How to Solve Data Sufficiency Questions (GRE/GMAT) – Complete Guide

How to Solve Data Sufficiency Questions (GRE/GMAT) – Complete Guide

Score Impact: This question type appears 6-8 times on every GMAT (and 3-4 times on the GRE Quantitative section). Mastering it can boost your Quant score by 30-50 points—enough to move you from the 60th to the 80th percentile or higher.

WHAT THIS QUESTION TYPE IS ACTUALLY TESTING

Data Sufficiency (DS) is not a math test—it’s a decision-making test disguised as math. The examiner is probing for:

1. Logical Precision – Can you determine exactly what information is needed to answer a question, no more, no less?
2. Trap Recognition – Can you spot when a condition seems sufficient but isn’t (e.g., giving a ratio when you need a value)?
3. Efficiency Under Pressure – Can you make the right call in 90 seconds or less without overcomputing?

ANATOMY OF THE QUESTION

Structure Breakdown

1. Stem (Question Prompt) – A math question (e.g., "What is the value of x?").
2. Conditions (Statements 1 & 2) – Two separate pieces of information (e.g., "x > 5" and "x² = 36").
3. Answer Choices (Always the Same) –
4. (A) Statement 1 alone is sufficient.
5. (B) Statement 2 alone is sufficient.
6. (C) Both statements together are sufficient.
7. (D) Each statement alone is sufficient.
8. (E) Neither statement is sufficient.

What to Ignore

• Overcomputing – You don’t need to solve for the exact value unless the question asks for it.
• Assumptions – Never assume a variable is an integer unless stated.
• Red Herrings – Some conditions look helpful but are irrelevant (e.g., "x is positive" when the question is about x²).

Representative Example

Question: What is the value of x? 1. x² – 5x + 6 = 0 2. x is a positive integer.

Answer Choices: (A) Statement 1 alone is sufficient. (B) Statement 2 alone is sufficient. (C) Both statements together are sufficient. (D) Each statement alone is sufficient. (E) Neither statement is sufficient.

THE DECISION FRAMEWORK (Step-by-Step)

Run this process every single time. No exceptions.

Step 1: Read the Stem First

• Action: Underline the exact question (e.g., "What is the value of x?").
• Why? Ensures you know what you’re solving for before looking at the conditions.

Step 2: Evaluate Statement 1 Alone

• Action: Cover Statement 2. Ask: "Can I answer the question with only this information?"
• If YES → Eliminate (B), (C), (E). Keep (A) and (D).
• If NO → Eliminate (A) and (D). Keep (B), (C), (E).

Step 3: Evaluate Statement 2 Alone

• Action: Cover Statement 1. Ask: "Can I answer the question with only this information?"
• If YES → Eliminate (A), (C), (E). Keep (B) and (D).
• If NO → Eliminate (B) and (D). Keep (A), (C), (E).

Step 4: Combine Statements (If Needed)

• Action: If neither statement alone is sufficient, ask: "Do the statements together give me a unique answer?"
• If YES → Choose (C).
• If NO → Choose (E).

Step 5: Confirm No Overlap

• Action: Double-check that you didn’t miss a case where one statement implies the other (e.g., Statement 1 gives x = 2 or 3, Statement 2 says x is odd → together, x = 3).

Worked Examples

Example 1 – Straightforward

Question: What is the value of x? 1. x + 3 = 7 2. 2x = 8

Process: 1. Stem: "What is the value of x?" → Need a single value. 2. Statement 1: x + 3 = 7 → x = 4 (sufficient alone). Eliminate (B), (C), (E). 3. Statement 2: 2x = 8 → x = 4 (sufficient alone). Eliminate (A). 4. Answer: (D) Each statement alone is sufficient.

Example 2 – Common Trap (Ratio vs. Value)

Question: What is the value of x? 1. x/y = 3/4 2. y = 8

Process: 1. Stem: "What is the value of x?" → Need a single value. 2. Statement 1: x/y = 3/4 → x = (3/4)y (not sufficient alone; y is unknown). Eliminate (A), (D). 3. Statement 2: y = 8 → Alone, no info about x. Eliminate (B). 4. Combine: x = (3/4)(8) = 6 (sufficient). Answer: (C).

Trap: Students see y = 8 and assume x is solvable without combining. Always check if the other variable is needed!

Example 3 – Hard Variant (Quadratic + Constraint)

Question: What is the value of x? 1. x² – 5x + 6 = 0 2. x is a positive integer.

Process: 1. Stem: "What is the value of x?" → Need a single value. 2. Statement 1: x² – 5x + 6 = 0 → (x-2)(x-3) = 0 → x = 2 or 3 (not sufficient alone). Eliminate (A), (D). 3. Statement 2: x is a positive integer → Alone, infinite possibilities (1, 2, 3, ...). Eliminate (B). 4. Combine: x = 2 or 3 (both positive integers). Still not unique. Answer: (E).

Why (E)? The question asks for the value of x, but we have two possible values. Never assume uniqueness unless proven!

WRONG ANSWER PATTERNS

Common Mistakes

TIME STRATEGY

• Target Time: 90 seconds per question.
• When to Skip: If you’re stuck after 2 minutes, flag and move on.
• Minimum Work Needed:
• Read the stem.
• Test Statement 1 (30 sec).
• Test Statement 2 (30 sec).
• Combine if needed (30 sec).
• Pro Tip: If both statements are identical (e.g., x = 5 and x = 5), the answer is (D).

BACKSOLVING AND SHORTCUTS

1. Plug in Numbers – If a statement gives a ratio (e.g., x/y = 2), pick numbers (e.g., x = 2, y = 1) to test sufficiency.
2. Eliminate First – If Statement 1 is insufficient, eliminate (A) and (D) immediately.
3. Look for Contradictions – If statements conflict (e.g., x > 5 and x < 3), the answer is (E).
4. Avoid Algebra When Possible – For inequalities, test boundary values (e.g., x ≥ 0 → test x = 0 and x = 1).

1-Minute Recap

"Here’s the deal: Data Sufficiency is a decision game, not a math test. Every time, follow these steps: 1. Read the stem first—know exactly what you’re solving for. 2. Test Statement 1 alone. If it gives a unique answer, eliminate (B), (C), (E). 3. Test Statement 2 alone. If it works, eliminate (A), (C), (E). 4. If neither works alone, combine them. If they give a unique answer, pick (C). If not, pick (E). That’s it. No overcomputing, no assumptions. Stick to the framework, and you’ll get 6-8 more points on test day. Now go practice—timed!

Final Note

Data Sufficiency rewards discipline, not genius. The students who score highest aren’t the best at math—they’re the best at not falling for traps. Use this framework on every question, and you’ll see your Quant score climb.