🧩 Data Sufficiency - Complete Theory

Master logical reasoning with data - unique to banking exams!

🎯 What is Data Sufficiency?

Data Sufficiency (DS) tests your ability to:

• Analyze whether given information is sufficient to answer a question
• Make decisions WITHOUT actually solving the problem
• Think logically about what data is needed

Key Point: You DON’T need to find the answer, only check if it CAN be found!

📐 Standard Answer Format

Most Common Pattern (5 Options):

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Either Statement I or II alone is sufficient
D) Both statements together are sufficient, but neither alone
E) Both statements together are NOT sufficient

Alternative Pattern (Some Banks):

A) Only I sufficient
B) Only II sufficient
C) Both I and II together sufficient
D) Either I or II sufficient
E) Neither I nor II sufficient (even together)

🎯 Decision Making Strategy

Step-by-Step Approach

Step 1: Read the Question

• Understand what is being asked
• Identify what data would be needed

Step 2: Check Statement I Alone

• Can you answer ONLY using Statement I?
• Mark: Sufficient ✓ or Not Sufficient ✗

Step 3: Check Statement II Alone

• Can you answer ONLY using Statement II?
• Mark: Sufficient ✓ or Not Sufficient ✗

Step 4: If Both Individually Failed

• Can you answer using BOTH statements together?

Step 5: Select Answer

• Use decision tree (shown below)

🌳 Decision Tree

                Start
                  ↓
          Check Statement I
                  ↓
          ┌───────┴───────┐
        I Suff?          I Not Suff?
          ↓                   ↓
    Check II           Check II
          ↓                   ↓
    ┌─────┴─────┐      ┌─────┴─────┐
  II Suff?  II Not?  II Suff?  II Not?
    ↓         ↓         ↓         ↓
Answer C  Answer A  Answer B  Check Both Together
                                    ↓
                              ┌─────┴─────┐
                        Both Suff?    Both Not Suff?
                              ↓             ↓
                        Answer D      Answer E

💡 Solved Examples

Example 1: Simple Age Problem

Q: What is the present age of Rahul?

Statement I: Rahul is 5 years older than Amit. Statement II: Amit’s present age is 25 years.

Solution:

Check I alone:
Only know relation, can't find exact age → Not Sufficient ✗

Check II alone:
Only Amit's age given, nothing about Rahul → Not Sufficient ✗

Check Both Together:
Amit = 25 (from II)
Rahul = 25 + 5 = 30 (from I)
Can find Rahul's age → Sufficient ✓

Answer: D (Both together sufficient, neither alone)

Example 2: Average Problem

Q: What is the average of 5 numbers?

Statement I: Sum of the 5 numbers is 200. Statement II: The largest number is 50.

Solution:

Check I alone:
Average = Sum/Count = 200/5 = 40
Can find answer → Sufficient ✓

Check II alone:
Only largest given, can't find average → Not Sufficient ✗

Answer: A (Statement I alone sufficient)

Example 3: Circle Area

Q: What is the area of a circle?

Statement I: Radius of circle is 7 cm. Statement II: Circumference of circle is 44 cm.

Solution:

Check I alone:
Area = πr² = (22/7) × 49 = 154 cm²
Can find → Sufficient ✓

Check II alone:
Circumference = 2πr = 44
r = 44/(2π) = 7 cm
Area = πr² = 154 cm²
Can find → Sufficient ✓

Either I or II alone is sufficient

Answer: C (Either statement alone sufficient)

Example 4: Speed Problem

Q: What is the speed of the train?

Statement I: Train crosses a pole in 10 seconds. Statement II: Length of train is 200 meters.

Solution:

Check I alone:
Time given, but no distance → Not Sufficient ✗

Check II alone:
Length given, but no time → Not Sufficient ✗

Check Both:
Speed = Distance/Time = 200/10 = 20 m/s
Can find → Sufficient ✓

Answer: D (Both together sufficient)

Example 5: Profit Percentage

Q: What is the profit percentage?

Statement I: CP = ₹500, SP = ₹600 Statement II: Profit = ₹100

Solution:

Check I alone:
Profit% = [(600-500)/500] × 100 = 20%
Can find → Sufficient ✓

Check II alone:
Only profit amount given, need CP for percentage
Not Sufficient ✗

Answer: A (Statement I alone sufficient)

Example 6: Insufficient Data

Q: What is the value of x?

Statement I: x + y = 10 Statement II: x - y = 2

Solution:

Check I alone:
One equation, two variables → Not Sufficient ✗

Check II alone:
One equation, two variables → Not Sufficient ✗

Check Both:
Two equations, two variables → Can solve!
x + y = 10
x - y = 2
Adding: 2x = 12, x = 6
Sufficient ✓

Answer: D (Both together sufficient)

Example 7: No Solution Possible

Q: What is the area of triangle ABC?

