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Data Sufficiency

Data Sufficiency

GMAT math data sufficiency
Data Sufficiency (DS) questions use the same math concepts as Problem Solving questions, but ask a unique type of question that many students initially find confusing. DS questions ask you a question, usually but not always accompanied by some initial information, followed by two statements labeled (1) and (2) which contain additional information. Your objective is to determine whether statements (1) and/or (2) separately or combined provide enough (i.e. sufficient) information to derive one definitive answer to the initial question. Other than the information explicitly stated, you cannot assume anything besides indisputable facts (e.g. there are 60 minutes in an hour).

Answer Choices on Data Sufficiency

DS questions always present the same five answer choices. In order to save time, it is best to memorize these answer choices rather than read them each time you face a DS question. A helpful acronym by which to memorize the answers is 12TEN.

        (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
        (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
        (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
        (D) EACH statement ALONE is sufficient.
        (E) Statements (1) and (2) TOGETHER are not sufficient.

In evaluating whether the statements provide sufficient information, you should first consider the information in (1), without taking the information in (2) into account. Then you should consider the information in (2), making sure to ignore the information in (1) that you just evaluated. Only if (1) by itself is not sufficient and (2) by itself is not sufficient, you should then evaluate sufficiency using (1) and (2) in combination. Consider the following answer elimination flowchart:

Data Sufficiency flowchart

How to Approach Data Sufficiency

When evaluating sufficiency, the key is to determine whether it is possible to derive one definitive answer to the question asked. There are two broad types of DS questions: numerical value and Yes/No.
  • For numerical value questions (e.g. What is the value of x?), you must be able to derive one exact number (e.g. x = 37) to have sufficient information. If you could come up with multiple numbers or a range of values, you do not have sufficient information.
  • As the name implies, Yes/No questions (e.g. Does x = 37?) can be answered only with a yes and/or a no (e.g. yes, x does equal 37). For these questions, you must be able to answer definitely yes or definitely no to have sufficient information.
There are two broad approaches to DS questions.
  • The often-faster, more theoretical approach entails offering a mathematical justification. For example, one general algebraic principle is that if you have an equal number of unique linear equations as you have unknowns, then you can solve for the unknowns. In this case, you do not actually have to solve out the equations; merely knowing that you could solve them and derive a unique answer is all that matters.
  • A second approach entails plugging in numbers. You try different numbers that meet any given constraints to check whether those different numbers could yield different answers or always yield the same answer to the question asked.

Sample GMAT Data Sufficiency Problem

In order to help make this more concrete, let’s try a sample problem. Attempt the problem on your own before viewing the answer and explanation.

If a, b, and c are positive integers, is (a + c)(b + c) an odd integer?

        (1) a is odd
        (2) b is even

See above for answer choices.

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