Module 1 · IBPS PO Reasoning Ability

Data Sufficiency

Determine if given data is sufficient to answer a question.

Sufficiency Analysis · Data Adequacy · Statement Combinations

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Learning Objectives

Understand the fundamental concepts of Data Sufficiency
Apply key formulas and techniques to solve problems
Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Data Sufficiency?

Data Sufficiency questions test your ability to determine whether the given data is sufficient to answer a question, without actually solving it completely. Each question is followed by two statements (I and II). You must decide if statement I alone, II alone, both together, or neither is sufficient. These questions appear in IBPS PO and RBI Grade B mains exams.

Answer Choices

In such questions, the standard options are: (a) Only statement I alone is sufficient; (b) Only statement II alone is sufficient; (c) Both statements together are sufficient, but neither alone is sufficient; (d) Both statements together are not sufficient; (e) Either statement I or II alone is sufficient.

Types of Data Sufficiency Questions

1. Age/Relation Based: Find ages of persons based on given relationships. Statements provide ratios, sums, or differences of ages.

2. Number Based: Find a number based on its properties — factors, multiples, digits, operations.

3. Percentage/Profit Based: Find profit percentage, discount, or marked price based on given transaction details.

4. Speed-Distance Based: Find speed, time, or distance based on motion parameters.

5. Comparison Based: Determine which is larger/smaller between two quantities based on given relationships.

Solved Examples

Example 1 (Age Problem)

What is the present age of A?
Statement I: The ratio of A's age to B's age 5 years ago was 3:4.
Statement II: B's present age is twice A's age 10 years ago.

a) Only I b) Only II c) Both together d) Neither e) Either

Solution: c) Both together are sufficient. Let present ages be A and B. From I: (A-5)/(B-5) = 3/4 → 4A - 20 = 3B - 15 → 4A - 3B = 5. From II: B = 2(A-10) → B = 2A - 20. Two equations, two unknowns. Solving: 4A - 3(2A-20) = 5 → 4A - 6A + 60 = 5 → -2A = -55 → A = 27.5 years. Neither statement alone gives a unique answer, but together they do.

Example 2 (Number Problem)

Is the integer N divisible by 12?
Statement I: N is divisible by 4.
Statement II: N is divisible by 3.

a) Only I b) Only II c) Both together d) Neither e) Either

Solution: c) Both together are sufficient. For a number to be divisible by 12, it must be divisible by both 3 and 4 (since 12 = 3 × 4, and 3 and 4 are coprime). Statement I alone → divisible by 4 but not necessarily by 3 (e.g., 8). Statement II alone → divisible by 3 but not necessarily by 4 (e.g., 9). Together → divisible by both 3 and 4 → divisible by 12.

Example 3 (Profit-Loss)

What is the profit percentage earned by selling an article?
Statement I: The selling price is ₹240 more than the cost price.
Statement II: The selling price is 120% of the cost price.

a) Only I b) Only II c) Both together d) Neither e) Either

Solution: b) Only II alone is sufficient. Profit % = (SP - CP)/CP × 100. Statement I: SP = CP + 240. Without knowing CP or SP, the profit % cannot be determined. Statement II: SP = 1.2 × CP → Profit = 0.2 × CP → Profit % = 20%. So statement II alone is sufficient.

Shortcut Techniques

Analyze each statement independently first. Do not carry over information from one statement to the other.
If a statement gives an equation with one unknown, it is usually sufficient. If it gives one equation with two unknowns, it is usually not sufficient.
For 'Yes/No' type questions, a statement is sufficient only if it gives a definite YES or a definite NO.
Remember: You don't need to find the exact answer — just determine whether the answer CAN be found.

Pro Tip

In RBI Grade B exams, data sufficiency questions are often tricky because statements may seem sufficient but actually aren't. Always check for hidden assumptions. For example, a statement giving a ratio of two ages is not sufficient unless there is another equation to find unique values.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Practice Questions

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