Statement I: Angle A = 60° Statement II: Angle B = 70°

Solution:

Check I alone:
Only one angle, can't find area → Not Sufficient ✗

Check II alone:
Only one angle, can't find area → Not Sufficient ✗

Check Both:
Two angles given (third = 50°)
But no side length given
Can't find area → Not Sufficient ✗

Answer: E (Even both together not sufficient)

🎯 Topic-Wise Approach

For Number Problems

Usually Need: The actual number OR equation to find it

For Average Problems

Usually Need: Sum and Count OR all individual values

For Ratio Problems

Usually Need: Actual value of one quantity OR total

For Percentage Problems

Usually Need: Base value (whole) OR actual amounts

For Geometry Problems

Usually Need: At least one measurement (side, radius, etc.)

For Speed/Time/Distance

Usually Need: Two of three (Speed, Time, Distance)

⚡ Quick Decision Rules

Rule 1: Single Variable

For finding value of one variable:
Need: One equation (if linear)
      OR special case like x² = 16

Rule 2: Two Variables

For finding values of x and y:
Need: Two independent equations

Rule 3: Geometric Shapes

For area/perimeter/volume:
Need: All required dimensions
- Circle: radius OR diameter OR circumference
- Square: side OR diagonal OR area/perimeter
- Triangle: base & height OR 3 sides OR special formulas

Rule 4: Ratios

Ratio alone is NOT sufficient
Need: Ratio + one actual value OR total

⚠️ Common Traps

Trap 1: Extra Information

Don't get confused by unnecessary data
Focus on what's NEEDED, not what's GIVEN

Example:

Q: What is area of square?
I: Side = 5 cm
II: Diagonal = 7.07 cm

Both give same info (redundant)
Answer: C (Either alone sufficient)

Trap 2: Insufficient Together

Don't assume "both together" is always sufficient!
Sometimes even combined data isn't enough

Example:

Q: What is x + y?
I: x - y = 5
II: 2x - 2y = 10

II is just 2 × I (not independent!)
Can't solve → Answer E

Trap 3: Hidden Sufficiency

Sometimes statement seems insufficient but actually is!
Think about formulas/relationships

Example:

Q: What is side of square?
I: Diagonal = 10 cm

Seems insufficient, but:
Side = Diagonal/√2 = 10/√2 = 5√2
Actually sufficient! → Answer A

📊 Statement Analysis Checklist

Before Deciding, Ask:

✓ Have I identified what the question needs? ✓ Have I checked Statement I independently? ✓ Have I checked Statement II independently? ✓ If both fail individually, can they work together? ✓ Are the statements truly independent (not repetitive)? ✓ Am I making any assumptions?

⚠️ Common Mistakes

❌ Mistake 1: Actually Solving

Wrong: Spending time to calculate answer ✗
Right: Just check IF it can be calculated ✓

❌ Mistake 2: Not Checking Individually

Wrong: Directly checking both together ✗
Right: Always check I and II separately first ✓

❌ Mistake 3: Assuming Values

Wrong: Assuming unstated information ✗
Right: Use only given data ✓

❌ Mistake 4: Dependent Statements

Wrong: Thinking two equations that are multiples are independent ✗
Right: Check if equations are truly different ✓

🎯 Time Management

Per Question:

• Read question: 5 seconds
• Check Statement I: 10 seconds
• Check Statement II: 10 seconds
• Check both (if needed): 10 seconds
• Total: 30-35 seconds per question

For 5 DS Questions:

• Target: 2.5 - 3 minutes total
• Don’t get stuck on any single question

📝 Practice Problems

Level 1:

1. Q: What is the value of x? I: 2x = 10 II: x + 5 = 10

2. Q: What is perimeter of rectangle? I: Length = 10 cm II: Breadth = 5 cm

3. Q: What is average of 3 numbers? I: Sum = 90 II: First number = 25

Level 2:

4. Q: What is CP of article? I: Profit = 20% II: SP = ₹600

5. Q: What is speed of boat in still water? I: Downstream speed = 15 km/hr II: Stream speed = 3 km/hr

6. Q: What is x² + y²? I: x + y = 10 II: xy = 21

Level 3:

7. Q: What is the ratio of men to women? I: Total people = 100 II: Number of men = 60

8. Q: Is x > y? I: x² > y² II: x + y > 0

9. Q: What is area of circle? I: Radius increased by 20% makes area 154 cm² II: Original circumference is 44 cm

🔗 Related Topics

Uses Concepts From:

• Number System - Variable problems
• Average - Average calculations
• Ratio & Proportion - Ratio problems
• Percentage - Percentage questions
• Mensuration - Geometry problems
• Time Speed Distance - Motion problems

Practice:

• Data Sufficiency Questions

Master Data Sufficiency - Think logically, don’t calculate! 🧩