Lesson: Data Sufficiency Intermeddiate - 04t01

Data Sufficiency And Number Properties

Data Sufficiency tests number properties extensively. The good news is that because the content for Data Sufficiency is the same as for Problem Solving, the same number properties rules that you use for Problem Solving will help you here!

Data Sufficiency often tests more than one content area at a time.

Apply the CAT Method to answer this number properties question. Choose the correct answer, then click Continue.

Is an integer?

1. m ? n
2. m - n is a prime number

	Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient.
	Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient.
	Both statements TAKEN TOGETHER are sufficient, but NEITHER statement BY ITSELF is sufficient.
	EACH statement BY ITSELF is sufficient.
	The two statements TAKEN TOGETHER are NOT sufficient.

Countinue

Did you recognize which number properties that this question was testing? They are:

• The definition of an integer
• Prime numbers
• Odd/even rules

Focus on the question stem.

This is a Yes/No question. What do you need to know to answer the question?

There is a subtle question within the question stem; is m - n even? For to equal an integer, m - n would have to yield an even number. A statement would have to lead you to information that proves m - n equals an even or odd number to be sufficient.

For example:

• The values of m and n would be sufficient.
• The quantity m - n would be sufficient.

Evaluate each statement separately.

Statement (1) is insufficient. The only information provided is that neither m nor n is equal to zero. Eliminate A and D.

Statement (2) is a trap. If you didn't know that 2 is the only even prime number, you might think that m - n equals an odd number. If that were the case, the statement would be sufficient because you could answer the question by saying "No." If m - n = 2 you can answer the question "Yes." Since m - n could be odd or even, there is no definite answer to the question, so, Statement (2) is insufficient and we eliminate Choice (B).

Combine the statements, if necessary.

mn ? 0 and m - n is a prime number

In combination, the statements don't tell us whether m - n is odd or even, so Choice (E) is correct.

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