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## Can Two Data Sufficiency Statements Contradict Each Other?

###### October 20, 2010

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A GMAT Data Sufficiency problem is like solving a mystery. Just as there is one solution to a murder mystery, so there is only one answer to a DS question. Like detectives, you may never find it, but there is a single correct conclusion.

Here's a simple example of a GMAT DS problem that is invalid:

What is the value of n?
(1) n is prime.
(2) n = 6

Technically, I suppose, you could solve such a problem: (1) is insufficient (n could be any prime number), and (2) is sufficient. You don't have any reason to combine the statements. But if you did, you'd discover a contradiction: 6 is not prime.

Rest assured, you won't be confronted by such a scenario on the GMAT.

Strategic Value

It doesn't do you much good to know what won't be on the test. But in this case, you can use the guideline to your advantage.

Let's take another simple example:

What is the value of x?
(1) x is negative.
(2) x^2 = 36

Statement (2) is one of the oldest traps in the book. Let's say you fall for the trap.

If you did, you first realize that (1) is insufficient. Then you decide that (2) asserts that x = 6 (forgetting it can also be -6), conclude that (2) is sufficient, and select answer choice (B).

But wait! If you're alert, you realize that x = 6 contradicts the first statement, that x is negative. You remember the rule--DS statements cannot contradict each other--and review the question. You recall that x could be 6 or -6 and change your answer to (C).

If you completely and flawlessly analyze every Data Sufficiency statement on every GMAT question, you'll never need to know that the statements cannot contradict each other. But if you're like most of us, you'll need to take advantage of a backup plan every now and again.

About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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