Data Sufficiency
What you'll learn
- Understand what it means for data to be "sufficient" to answer a question
- Apply the 5 standard answer choices correctly
- Evaluate each statement independently before combining them
- Avoid the common trap of solving the problem instead of testing sufficiency
Key concepts
What is Data Sufficiency?
In a Data Sufficiency problem, you are given a question followed by two statements (Statement I and Statement II). You must decide whether the given statements provide enough information to answer the question definitively — you do NOT need to actually find the answer.
Key insight: The question is "Can this be answered?" not "What is the answer?" A statement is sufficient if it leads to exactly one answer — not two or more possibilities.
The 5 Standard Answer Choices
| Option | Meaning |
|---|---|
| (A) | Statement I alone is sufficient, but Statement II alone is not. |
| (B) | Statement II alone is sufficient, but Statement I alone is not. |
| (C) | Both statements together are sufficient, but neither alone is. |
| (D) | Either statement alone is sufficient (both independently work). |
| (E) | Neither statement alone nor both together are sufficient. |
Memorize these options. They are fixed in every data sufficiency question. The same 5 choices appear every time.
The Approach: 3-Step Method
Step 1: Read the question and identify what you need to determine. Step 2: Test Statement I alone. Can the question be answered? Mark S (Sufficient) or NS (Not Sufficient). Step 3: Test Statement II alone. Mark S or NS. Then combine: If both are NS alone, test them together.
Decision table:
| Stmt I | Stmt II | Answer |
|---|---|---|
| S | S | (D) |
| S | NS | (A) |
| NS | S | (B) |
| NS | NS | Test together → if S: (C), if NS: (E) |
Worked Example 1 (Number problem)
Question: Is x an even number?
Statement I: x is divisible by 4. Statement II: x + 1 is odd.
Test Statement I alone: Any number divisible by 4 is also divisible by 2, so it is even. → Sufficient (S)
Test Statement II alone: If x + 1 is odd, then x is even (even + 1 = odd). → Sufficient (S)
Both work independently → Answer: (D)
Worked Example 2 (Age problem)
Question: How old is Karan?
Statement I: Karan is 5 years older than his sister. Statement II: His sister is 12 years old.
Test Statement I alone: We know the difference but not either age. → Not Sufficient (NS)
Test Statement II alone: Sister = 12, but we don't know Karan's age without Statement I. → Not Sufficient (NS)
Test both together: Sister = 12, Karan = 12 + 5 = 17. Definite answer. → Sufficient together
Answer: (C)
Worked Example 3 (Geometry)
Question: What is the area of a rectangle?
Statement I: The perimeter of the rectangle is 40 cm. Statement II: The length is twice the breadth.
Test Statement I alone: Perimeter = 2(l + b) = 40 → l + b = 20. Many combinations (10+10, 15+5...). → NS
Test Statement II alone: l = 2b. But we don't know actual values. → NS
Test both together: l = 2b and l + b = 20 → 2b + b = 20 → b = 6.67, l = 13.33. Unique values → area = unique. → Sufficient
Answer: (C)
Common Mistakes to Avoid
| Mistake | Why it's wrong |
|---|---|
| Using information from Statement II while testing Statement I | Statements must be tested independently first |
| Confusing "can be determined" with "I know the value" | You must determine it uniquely from the data |
| Choosing (E) just because the numbers are ugly | If a unique answer exists (even a fraction), the data is sufficient |
| Forgetting to test statements TOGETHER when both are NS | The combination may still be sufficient |
Special Cases
- Inequality questions: "Is x > 5?" — sufficient only if ALL values allowed by the statements are either ALL > 5 or ALL ≤ 5.
- Yes/No questions: Data is sufficient if the answer is always "yes" OR always "no" — not sometimes one and sometimes the other.
Tip for yes/no questions: If Statement I gives "always yes" → sufficient. If it sometimes gives "yes" and sometimes "no" → NOT sufficient.
Quick check
- Question: Is n divisible by 6? Stmt I: n is divisible by 3. Stmt II: n is divisible by 2. Which answer choice applies?
- Question: What is the value of y? Stmt I: y² = 25. Stmt II: y > 0. Which answer choice applies?
- Question: What is the area of a square? Stmt I: Its perimeter is 36 cm. Is Stmt I alone sufficient?
- When is answer choice (E) selected?
- What is the critical difference between solving the problem and testing for sufficiency?
Open the Practice tab for graded questions on Data Sufficiency.
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