Giveaway Data Sufficiency Statements


gmat unicornData sufficiency question are a strange animal that exists only in GMAT land.  The newness of this question type creates high levels of anxiety because we don’t know how to react when we see something new (How do you think you would react if you were standing face to face with a unicorn?).   Once we get over this newness, data sufficiency questions all follow a specific morphology, and in my opinion actually contain less diversity than problem solving questions.  There is always either a yes/no question (is ab even?) or value question (how many boys are in the class?), followed by two statements, and the five answer choice are always the same and in the same order. (If you are completely unfamiliar with data sufficiency questions take a look at an example here)

Because of this very confined structure, there are actually cases where the structure of question and statements can give you information regardless of the specifics of the problem. There are at least four instances where a specific form of the statement(s) will allow you to eliminate several responses without evaluating the full content of the problem.

1) A value statement for a yes/no question

If a statement provides a value for the sole variable in the question, it is definitely sufficient to answer any yes or no question.

For example:

Does the integer x have more than two positive factors?
1) x = 104,381

There is no need to spend time considering the factors of 104,381 or trying to use divisibility rules to see if x is divisible by 3 or 9.  If I know the value of the number, I can answer any yes or no question about that number.  Thus, statement 1 is sufficient (meaning the only possible answers are A or D).  One caveat to this rule is that it only applies if the yes/no question is about a single variable (e.g. is the question was Does xy have more than two positive factors? just knowing the value of x may not be sufficient).


2) The two statements provide the same information.

If the two statements for data sufficiency questions provide the exact same information, the answer is either D or E.

For example

Company X has a total of 400 employees. (additional information in question). What percentage of Company X employees received a raise?

1) 80 of Company X’s employees are managers.
2) 320 of Company X’s employees are not managers.


Given that we know, Company X has a total of 400 employees from the question, it is easy to see that providing the number of managers allows us to calculate the number of non-managers and vice versa.  The statements have told us exactly the same information.  Repeating the same thing twice (even if you do so at a louder volume) does not actually provide any new information. Either this information allows us to answer the question (in which case the answer is D, either statement is sufficient), or the information is not useful (in which case the answer is E, not enough information).  Make sure to assess that the statements do actually provide the same information and you are not assuming information from one statement when considering the other one.


3) Statements that give only relative numbers when the question asks for a magnitude

If only relative numbers are provided in the question, a statement that provides only relative numbers will not be sufficient to answer questions of magnitude.

Company Y’s costs were 75% of its revenues in 2011.  What were Company Y’s profits in 2012?

1) Revenues increased by 1/3 and costs increased by ¼ for Company Y in 2012 relative to 2011.

In the problem above, the question asks about an actual number “ company profits.  In the question and the statements, we are only provided with relative information (i.e. percentages, fractions, and ratios).  You can never answer a question of magnitude based only on relative information.  In the context of this question, when we only know percentage costs and fractional increases year over year, we have no sense of how large this company is.  Is it a hot dog stand on the corner or a multinational corporation?  Thus, we have no potential to answer this question, or any question of magnitude with statement 1 and should eliminate answers A and D.

Be careful because a statement with relative information could be helpful for this question if magnitudes are provided in the question.  Consider statement 1 if question instead read Company Y’s  revenues were 100,000 and its costs were 75% of its revenues in 2011.  What were Company Y’s profits in 2012?


4) Statements that give only angle measures for a geometry problem that asks about size (side length, perimeter, area).

If only angle measure are provided in the question, a statement that provides only angle measure will not be sufficient to answer a geometry question about size (e.g. side length or area).

Line k is parallel to line l. What is the perimeter of quadrilateral wxyz?
(Diagram that includes only information about angles)
1) Angle xyz measures 60 degrees.

This rule is essentially the geometry equivalent to rule 3.  Angle measures don’t tell me anything about the size of a shape.  Even give all three angle measures of a triangle that triangle could be microscopic or the face of one the great pyramids.  You cannot answer any question relating to the size of a shape (side length, perimeter, area, etc.) given only angle measures.  Thus, in this question, I would immediately eliminate answers A and D because statement 1 is not sufficient.

The same caveat applies as in rule 3.  If, for example, the diagram included some information about the size of the shape, such as one or more side lengths, the angle information provided in the statement could be sufficient to answer the question.

In a broader sense, understanding the meaning of these four statements is about recognizing the repetition and patterns present on the GMAT.  As your recognition grows, you should feel you are not always starting from ground zero when you see a new GMAT problem, rather you can apply some of the logic or lessons from prior problems you have done.  As you continue you doing GMAT practice problems, consider for yourself other common question and statement types that should inform your potential answers.

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