Quick Concept Summary
In data sufficiency, you are NOT asked to solve a problem completely. You are asked to decide whether the given information is enough to answer the question.
Answer Choices (standard format):
- (A) Statement 1 alone is sufficient; Statement 2 alone is not.
- (B) Statement 2 alone is sufficient; Statement 1 alone is not.
- (C) Both statements together are sufficient; neither alone is.
- (D) Each statement alone is sufficient.
- (E) Neither statement alone nor both together are sufficient.
Method — Always Follow This Order
1. Read the question — identify what you need to find. 2. Test Statement 1 alone — can you uniquely determine the answer? Mark: sufficient / not sufficient. 3. Test Statement 2 alone — same check. 4. If both were insufficient alone, test them together. 5. Stop as soon as you have the answer — do not over-solve.
Key rule: A statement is sufficient only if it gives one unique answer. If there are two or more possible answers, it is NOT sufficient.
Worked Examples
Example 1 — Basic
Question: What is the value of x?
- Statement 1: x + 2 = 8
- Statement 2: x is an even number
Analysis:
- Statement 1: x = 6 — unique answer → Sufficient
- Statement 2: x could be 0, 2, 4, 6, 8, … — not unique → Not sufficient
Example 2 — Geometry
Question: What is the area of rectangle ABCD?
- Statement 1: The perimeter of ABCD is 40 cm.
- Statement 2: The length of ABCD is 12 cm.
Analysis:
- Statement 1: P = 2(l + b) = 40 → l + b = 20. Multiple combinations possible (12+8, 15+5, 10+10, …) → Area not unique → Not sufficient
- Statement 2: l = 12, but breadth unknown → Area = 12 × b → not unique → Not sufficient
- Both together: l = 12, l + b = 20 → b = 8 → Area = 12 × 8 = 96 cm² → Sufficient
Example 3 — Number Problem
Question: Is x > 0?
- Statement 1: x² = 25
- Statement 2: x³ = 125
Analysis:
- Statement 1: x = 5 or x = −5 → cannot determine sign → Not sufficient
- Statement 2: x³ = 125 → x = 5 (cube root is unique for real numbers) → x > 0 → Sufficient
Example 4 — Age Problem
Question: What is Ravi's age?
- Statement 1: Ravi is 5 years older than Priya.
- Statement 2: Priya is 15 years old.
Analysis:
- Statement 1: Ravi = Priya + 5, but Priya's age unknown → Not sufficient
- Statement 2: Priya = 15, but Ravi's age not connected → Not sufficient
- Both together: Ravi = 15 + 5 = 20 → Sufficient
Example 5 — Both Sufficient Independently
Question: What is the value of n, given n is a positive integer?
- Statement 1: 2n = 14
- Statement 2: n + 3 = 10
Analysis:
- Statement 1: n = 7 → Sufficient
- Statement 2: n = 7 → Sufficient
Practice Questions
Q1. Is the integer p divisible by 6?
- Statement 1: p is divisible by 2.
- Statement 2: p is divisible by 3.
Q2. What is the value of a + b?
- Statement 1: a − b = 4
- Statement 2: a = 2b
Q3. A train covers a certain distance. What is the speed of the train?
- Statement 1: The train covers the distance in 3 hours.
- Statement 2: The distance is 240 km.
Q4. Is triangle ABC equilateral?
- Statement 1: AB = BC
- Statement 2: BC = CA
Q5. What is 20% of N?
- Statement 1: 10% of N is 45.
- Statement 2: N is a multiple of 450.
Q6. How many students are in Class 6?
- Statement 1: Class 6 has 10 more students than Class 5.
- Statement 2: The total students in Class 5 and Class 6 together is 80.
Common Mistakes
- Combining statements prematurely — always test each statement alone first
- Assuming extra information not given in the statements
- Not checking uniqueness — a statement is sufficient only if it gives exactly one answer
- Over-solving — once you know it's sufficient, stop; you don't need the final numerical answer
- Treating "probably true" as "always true" — look for exceptions
Revision Checklist
- [ ] Know the 5 standard answer choices and what each means
- [ ] Always test Statement 1 alone, then Statement 2 alone, then both together
- [ ] A statement is sufficient only when it gives a unique answer
- [ ] For "Is X true?" questions, sufficiency means the answer is definitively yes OR definitively no
- [ ] Never bring outside assumptions into your analysis