Rephrasing

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Rephrasing The Target Question
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When it comes to answering data sufficiency questions, one of the biggest mistakes a student can make is jumping to the statements too quickly. Consider this question:

Is 4x < 3x?
(1) 3x + 4 < 3
(2) 2 > 2x ”“ 3

Given the GMAT’s cruel time constraints, it’s understandable that many students automatically begin analyzing the statements once they understand the target question. However, many problems can be solved much faster if we spend some time rephrasing the target question before moving on to the statements.

Notice that we can take the target question, “Is 4x < 3x?” and subtract 3x from both sides of the inequality to get, “Is x < 0?” If you compare this new wording of the target question to the original wording, you can see that the new wording provides much more insight into our objective. With the new wording, we can clearly see that our goal is to check whether each statement provides sufficient information to determine whether or not x is a negative number.

Now we’ll move on to the statements.

Statement 1: 3x + 4 < 3
If we subtract 4 from both sides of the inequality, and then divide both sides by 3, we get: x < -1/3. Does this provide sufficient information to answer the new target question, “Is x < 0?” Yes! If x is less than -1/3, then x is most definitely less than 0. So, statement 1 is sufficient.

Statement 2: 2 > 2x ”“ 3
If we add 3 to both sides of the inequality, and then divide both sides by 2, we get: 2.5 > x. Does this provide sufficient information to answer the new target question, “Is x < 0?” No. If 2.5 > x, then x could equal 1 in which case the answer to the new target question is NO. Conversely, x could equal -1 in which case the answer to the new target question is YES.

So, statement 2 is not sufficient, and the correct answer is A.

In many cases, we can save ourselves considerable time by taking a moment to rephrase (and simplify) the target question before we begin examining the statements.

Let’s look at another example. Consider this target question:

If a person is randomly selected from Peter’s chess club, is the probability less than 0.1 that Peter will be selected?

Is there a way to rephrase this target question that makes it easier to analyze the statements? Sure, notice that if there were 10 people in the chess club, the probability of selecting Peter would be exactly 1/10 (or 0.1). So, for the probability to be less than 0.1, there would need to be more than 10 people in the chess club.

We can now rephrase the target question as: “Are there more than 10 people in the chess club?”

As you can see, the original target question was just a tricky way to ask whether or not the chess club has more than 10 members.

So, before you begin analyzing the statements in a data sufficiency question, be sure to spend some time looking for possible ways to rephrase the target question in simpler terms. Doing so can often provide insight into a problem and help you analyze the statements faster.

For more information about rephrasing the target question, you might wish to watch the following video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

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