Tuesday’s Tip: Data Sufficiency Is NOT Math!

Ok, folks, here we go again with a review of the main stumbling block to success on the GMAT—taking it as a math test. We’ve explored in earlier blogs how the design of the question types and timing structure on the GMAT make it clear that management, not math, is what is being tested. Nowhere is this more evident than on data sufficiency questions.

With these infernal beasts, the first thing you want to determine is, what are you being asked? If you think it’s the question itself, you’re wrong. Let’s take a look at an example to illustrate this point:

EXAMPLE:

Is xy an integer?

(1)  x is the ratio of the areas of the largest square that can fit into a circle

(2)  y is the ratio of the areas of the largest circle that can fit into a square

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • EACH statement ALONE is sufficient to answer the question asked.
  • Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

On the face of it, this is a math question. But let’s dig deeper. Is the question actually asking us whether or not xy is an integer? No! Rather, the question is asking us whether or or not there is enough information to determine whether xy is an integer. What’s the difference? It’s huuuuge! Let’s look at a simple non-math data sufficiency question first and we’ll return to the one above later:

Is my name Avi?

(1)  My name is John

(2)  My name is not Avi

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • EACH statement ALONE is sufficient to answer the question asked.
  • Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

So what’s the answer here? When we ask students in our classes this very question we find that answers are roughly split evenly among the five answer choices. This result suggests that most people have a fundamental deficiency in the way they understand DS questions. Since DS questions account for roughly 40% of the entire quant portion, as your DS performance goes, so goes your final score.

Now, back to the question. The first mistake students make is going straight to the statements without even understanding what they’re being asked. All DS questions are the same in that they ask you to determine if enough information is supplied to answer the question. “Is my name Avi?”If I can answer this question with a definitive ‘yes’ or a definitive ‘no’ then the information supplied is indeed sufficient. Look at statement one: “My name is John”. If my name is John, then is my name Avi? NO! Absolutely not! Therefore, using the information supplied in statement one, I can answer the question—statement one is SUFFICIENT.

Now look at statement two. For the same reason, it is also sufficient. If my name is NOT Avi, then can I definitively answer the question “Is my name Avi?” Yes I can–the answer is no! Therefore, the information supplied in statement two is also sufficient and the final answer is D—either statement alone is sufficient to answer the question.

Note that we did not actually answer the question, we just determined if there was enough infomraiton to answer the question—two very different things. Herein lies the secret to data sufficiency questions: oftentimes, you will not have to do any math and pen will not meet paper if you know the design of what the question is really asking.

Adding math to the question complicates the matter but if you are clear about the intent of the question, it can oftentimes be handled in the same way as the previous example. Back to our original question: Is xy an integer? Remember, an integer is just a whole number, not a fraction.

Well, statement one is clearly insufficient because it tells me nothing about y. For the same reason, statement two is insufficient because it tells me nothing about x. Combined, however, they will be SUFFICIENT and the answer is C. Why? How can I tell this without doing any rigorous math?

Well, recall that DS questions are not asking you the actual question but rather whether there is enough information to answer the question—two different things. In this case, I am not being asked if xy is an integer; but rather if there is enough information to determine whether or not xy is an integer. If you tell me that x is a ratio of some sort and y is a ratio of some sort and I know that the ratio of the area of an inscribed circle in a square never changes and vice versa, then the answer will ALWAYS either be yes or no. Which it is, we don’t care, as it is irrelevant to the question. The only thing we care about is that a definitive answer can be reached using both statements. Again, what the answer actually is does not matter.

So, to sum up:

  1. GMAT tests management not math.
  2. You cannot break 600–to say nothing of the vaunted 700-mark–on the GMAT without mastering DS questions.
  3. To master DS questions, understand that the stated question is different than the actual question.

Keep studying and good luck!

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