Data Sufficiency

1. What It Is

  • Data Sufficiency problems test your ability to decide if given statements provide enough information to answer a question.
  • You do not need to solve the question fully—just determine whether the data is sufficient.

Key Idea:

  • Question is given.
  • One or more statements are provided.
  • Decide which statements alone or together are enough to answer.

2. How to Approach

  1. Read the question carefully – know exactly what you are asked.
  2. Examine each statement separately – see if it alone is enough.
  3. Combine statements if needed – check if together they give a solution.
  4. Do NOT assume anything not given – use only provided info.
  5. Select the answer from standard options:
    1. Statement 1 alone is sufficient
    2. Statement 2 alone is sufficient
    3. Both together sufficient, neither alone
    4. Either statement alone sufficient
    5. Even both together are not sufficient

3. Rules & Key Points

  • Focus only on sufficiency, not solving the exact value.
  • Use statements one by one first, then together.
  • Do not assume patterns unless explicitly given.
  • Always check for multiple possibilities – if more than one answer possible → insufficient.

4. Tricks & Shortcuts

  1. Always check each statement independently.
  2. Use yes/no or numeric approach depending on the question type.
  3. Combine statements only if neither alone is sufficient.
  4. Watch out for trick statements – e.g., partial data, conditions, ranges.
  5. Memorize the standard answer codes:
CodeMeaning
1Statement 1 alone sufficient
2Statement 2 alone sufficient
3Both together sufficient, neither alone
4Either statement alone sufficient
5Even both together insufficient

5. Types of Questions

  1. Arithmetic / Numbers – find a value, sum, or product.
  2. Algebra / Age Problems – find age, difference, or ratio.
  3. Geometry / Shapes – find area, perimeter, angles.
  4. Logic / Comparisons – rank, order, or arrangement.
  5. Miscellaneous – any problem requiring combining statements for sufficiency.

6. Stepwise Solving Strategy

  1. Identify what exactly is asked.
  2. Check Statement 1 alone – sufficient or not?
  3. Check Statement 2 alone – sufficient or not?
  4. Check both statements together – sufficient or not?
  5. Decide final answer code.

7. Practice Questions – Easy Examples

Question 1 (Arithmetic)

Question: What is the value of x?

  1. x + 5 = 12
  2. 2x = 14

Solution:

  • Statement 1 → x = 12 – 5 → x = 7 ✅ sufficient
  • Statement 2 → 2x = 14 → x = 7 ✅ sufficient
  • Answer: Either alone sufficient → Code 4

Question 2 (Age)

Question: What is A’s age?

  1. A is 4 years younger than B.
  2. B is 10 years old.

Solution:

  • Statement 1 alone → Age of A unknown (B’s age unknown) ❌ insufficient
  • Statement 2 alone → Age of A unknown (A’s difference unknown) ❌ insufficient
  • Both together → A = B – 4 = 10 – 4 = 6 ✅ sufficient
  • Answer: Both together sufficient → Code 3

Question 3 (Numbers)

Question: Is x > 10?

  1. x + 5 = 20
  2. x – 2 = 12

Solution:

  • Statement 1 → x = 15 → Yes ✅ sufficient
  • Statement 2 → x = 14 → Yes ✅ sufficient
  • Answer: Either alone sufficient → Code 4

Question 4 (Logic/Comparison)

Question: Who is taller, A or B?

  1. C is taller than A.
  2. B is taller than C.

Solution:

  • Statement 1 → Cannot compare A & B ❌
  • Statement 2 → Cannot compare A & B ❌
  • Both together → B > C > A → B taller ✅ sufficient
  • Answer: Both together sufficient → Code 3

Question 5 (Difficult)

Question: What is the value of y?

  1. y² – 5y + 6 = 0
  2. y is a positive integer

Solution:

  • Statement 1 → y² – 5y + 6 = 0 → y = 2 or 3 ❌ multiple values → not sufficient
  • Statement 2 → Alone → nothing known ❌
  • Both together → y = positive integer → y = 2 or 3 → still not unique ❌
  • Answer: Even together insufficient → Code 5

✅ Quick Tips

  1. Always read question carefully – know what is asked.
  2. Test each statement independently first.
  3. Combine only when necessary.
  4. Watch for multiple solutions → insufficient.
  5. Remember the answer codes by heart.

