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The GMAT - A Study in Complexity

The GMAT: A Study in Complexity

The GMAT offers a different experience for standardized test takers. Rather than simple data computation, interpretation, comparison, and analysis, the GMAT adds data sufficiency questions that can confuse even the most seasoned standardized test taker. Data sufficiency problems have three parts. First, they propose a question. Second, they offer two separate statements related to the question; and three, they then ask whether one or both of the statements is sufficient alone or in tandem to answer the original question.
Below is a question from a recent GMAT.
Sammy’s long distance telephone plan charges him x dollars for the first 3 minutes of a call and x – 0.50 cents per minute for each subsequent minute. Sammy made a call to Nate for t minutes, where t is an integer. If the call costs $7.50, how many minutes was Sammy’s call to Nate?

Statement 1: The rate for the first 3 minutes of the call costs $2 per minute.
Statement 2: If Sammy’s call to Nate had been five minutes longer, it would have cost twice as much.

[A] Statement 1 alone is sufficient
[B] Statement 2 alone is sufficient but statement 1 alone is insufficient
[C] Both statements together are not sufficient
[D] Statements 1 and 2 alone are sufficient Do you see what I mean by adding another level of complexity? This particular question--and many like it--require three to four steps to solve the problem.
To solve this problem, you must employ a four-step approach. The first step is to determine whether the original question or statement tells you whether you can develop an equation from the question. In this case, you can develop an equation:
x + (x – 0. 50) (t-3) = $7.50

Unfortunately, you cannot solve this equation. Therefore you need to turn your attention to statement 1 and determine whether it provides you with any information that allows you to solve the equation the original problem asked.
Statement 1 states: The rate for the first three minutes of the call costs $2 per minute. This information provides you with a second equation, once you realize that $2 for each of 3 minutes equals 6 dollars. This is the value of “x.” Substituting this value into the original equation, you can solve the equation for “t.” Because you can solve for t, statement 1 is sufficient to solve the original question. However, you are not done. If you look at the answer choices, you must also determine the sufficiency of statement 2.
Statement 2 states: If Sammy’s call to Nate had been 5 minutes longer, it would have cost twice as much. From this information you can infer five times the original equation can be set equal to the original equation, such that:
5 (x – 0.50) = x + (6 – 0.50) (t – 3)

Once again, you can solve this equation for “t.” Therefore, since statement 2 can be used to solve the original question, it, too, is sufficient.
Both statements alone can be used to solve the original equation. Thus, the answer must be D.
A second GMAT example of a data sufficiency question follows.
Is the mean of set S greater than its median?
Statement 1: All members of S are consecutive multiples of 3

Statement 2: The sum of S = 75
[A] Statement 1 alone is sufficient
[B] Statement 2 alone is sufficient but statement 1 alone is insufficient
[C] Both statements together are not sufficient
[D] Statements 1 and 2 alone are sufficient
[E] Statements 1 and 2 are not sufficient
The original statement gives you no information and no equation. Statement 1, on the other hand, tells you all members of S are multiples of 3. If you use an odd number of elements in S (say 3, 6, and 9) then the median of the set will equal its mean (both will equal the middle element). If, however, set S contains an even number of elements (say 3, 6, 9, and 12) the median, as well as the mean of this set, will equal the mean of the two middle elements. Then the mean is NOT greater than the median. Thus statement 1 is sufficient.
Statement two tells you the sum of S is 75. You can choose five 15’s as the set elements and their sum would equal 75. This means the mean is 15 as is their median. However, you can choose another set of elements for S where the mean IS greater than the median. Thus, statement two is insufficient. Thus the answer must be A.
As you can see, the GMAT data sufficiency problems are more complex, more in-depth, and more time-consuming that normal data computation, interpretation, comparison, and analysis. Mastering these requires a continuous exposure to and work with them.
I hope this provides some insight for all GMAT test takers.