Avoiding a Data Sufficiency Hangover

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This tip for improving your GMAT score was provided by David Newland at Veritas Prep.

After a hard day of GMAT testing, you might find yourself sporting a “data sufficiency hangover.” But there are ways to avoid this condition.
Data Sufficiency Hangover: When you fail to clear your mind between statements and wind up carrying over some of the information from one statement (usually statement 1) into your analysis of the other statement (usually statement 2).

As an example, let’s use the following problem, from the Veritas Prep Data Sufficiency book:

Is Integer k a Prime Number?
(1) k = 10! + m, where 1 (2) k is a multiple of 7

Statement 1 can be daunting for some students. Even if you are comfortable with factorials, there is still the matter of what “m” equals. Let’s break it down into a number of logical steps.

First, understand what 10! means. This is 10 factorial, which means 10 multiplied by each subsequent smaller number. So 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1.

Second, determine that the variable “m” must be an integer. You know this because “k” is an integer and 10! is an integer. So “m” must be an integer in order for “10! + m” to be an integer.

Third, now that you know that “m” is an integer you can list the possible values. “m” can equal 2, 3, 4, 5, 6, or 7. It cannot equal 1 or 8 since the inequality excludes those values.

Fourth, use the possible values of “m” to determine whether k can be a prime number. Let’s start with the smallest possible value of “m.” If “m = 2” then “k” will not be a prime number because “10!” is already a multiple of “2” so adding “2” will maintain the cycle of multiples. (You know that 10! Is a multiple of 2 because 2 is one of the numbers that are multiplied together to equal 10!).

The same result occurs if you have “m = 3.” “10!” is already a multiple of 3, and if you add 3 you will still have a multiple of 3. The same is true for 4, 5, 6, and 7. “10!” is already a multiple of each of these numbers. So it does not matter which value we use for “m” in every case “10! + m” is NOT a prime. Therefore “k” is not prime and statement 1 is sufficient.

The Hangover
This is when the hangover can occur. You have just been working with “10!” – a really large number. Now you come to statement 2, which is much simpler than statement 1. As you begin to work with statement 2 you may still have a residue of statement 1 in your mind. This is probably why the test writers tend to place the more complicated statement first, so that you will mistakenly carry some information over to the second statement.

In this case the carry over is as simple as thinking that you are still dealing with very large numbers. (This is something that can happen to even the most talented test-takers). Statement 2 simply says, “K is a multiple of 7.” If you are still thinking about large numbers then you make the assumption that “k” is a big multiple of 7 and therefore not prime. So you might mistakenly choose answer choice D, thinking that statement 2 was sufficient as well.

But, of course, statement 2 does not say that “k” has to be a large number. “K” could be 7, which is a multiple of 7 and is a prime number. Or “k” could be 14, which is not prime. So statement 2 is not sufficient and the answer is A.

Avoiding the Hangover

It is a tragedy to do all of that work on statement 1, just to have a hangover on statement 2. There are some things that you can do to avoid the hangover.

1) Evaluate the “easier” or “more obvious” statement first. Sometimes it is better to begin with statement 2 when that statement is less complicated. Since I began advising students in my classes to begin with statement 2 on this question the number of people choosing the trap answer “D” has fallen.

Working with the less complicated statement first is often a good idea anyway as this can help you to get in to the problem and help you to guess from fewer choices if that becomes necessary.

2) Clear the mechanism between statements. Take a second or two, perhaps even say, “Clear the mechanism” and purge your mind of the information that is specific to the other statement.

3) Use your pen! If you keep track of where the information came from it is easier to know what to use with each statement. Carefully note the information that comes from the question stem – and can be used with each statement – and the information that is specific to a particular statement.
A data sufficiency hangover is bad for your GMAT score, but fortunately it can be avoided if you take the proper precautions!

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