Try your hand at this data sufficiency question focusing on Standard Deviation. Standard deviation is a rare topic on test day, but it can be challenging for many test takers.

Data Sufficiency Question:

For a certain exam, was the standard deviation of the scores for students U, V, W, X, Y and Z less than the standard deviation of the scores for students A, B and C?

(1) The standard deviation of the scores of students U, V, and W was less than the standard deviation of the scores of students A, B and C on the exam.

(2) The standard deviation of the scores of students X, Y and Z was less than the standard deviation of the scores of students A, B and C on the exam.

Solution:

Remember that standard deviation is a measurement of how spread-out a set of numbers are around the mean. As is usually the case on the GMAT, this problem does not require us to calculate standard deviation. Rather, we just need to understand the CONCEPT of standard deviation.

Statement 1 tells us that U, V and W have a lower standard deviation that A, B and C. However, this tells us nothing about X, Y and Z. Without knowing all of the numbers in the set, you are unable to calculate standard deviation. Statement 1 is, therefore, insufficient.

Statement 2 tells us that X, Y and Z is smaller than the standard deviation of A, B and C. Now, we do not know anything about U, V and W. For the same reasons as in statement 1, statement 2 is not sufficient.

When the statements are considered together, we know that the sets U, V and W and X, Y and Z both have a standard deviation that is less than the set of A, B and C. However, we do not know the relationship between the two former sets. It is possible that U, V, W, X, Y and Z are all closer together than A, B and C are, but it is also possible that the sets U, V and W and X, Y and Z are so far apart from each other that the overall set ends up having a larger standard deviation than the set A, B and C. Therefore, together the statements are still insufficient; answer choice (E) or (5)—not enough information here to answer the question.

Even though this appears to be a challenging problem on first glance, including data sufficiency and standard deviation, we did not have to use our scratch paper necessarily or compute any actual mathematical calculations….sometimes questions on test day will be more focused on your conceptual understanding, and instead of becoming overwhelmed when you see words like “standard deviation”, you should stay calm, read carefully, and remind yourself of the concepts you do know as you analyze the question.

Data Sufficiency can be a major obstacle for any GMAT student, but one advantage that you have against this infamous question type is that every Data Sufficiency question has the same answer choices.  One of the first steps towards success on the GMAT Quantitative section is to learn and internalize these answer choices, but another huge advantage you can give yourself is to internalize the method for eliminating wrong answer choices once you’ve started to determine sufficiency for the statements.

In case you haven’t committed them to memory yet, here are those familiar choices:

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient to answer the question asked.

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Let’s say you run into the following problem:

1. Is x positive?

(1) x > 5

(2) x > -5

If you, like most students, look at statement (1) first, you’ll probably say to yourself, “Well, if x is greater than 5, then x must be positive!” and you’d be right: statement (1) is definitely sufficient to answer the question.  But before we move on to statement (2), what does this mean for our (A)-(E) answer choices?  Well, since statement (1) is sufficient, we can eliminate all choices that would require statement (1) to be insufficient, and that’s choices (B), (C), and (E).

Similarly, if you had a question where statement (1) was NOT sufficient by itself, you could immediately axe choices (A) and (D), since both of those choices require statement (1) to be “sufficient ALONE” to answer the question.  And what if NEITHER statement ALONE is sufficient?  Well then, we’d be down to (C) and (E) as our only possibilities, with a final answer hinging on the sufficiency of the statements in combination.  (The system even works if you look at statement (2) before statement (1), you just have to eliminate slightly different choices.  Try it!)

Memorizing this simple method is a cornerstone to mastering Data Sufficiency; using it means you never have to waste valuable time deciphering the intricacies of the question type itself, freeing up valuable time and effort for mathematics and critical thinking.  Plus, as with any elimination strategy, it makes guessing much more efficient.  If you can eliminate 2-3 answer choices and end up with a 33-50% chance to guess correctly on Data Sufficiency questions—rather than a 20% chance with a blind (A)-(E) guess—it really adds up in your final score.

In every class I teach, the reaction students have when they first encounter a data sufficiency problem is always the same. They are unsure of the correct approach, but feel they could do much better on such a problem if they had a firm grasp on the concept of data sufficiency.

To gain this grasp, we must start with the most basic idea of what exactly data sufficiency is asking you to do. A data sufficiency question is not centered around the actual solution. Rather, data sufficiency tests whether you are able to reach a single answer to the question.

You will be given a question and two statements. You must figure out if the information in the statements, alone or together, is sufficient to answer the question being asked. In other words, based on the statements could you solve the problem if you wanted?

The five answer choices never change and all refer to which statement(s) are sufficient: Statement One but not Statement Two; Statement Two but not Statement One; the Statements together are sufficient but not alone; each Statement is sufficient on its own; or the Statements are not sufficient together nor alone.

This means that you can avoid doing quite a bit of work when encountering a data sufficiency problem. For example, once you have set up an equation, you have no reason to actually solve it as long as you can see that you could solve it enough to have a clear answer to whatever you are asked.

So, next time you see a data sufficiency problem, do not let it intimidate you. Rather, tell yourself that you are lucky to be seeing such a problem. Unlike the problem solving portion of the test, you may be able to avoid doing as much actual math. This, in turn, saves you time for problems that genuinely do take longer to complete and leads directly to a higher score.