GMAT by the Numbers: Number Properties

Now that you’ve learned how to approach number properties questions on the GMAT, let’s add one more dimension to your understanding of how they work.

Take a moment to try this question. Following is performance data from thousands of people who have studied with Kaplan over the decades. Through analyzing this data, we will show you how to approach questions like this one most effectively and how to avoid similarly tempting wrong answer choice types on Test Day.

1. If a and b are positive integers, is 3a²b divisible by 60?
   1. a is divisible by 10.
   2. b is divisible by 18.
   1. Statement (1) ALONE is sufficient, but Statement (2) is not sufficient.
   2. Statement (2) ALONE is sufficient, but Statement (1) is not sufficient.
   3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
   4. EACH statement ALONE is sufficient.
   5. Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation

This Yes/No question asks whether 3a²b is divisible by 60. In other words, it asks whether is an integer. The 3 in the numerator cancels out a factor of 3 from the denominator, so it’s really asking whether is an integer. For this expression to be an integer, the remaining factors in the denominator will have to be canceled out by the numerator. Since 20 = 2 × 2 × 5, you’re really being asked whether a²b contains two 2s and one 5 among its factors.

Statement (1) says that a is divisible by 10. Since 10 = 2 × 5, you know that a contains at least one 2 and at least one 5 among its factors. Therefore, the a² in the numerator must have at least two 2s and at least two 5s. It doesn’t matter what factors b contains, since a² alone provides all the factors needed to cancel out the 20. Statement (1) is therefore sufficient.

Since 18 = 2 × 3 × 3, Statement (2) tells you that b has at least one 2 and at least two 3s among its factors. By itself, b does not guarantee two factors of 2, let alone any factor of 5. Therefore, Statement (2) is insufficient.

Since Statement (1) alone is sufficient but Statement (2) is not, (A) is correct.

Question Statistics

49% of test takers choose (A)

3% of test takers choose (B)

37% of test takers choose (C)

3% of test takers choose (D)

8% of test takers choose (E)

Sample size = 5,507

As the question statistics reveal, many test takers automatically assume that they need information about every variable in order to answer a question. Knowing this, the test maker often writes statements that provide sufficient information despite not telling you about each variable. Don’t automatically think that you need information on all the variables—analyze the question stem carefully to see what you really need, and you’ll put yourself well ahead of your competition.

More GMAT by the Numbers . . .

To see more questions with answer choice statistics, be sure to review the full-length CATs in your online resources.