Data Sufficiency – Practice Questions with Solutions

Easy Questions

1. Arithmetic / Numbers

Question: What is x?

  1. x + 7 = 15
  2. 3x = 24

Solution:

  • Statement 1 → x = 15 – 7 = 8 ✅ sufficient
  • Statement 2 → x = 24 ÷ 3 = 8 ✅ sufficient
  • Answer: Either alone sufficient → Code 4

2. Age Problem

Question: What is A’s age?

  1. B is 5 years older than A.
  2. B is 12 years old.

Solution:

  • Statement 1 alone → Age of A unknown ❌
  • Statement 2 alone → Age of A unknown ❌
  • Both together → A = 12 – 5 = 7 ✅ sufficient
  • Answer: Both together sufficient → Code 3

3. Number Comparison

Question: Is x > y?

  1. x – y = 4
  2. y = 7

Solution:

  • Statement 1 → x > y? Cannot say ❌
  • Statement 2 → x > y? Cannot say ❌
  • Both together → x – y = 4, y = 7 → x = 11 → Yes ✅ sufficient
  • Answer: Both together sufficient → Code 3

4. Simple Algebra

Question: What is the value of a + b?

  1. a = 5
  2. b = 3

Solution:

  • Statement 1 alone → b unknown ❌
  • Statement 2 alone → a unknown ❌
  • Both together → a + b = 5 + 3 = 8 ✅ sufficient
  • Answer: Both together sufficient → Code 3

5. Logical Comparison

Question: Who is taller, X or Y?

  1. Z is taller than X
  2. Y is taller than Z

Solution:

  • Statement 1 alone → Cannot compare X & Y ❌
  • Statement 2 alone → Cannot compare X & Y ❌
  • Both together → Y > Z > X → Y taller ✅ sufficient
  • Answer: Both together sufficient → Code 3

Difficult Questions

6. Quadratic Equation

Question: What is y?

  1. y² – 7y + 10 = 0
  2. y > 0

Solution:

  • Statement 1 → y² – 7y + 10 = 0 → y = 2 or 5 ❌ multiple values → not sufficient
  • Statement 2 → Alone → nothing known ❌
  • Both together → y > 0 → y = 2 or 5 → still not unique ❌
  • Answer: Even both together insufficient → Code 5

7. Ratio Problem

Question: What is the ratio of A’s marks to B’s marks?

  1. A + B = 50
  2. A – B = 10

Solution:

  • Statement 1 alone → Cannot find ratio ❌
  • Statement 2 alone → Cannot find ratio ❌
  • Both together → A + B = 50, A – B = 10 → Solve: A = 30, B = 20 → Ratio = 3:2 ✅ sufficient
  • Answer: Both together sufficient → Code 3

8. Work / Time

Question: How long will A take to finish the work?

  1. A alone can do half the work in 6 hours
  2. B alone can do the same work in 12 hours

Solution:

  • Statement 1 → Half work in 6 hours → Full work in 12 hours ✅ sufficient
  • Statement 2 → Information about B only → A’s time unknown ❌
  • Answer: Statement 1 alone sufficient → Code 1

9. Algebra with Condition

Question: Find value of x + y.

  1. x – y = 4
  2. x² – y² = 16

Solution:

  • Statement 1 alone → x + y unknown ❌
  • Statement 2 alone → x² – y² = (x – y)(x + y) = 16 → x + y = 16 / (x – y) → x – y unknown ❌
  • Both together → x – y = 4 → x + y = 16 / 4 = 4 ✅ sufficient
  • Answer: Both together sufficient → Code 3

10. Mixed Logic / Age

Question: Find C’s age.

  1. A is twice as old as B.
  2. B is 5 years older than C.

Solution:

  • Statement 1 alone → C’s age unknown ❌
  • Statement 2 alone → C’s age unknown ❌
  • Both together → Still no absolute age given (A or B’s exact age unknown) ❌ insufficient

Answer: Even both together insufficient → Code 5