Data Sufficiency questions with answers and concepts

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Data Sufficiency is a unique question type that tests your ability to determine whether the given information is sufficient to answer a question, rather than solving for the actual answer. These questions appear in logical reasoning sections and require careful analysis of two statements to assess if they individually or together provide enough data.

Key formulas and rules

3 rules

Sufficiency Truth Condition: Statement $S$ is sufficient $⟺ ∣ {x \in Domain : S (x) \land Question (x)} ∣ = 1$ (determines a unique answer value or definite YES/NO)

Five Standard Decision States: (A) Statement (1) ALONE is sufficient; (B) Statement (2) ALONE is sufficient; (C) BOTH TOGETHER are sufficient; (D) EACH ALONE is sufficient; (E) STATEMENTS (1) and (2) TOGETHER are NOT sufficient

Evaluation Independence Protocol: Analyze Statement (1) in isolation $\to$ Analyze Statement (2) in isolation $\to$ Combine $(1) \land (2)$ only if both fail individually

Key concepts

Understanding the Answer Options

Option A: Statement I alone is sufficient, but Statement II alone is not sufficient.
Option B: Statement II alone is sufficient, but Statement I alone is not sufficient.
Option C: Both statements together are sufficient, but neither alone is sufficient.
Option D: Each statement alone is sufficient.
Option E: Both statements together are NOT sufficient, and additional data is needed.

Analyzing Statement I

First, examine Statement I independently of Statement II. Ask: Does this statement provide ALL the information needed to answer the question? If yes, note that I alone might be sufficient. If no, determine what additional information would be needed.

Analyzing Statement II

Next, examine Statement II independently of Statement I. Apply the same test: Does this statement alone provide enough information? If yes, note that II alone might be sufficient. Be careful not to carry over information from Statement I when evaluating Statement II.

Combining Both Statements

If neither statement alone is sufficient, check if combining them provides the answer. Consider: Can I form equations or relationships using both pieces of information? Is there a unique solution when both are used together? Watch out for cases where even together they are insufficient.

Common Traps and Pitfalls

Trap 1: Assuming information from one statement when evaluating the other.
Trap 2: Solving for the actual answer instead of just checking sufficiency.
Trap 3: Missing that the statements might give the same information redundantly.
Trap 4: Overlooking that 'No unique answer' means the data is insufficient.

Question Types in Data Sufficiency

Numerical Questions: Finding a specific value (age, price, speed, etc.).
Yes/No Questions: Determining if something is true or false.
Relationship Questions: Determining relationships between variables or people.
Ranking/Ordering Questions: Finding positions in a sequence or hierarchy.

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Worked examples

Example 1

Question: What is the present age of Ramesh?
Statement I: Ramesh is 5 years older than Suresh.
Statement II: The sum of the ages of Ramesh and Suresh is 45 years.

Solution

Step 1: Check Statement I alone.
Ramesh = Suresh + 5
This gives a relationship but no absolute value. Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
Ramesh + Suresh = 45
This gives the sum but cannot determine individual ages. Statement II alone is NOT sufficient.

Step 3: Check both statements together.
From I: Ramesh = Suresh + 5
From II: Ramesh + Suresh = 45
Substituting: (Suresh + 5) + Suresh = 45
2 x Suresh = 40
Suresh = 20, Ramesh = 25

Both together ARE sufficient. Answer: C

Example 2

Question: Is x > y?
Statement I: $x^{2}$ > $y^{2}$
Statement II: $x^{3}$ > $y^{3}$

Solution

Step 1: Check Statement I alone.
$x^{2}$ > $y^{2}$ means |x| > |y|, but doesn't tell us about signs.
Example: $x = 3$ , $y = 2$ -> x > y (Yes)
Example: x = -3, $y = 2$ -> x < y (No)
Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
x^3 > $y^{3}$ implies x > y for all real numbers (cube preserves order).
Statement II alone IS sufficient.

Answer: B

Example 3

Question: What is the area of rectangle ABCD?
Statement I: The perimeter of the rectangle is 30 cm.
Statement II: The diagonal of the rectangle is 13 cm.

