Lesson: Data Sufficiency Intermeddiate - 05t01

Number Properties In Data Sufficiency, continued.

Let's try another Number Properties question, and here's a hint. You'll want to use one of the most important GMAT math strategies, Picking Numbers. As with Problem Solving, using this great strategy will often help you to find the right answer!

Do another number properties question using your picking numbers strategy. Choose an answer, then click Continue.

If x is an integer, is 15 a factor of x?

1. 15 is a factor of 10x
2. 15 is a factor of 11x

	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

Focus on the question stem.

First thing to note: this is a Yes/No question.

You could rewrite the question two ways:

Does equal an integer? Or, is x divisible by 15?

Remember, there are signals in the question stem that it pays you to notice. Here, the word factor tells you that this is a number properties question. Factors and multiples are related, so you should expect the statements to give you information about factors and/or multiples of x.

What do you need to know to answer the question?

• The value of x would be sufficient.
• Any information that allows you to determine whether 15 is a factor of x would be sufficient.

Evaluate the statements separately.

Unless a statement gives you a value for x use the information in the statement to tell you what kinds of numbers to pick for x.

Statement (1) is insufficient. Rewrite the statement as a fraction and then reduce.

If an integer, then must be an integer.

The 2 in the numerator is not divisible by 3, so x must be divisible by 3. Knowing this tells you what kind of numbers to pick for x multiples of 3. If you let x = 3 then Remember the question is whether an integer. When x = 3 the answer is "No." When x = 30, the answer is "Yes." Both numbers, 3 and 30, satisfy the conditions of the statement but each yields a different answer to the question stem. Therefore, the statement is insufficient.

Statement (2) is sufficient. If an integer, then must be an integer.

The number 11 in the numerator is not divisible by 15 so, x must be divisible by 15.

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