GMAT by the Numbers: Arithmetic

Now that you’ve learned how to approach arithmetic 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. What is the value of integer n?
    1. n = n4
    2. 1n ≠ n
    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 question asks for the value of n and tells you only that it’s an integer. This leaves all integers as possible values—an important observation because some integers behave differently in certain arithmetic operations than others. The values 1, 0, and negative numbers all have special properties that are often crucial to consider.

Statement (1) tells you that n = n4. It may be tempting to think that n must equal 1, but 0 also equals its own fourth power: 0. The question statistics reveal that test takers often overlook this possibility, choosing (A), so it’s no surprise that the test maker creates questions that exploit this error. Since n could equal either 1 or 0, Statement (1) is insufficient.

Statement (2) tells you only that 1n ≠ n. No matter what exponent 1 is raised to, the value will remain 1. For example, 12 = 1, as do 13 and 14. So the only value of n that Statement (2) excludes is n = 1. Alone, this statement is certainly insufficient. But when combined with Statement (1), you have an answer. Statement (1) permits only n = 1 and n = 0. Statement (2) removes n = 1 from consideration, leaving n = 0 as the only possibility. The correct answer is (C).

Considering different values, such as 0, will help you to avoid traps. Also noteworthy is how many test takers select (E) on this problem. Such a response reflects a common error on difficult Data Sufficiency questions: these two statements are abstract, so many test takers—unsure of how to handle them—decide that they are insufficient. Correct these common assumptions—that values are positive integers and that abstract statements don’t contain useful information—and you’ll see a much higher score on Test Day.

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.