Solution

Step 1: Check Statement I alone.
Perimeter = 2(l + w) = 30
$l + w = 15$
Multiple solutions: (10,5), (11,4), (12,3), etc.
Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
$l^{2} + w^{2} = 1 3^{2} = 169$
Multiple solutions possible.
Statement II alone is NOT sufficient.

Step 3: Check both together.
$l + w = 15$ and $l^{2} + w^{2} = 169$
We know ( $l + w)^{2} = l^{2} + 2 l w + w^{2}$
$225 = 169 + 2 l w$
$l w = 28$

Area = 28 $c m^{2}$ (unique answer)
Both together ARE sufficient. Answer: C

Example 4

Question: Who is tallest among A, B, and C?
Statement I: A is taller than B.
Statement II: C is taller than A.

Solution

Step 1: Check Statement I alone.
A > B, but no info about C.
C could be tallest or shortest.
Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
C > A, but no info about B.
B could be taller than C or shorter.
Statement II alone is NOT sufficient.

Step 3: Check both together.
From I: A > B
From II: C > A
Combining: C > A > B
C is definitely the tallest.
Both together ARE sufficient. Answer: C

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Is x > y > z?
Statement I: x > y and y > z.
Statement II: x - z > 0.

Statement II alone is sufficient
Statement I alone is sufficient
Both statements together are necessary
Neither statement alone is sufficient

Answer: B. Statement I alone is sufficient

Explanation

Step 1: Statement I directly gives x > y and y > z, so x > y > z.
Step 2: Statement II only says x > z, which does not place y.
Step 3: Thus Statement I alone is sufficient.
Answer: Statement I alone is sufficient.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Is n divisible by 12?
Statement I: n is divisible by 3.
Statement II: n is divisible by 4.

Statement I alone is sufficient
Both statements together are necessary
Statement II alone is sufficient
Either statement alone is sufficient

Answer: B. Both statements together are necessary

Explanation

Step 1: Divisibility by 12 requires divisibility by both 3 and 4.
Step 2: Statement I alone is not enough; for example 6 is divisible by 3 but not by 12.
Step 3: Statement II alone is not enough; for example 8 is divisible by 4 but not by 12.
Step 4: Together, n is divisible by both 3 and 4, so n is divisible by 12.
Answer: Both statements together are necessary.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

What is the value of x?
Statement I: $2 x + y = 17$ .
Statement II: $y = 5$ .

Statement II alone is sufficient
Statement I alone is sufficient
Both statements together are necessary
Neither statement alone is sufficient

Answer: C. Both statements together are necessary

Explanation

Step 1: Statement I alone contains two variables, so x cannot be found.
Step 2: Statement II alone gives y only.
Step 3: Using both, $2 x + 5 = 17$ => $2 x = 12$ => $x = 6$ .
Answer: Both statements together are necessary.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Never solve for the actual answer - only determine if you CAN solve it. This saves precious time.
Systematically check: I alone -> II alone -> Both together. This prevents haphazard analysis.
When evaluating one statement, completely ignore the other statement to avoid contamination.
For numerical answers, ensure the data yields a unique value, not multiple possibilities.
Watch for redundant information - if both statements say the same thing, the answer is likely A, B, or E.
Practice with various question types (age, work, speed, geometry) to recognize patterns quickly.
If stuck between C and E, ask: Do I get a unique answer using both, or could there still be multiple answers?

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Next topic: Deductive Reasoning

Data Sufficiency questions with answers and concepts

120 practice questionsPage updated 24 Sept 2026Review metadata pendingPractice questions

Practise this concept

Key formulas and rules

3 rules

Sufficiency Truth Condition: Statement $S$ is sufficient $⟺ ∣ {x \in Domain : S (x) \land Question (x)} ∣ = 1$ (determines a unique answer value or definite YES/NO)

Evaluation Independence Protocol: Analyze Statement (1) in isolation $\to$ Analyze Statement (2) in isolation $\to$ Combine $(1) \land (2)$ only if both fail individually

Key concepts

Understanding the Answer Options

Analyzing Statement I

Analyzing Statement II

Combining Both Statements

Common Traps and Pitfalls

Question Types in Data Sufficiency

Check the idea while it is fresh.Open a focused exercise without losing this article.Practise this concept

Worked examples

Example 1

Question: What is the present age of Ramesh?
Statement I: Ramesh is 5 years older than Suresh.
Statement II: The sum of the ages of Ramesh and Suresh is 45 years.

