Data Sufficiency questions are a unique and sometimes intimidating part of the GMAT’s Data Insights section. While they require math skills, the heart of these questions isn’t so much about calculating a numeric value, but rather deciding whether an answer can be determined with the information given. This subtle shift can trip up test takers, but once you understand the format and approach, these questions become much more manageable.
What Do Data Sufficiency Questions Assess?
In Data Sufficiency questions, you’re not asked to solve for a specific value. Instead, you’re tasked with figuring out whether the given information (in the form of two statements) provides enough data to solve the problem. Each question is framed with a question stem followed by two numbered statements.
Your goal? Determine whether:
- Statement 1 alone is sufficient.
- Statement 2 alone is sufficient.
- Both together are needed.
- Neither provides enough data.
In essence, it’s about determining whether you COULD find the solution, not actually working out the solution.
The Five Answer Choices: What They Mean
Data Sufficiency questions always offer the same five answer choices:
(A): Statement 1 alone is sufficient, but statement 2 alone is not.
(B): Statement 2 alone is sufficient, but statement 1 alone is not.
(C): Both statements together are sufficient, but neither alone is sufficient.
(D): Each statement alone is sufficient.
(E): Neither statement is sufficient, even when combined.
These answer choices require careful analysis of the statements, individually and together, to decide whether you can derive the needed information.
How to Approach Data Sufficiency Questions
Understand the question: Make sure you’re clear about what’s being asked. Are you solving for a value, a relationship, or some other mathematical property?
Evaluate each statement independently: First, examine Statement 1 on its own; don’t bring in any information from Statement 2. Can you answer the question with this information? Then, evaluate Statement 2 on its own. Again, resist the urge to combine it with the first statement.
Consider both statements together: If neither statement alone provides enough information, see if the two statements combined allow you to solve the problem.
Select the best answer: Based on your analysis of the statements, choose the appropriate answer from the five options.
Worked Example #1
Question: What is the value of y?
Statement 1: y = 2x
Statement 2: x = 5
Step-by-step breakdown:
Statement 1 alone: Knowing that y = 2x gives us a relationship between x and y, but without a specific value for x, we can’t determine the exact value of y. Thus, Statement 1 alone is insufficient.
Statement 2 alone: Knowing that x = 5 gives us a specific value for x, but we have no information about y. This statement alone is also insufficient, but this is exactly the step in which test takers might be tempted to combine the two statements prematurely.
Combining both statements: Statement 1 gives us the equation y = 2x, and Statement 2 provides x = 5. If we have a value for x, we can substitute that value into the first equation, which would allow us to find the value of y. Therefore, the two statements together are sufficient.
Answer: (C) Both statements together are sufficient, but neither alone is sufficient. Note that we could go one step further and determine that y = 10, but we’ve accomplished our goal by determining that we COULD find the value of y with both statements combined.
Worked Example #2
Question: Is x an integer?
Statement 1: x2 is an integer.
Statement 2: x3 is an integer.
Step-by-step breakdown:
Statement 1 alone: x2 is an integer. This means that squaring x results in an integer. However, this does not guarantee that x itself is an integer. For example, if x = √2, then x2 = 2, which is an integer, but x is not an integer. Therefore, Statement 1 alone is insufficient.
Statement 2 alone: x3 is an integer. Similar to the reasoning with squares, knowing that the cube of x is an integer does not ensure that x itself is an integer. For instance, x = ∛2 would give x3 = 2, which is an integer, but x is not an integer. Therefore, Statement 2 alone is insufficient.
Combining both statements: Let’s analyze what happens when both statements are used together.
- Statement 1 tells us that x2 is an integer, meaning that x could be either an integer or a rational number where squaring the number results in an integer.
- Statement 2 tells us that x3 is an integer, meaning that cubing x results in an integer.
- Consider what happens if x is rational but not an integer. For example, if x = 1/2, then x2 = 1/4, which is not an integer, and x3 = 1/8, also not an integer. However, the only numbers where both x2 and x3 are integers are integers themselves. Non-integer rational numbers or irrational numbers would not satisfy both conditions. Thus, the two statements together are sufficient to conclude that x must be an integer.
Answer: (C) Both statements together are sufficient, but neither alone is sufficient.
Key Takeaways for Tackling Data Sufficiency Questions:
- Don’t solve: Your task is to determine if the information is enough to solve, not to actually solve the problem.
- Work systematically: Always start by evaluating each statement independently before combining them.
- Be wary of traps: Some statements might seem sufficient but can mislead you if you don’t thoroughly analyze all possibilities.
- Practice, practice, practice: With repetition, the structure of these questions will become more familiar, and you’ll develop a stronger instinct for assessing sufficiency.
Conclusion
Mastering Data Sufficiency on the GMAT can save you time and improve your score, as it emphasizes logical reasoning as much as math skills. By focusing on the process of analysis rather than solution, you’ll be better equipped to handle this type of question confidently and effectively. If you’re looking for more help with Data Sufficiency questions (or any other section of the GMAT), click here to learn more about Mindfish’s GMAT prep programs or reach out to our Admin team today at (720) 204-1041 or admin@mindfish.com.
