DAT Quantitative Reasoning: The Statement Sufficiency Answer System

DAT High-Yield Concept

Standard Answer Order: The 5 answer choices always appear in a fixed sequence: statement (1) alone, statement (2) alone, both together but neither alone, each statement alone, and neither statement even together.
Sufficiency vs. Calculation: A statement is sufficient if it guarantees a unique answer (a single numeric value or a definitive "Yes" or "No"), even if you do not calculate the exact final figure.
Stop Calculating Early: Once mathematical determinability is confirmed, stop working immediately to preserve time on the DAT Quantitative Reasoning section.
Non-Contradictory Facts: Statements (1) and (2) are always true facts that never contradict each other; evaluate statement (1) independently before looking at statement (2).

1. The Fixed Five Sufficiency Choices

Data Sufficiency questions on the DAT follow a standardized structure. You are presented with a question stem followed by two mathematical statements, labeled (1) and (2). Your task is not to compute a final numerical answer for its own sake, but to determine which statement provides enough information to solve the problem. The five multiple-choice options always follow this exact fixed sequence:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient (neither statement is sufficient even together).

Mnemonic Aid — 12TEN: Remember the fixed choices in order as 1 (statement 1 alone), 2 (statement 2 alone), T (together), E (each alone), and N (neither even together).

Choice	Statement (1) Alone	Statement (2) Alone	Combined Requirements
1 (A)	Sufficient	Not Sufficient	Not evaluated together
2 (B)	Not Sufficient	Sufficient	Not evaluated together
3 (C)	Not Sufficient	Not Sufficient	Sufficient when combined
4 (D)	Sufficient	Sufficient	Not needed together
5 (E)	Not Sufficient	Not Sufficient	Still Not Sufficient combined

2. Sufficiency Meaning: Determinability vs. Computation

Core Definition: A statement is sufficient when it uniquely determines the answer to the question stem. For value questions, sufficiency requires exactly one numeric outcome. For Yes/No questions, sufficiency requires a definitive Yes or a definitive No.

Sufficiency means a statement determines the answer rather than that it hands you the answer directly. If a statement allows you to set up a linear equation with one variable, such as $5x - 7 = 18$ , you know that a single unique value for $x$ exists without completing the arithmetic. Conversely, if a statement leads to two distinct possible outcomes (such as $x = 5$ or $x = -5$ ), the statement is insufficient.

Worked Example: Value Question

Question: What is the value of $x$ ?

Statement (1): $3x + 15 = 45$

Statement (2): $x^2 = 100$

Step-by-Step Solution:

Evaluate Statement (1) alone: Solving $3x + 15 = 45$ yields $3x = 30$ , so $x = 10$ . Statement (1) gives a single, unique numeric value for $x$ . Statement (1) alone is sufficient.
Evaluate Statement (2) alone: Solving $x^2 = 100$ yields two possible real roots: $x = 10$ or $x = -10$ . Because $x$ could be positive or negative (a concept tied to picking test values across ranges like $x < 0$ , $0 < x < 1$ , and $x > 1$ , which is covered in depth in its own lesson), Statement (2) does not determine a single value. Statement (2) alone is not sufficient.

Conclusion: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Common Exam Trap: Spending valuable time calculating the arithmetic to the end in Statement (1), or assuming $x^2 = 100$ implies only $x = 10$ by forgetting the negative square root.

3. Stopping Early and Non-Contradictory Fact Rules

Golden Rules of Data Sufficiency:

Stop early: Stop the instant you verify that a single solution can be determined. Do not waste precious test seconds carrying arithmetic all the way out.
Fact consistency: Both statements are given as indisputable truths. They will never contradict each other or the question stem.

When evaluating Statement (1), treat Statement (2) as though it does not exist. Only if Statement (1) and Statement (2) are individually insufficient should you combine them. When combined, both statements remain true simultaneously.

Worked Example: Yes/No Question and Stopping Early

Question: Is $y$ an even integer?

Statement (1): $y = 2k$ where $k$ is an integer.

Statement (2): $y = 4m + 6$ where $m$ is an integer.

Step-by-Step Solution:

Evaluate Statement (1) alone: By definition, any integer multiplied by $2$ is even. Thus, Statement (1) guarantees that $y$ is even. The answer to the question stem is a definitive "Yes". Statement (1) alone is sufficient.
Evaluate Statement (2) alone: Factoring out $2$ yields $y = 2(2m + 3)$ . Because $m$ is an integer, $2m + 3$ is an integer, so $y$ is a multiple of $2$ . Statement (2) also yields a definitive "Yes". Stop here without plugging in sample values for $m$ . Statement (2) alone is sufficient.

Conclusion: Each statement ALONE is sufficient.

Common Exam Trap: Selecting "Both statements together" (Choice 3) simply because both statements lead to a "Yes" answer, or erroneously believing that a "No" answer means insufficient. A statement that definitively proves "No" is fully sufficient!

DAT Critical Thinking Questions

If a statement yields a definitive "No" to a question stem such as "Is $x > 0$ ?", why is that statement considered mathematically sufficient rather than insufficient?
Why is it a logical violation on Data Sufficiency questions to use information from Statement (2) while assessing whether Statement (1) alone is sufficient?
If Statement (1) narrows a variable down to $x = 4$ and Statement (2) narrows it down to $x = 4$ or $x = -4$ , why is Choice 1 correct rather than Choice 3?

References

Sources returned by Google Search grounding during lesson verification.

Data Sufficiency and Quantitative Comparison for the DAT — shemmassianconsulting.com
How Data Sufficiency Works - Manhattan Prep — manhattanprep.com

The Statement Sufficiency Answer System

Summary

Practice Questions

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