Solution

Step 1: Check Statement I alone.
Ramesh = Suresh + 5
This gives a relationship but no absolute value. Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
Ramesh + Suresh = 45
This gives the sum but cannot determine individual ages. Statement II alone is NOT sufficient.

Step 3: Check both statements together.
From I: Ramesh = Suresh + 5
From II: Ramesh + Suresh = 45
Substituting: (Suresh + 5) + Suresh = 45
2 x Suresh = 40
Suresh = 20, Ramesh = 25

Both together ARE sufficient. Answer: C

Example 2

Question: Is x > y?
Statement I: $x^{2}$ > $y^{2}$
Statement II: $x^{3}$ > $y^{3}$

Solution

Step 2: Check Statement II alone.
x^3 > $y^{3}$ implies x > y for all real numbers (cube preserves order).
Statement II alone IS sufficient.

Answer: B

Example 3

Question: What is the area of rectangle ABCD?
Statement I: The perimeter of the rectangle is 30 cm.
Statement II: The diagonal of the rectangle is 13 cm.

Solution

Step 1: Check Statement I alone.
Perimeter = 2(l + w) = 30
$l + w = 15$
Multiple solutions: (10,5), (11,4), (12,3), etc.
Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
$l^{2} + w^{2} = 1 3^{2} = 169$
Multiple solutions possible.
Statement II alone is NOT sufficient.

Step 3: Check both together.
$l + w = 15$ and $l^{2} + w^{2} = 169$
We know ( $l + w)^{2} = l^{2} + 2 l w + w^{2}$
$225 = 169 + 2 l w$
$l w = 28$

Area = 28 $c m^{2}$ (unique answer)
Both together ARE sufficient. Answer: C

Example 4

Question: Who is tallest among A, B, and C?
Statement I: A is taller than B.
Statement II: C is taller than A.

Solution

Step 1: Check Statement I alone.
A > B, but no info about C.
C could be tallest or shortest.
Statement I alone is NOT sufficient.

Step 2: Check Statement II alone.
C > A, but no info about B.
B could be taller than C or shorter.
Statement II alone is NOT sufficient.

Step 3: Check both together.
From I: A > B
From II: C > A
Combining: C > A > B
C is definitely the tallest.
Both together ARE sufficient. Answer: C

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Is x > y > z?
Statement I: x > y and y > z.
Statement II: x - z > 0.

Statement II alone is sufficient
Statement I alone is sufficient
Both statements together are necessary
Neither statement alone is sufficient

Answer: B. Statement I alone is sufficient

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Is n divisible by 12?
Statement I: n is divisible by 3.
Statement II: n is divisible by 4.

Statement I alone is sufficient
Both statements together are necessary
Statement II alone is sufficient
Either statement alone is sufficient

Answer: B. Both statements together are necessary

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

What is the value of x?
Statement I: $2 x + y = 17$ .
Statement II: $y = 5$ .

Statement II alone is sufficient
Statement I alone is sufficient
Both statements together are necessary
Neither statement alone is sufficient

Answer: C. Both statements together are necessary

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Never solve for the actual answer - only determine if you CAN solve it. This saves precious time.
Systematically check: I alone -> II alone -> Both together. This prevents haphazard analysis.
When evaluating one statement, completely ignore the other statement to avoid contamination.
For numerical answers, ensure the data yields a unique value, not multiple possibilities.
Watch for redundant information - if both statements say the same thing, the answer is likely A, B, or E.
Practice with various question types (age, work, speed, geometry) to recognize patterns quickly.
If stuck between C and E, ask: Do I get a unique answer using both, or could there still be multiple answers?

Ready to test your understanding?

Work through 120 questions with explanations after each answer.

Start practice

Next topic: Deductive Reasoning

Key formulas and rules

Key concepts

Understanding the Answer Options

Analyzing Statement I

Analyzing Statement II

Combining Both Statements

Common Traps and Pitfalls

Question Types in Data Sufficiency

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.

Key formulas and rules

Key concepts

Understanding the Answer Options

Analyzing Statement I

Analyzing Statement II

Combining Both Statements

Common Traps and Pitfalls

Question Types in Data Sufficiency

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.