?

1) x ³ < x ²

2) xy ? – y

The first thing you need to do when you get a question this tough is to get the lay of the land, so to speak, by evaluating the question stem.

Do you recognize the math concept that this is testing? Type it into the Text Box, and click Continue.

This question is testing

Countinue

Negative exponents are not often tested on simpler problems because they're considered more difficult math. However, they’re really straightforward: they’re the reciprocal of the corresponding positive power. For example, .

Now, this question is asking whether a number raised to itself is always greater than that number raised the corresponding power of the opposite sign. Think about the logic of the question: If x ^x > x ^-x were always true or always false, regardless of the value of the number involved, it wouldn’t make any sense to use this expression in a Data Sufficiency question because the answer would just be a mathematical given and you wouldn’t need any additional info. Just as it wouldn’t make any sense for a Data Sufficiency question to ask "Is 5 > 4 ?" So if the Exam asks "If x is an odd integer, isx ^x > x ^-x " , there’s probably at least one exception to an otherwise consistent pattern. The Exam is hoping you’ll see the general pattern and blank on the exceptions.

So far we have two number property characteristics determined for x: we know it's odd and we know it's an integer, because the stem tells us both. Our exception must deal with some other number property characteristic.

Countinue

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