Practice Questions: Data Sufficiency

Introduction

Data Sufficiency questions test your ability to analyze problems and determine whether given data is sufficient to answer them. These appear in IBPS PO, SBI PO, RBI Grade B and other bank exams. Each question has two statements, and you must decide if:

(A) Only statement 1 is sufficient

(B) Only statement 2 is sufficient

(C) Both statements together are sufficient

(D) Either statement alone is sufficient

(E) Neither statement is sufficient

Here are 10 practice questions with solutions to help you prepare. 

Practice Questions

Question 1: ​A person starts walking from point A and moves 5 km east to reach point B, then turns left and walks 3 km to reach point C. What is the shortest distance between point A and point C?
Statements:
I. Point C is to the northeast of point A.
II. After reaching point C, the person turns right and walks 4 km to reach point D.

Explanation:

• The initial movement:

  • 5 km East (A → B)

  • Left turn (North) → 3 km (B → C)

• Shortest distance (AC) = √(5² + 3²) = √34 km (Pythagoras theorem).

• Statement I confirms direction but doesn't add new info.

• Statement II introduces a new point D but doesn't help find AC.
  Answer: (A) Statement I alone is sufficient (since the path is already clear).

Question 2: Can we conclude that "Some cats are dogs"?
Statements:
I. All dogs are animals. Some animals are cats.
II. No cats are dogs. All dogs are pets.

Explanation:

• Statement I: "All dogs are animals" + "Some animals are cats" → No direct relation between cats and dogs. (Insufficient).

• Statement II: "No cats are dogs" → Directly negates the conclusion.
  Answer: (B) Statement II alone is sufficient to conclude that the statement is false.

Question 3: In a certain code language, "APPLE" is written as "CRRNG". How is "ORANGE" written in that code?
Statements:
I. Each vowel is replaced by the next vowel (A→E, E→I, etc.), and consonants are replaced by the next consonant (P→Q→R, etc.).
II. The code shifts each letter +2 positions forward (A→C, P→R, etc.).

Explanation:

• APPLE → CRRNG:

  • A→C (+2), P→R (+2), P→R (+2), L→N (+2), E→G (+2).

• Statement I is incorrect (vowels in "APPLE" don't follow the given pattern).

• Statement II matches perfectly.

• Applying +2 to "ORANGE" → QTCPIG.
  Answer: (B) Statement II alone is sufficient.

Question 4: Five friends-A, B, C, D, E-are sitting in a row facing north. Who is sitting in the middle?
Statements:
I. A is to the immediate left of C, and D is at one of the ends.
II. B is second to the right of E, who is not at any end.

Explanation:

• From Statement II: E is not at the ends, so possible positions: 2, 3, or 4.

  • "B is second to the right of E" → E _ B or _ E _ B.

• From Statement I: D is at an end, and A is left of C (A, C adjacent).

• Combining both: Possible arrangement: D, A, C, E, B → Middle is C.
  Answer: (C) Both statements together are sufficient.

Question 5: What is the next term in the series: A1, C3, E5, G7, ___?
Statements:
I. Letters skip one alphabet (A, C, E, G...), numbers follow odd numbers (1, 3, 5, 7...).
II. Series alternates between vowel and consonant (incorrect here).

Explanation:

• Pattern:

  • Letters: A (+2)→ C (+2)→ E (+2)→ G → I.

  • Numbers: 1, 3, 5, 7 → 9.

• Statement I fits perfectly (next term = I9).

• Statement II is irrelevant (A is vowel, C is consonant, but E is vowel, breaking alternation).
  Answer: (A) Statement I alone is sufficient.

Question 6: If '∆' means 'greater than', '□' means 'less than', and '○' means 'equal to', what does "A ∆ B □ C ○ D" mean?
Statements:
I. A > B < C = D
II. Symbols follow left-to-right precedence unless brackets are used.

Explanation:

• Statement I directly decodes the symbols:

  • A ∆ B □ C ○ D → A > B < C = D.

• Statement II clarifies precedence but isn't needed here.
  Answer: (A) Statement I alone is sufficient.

Question 7: How is P related to Q?
Statements:
I. Q is the son of R, who is P's sister.
II. P is the uncle of S, who is Q's brother.

Explanation:

• Statement I:

  • R (P's sister) → Q (R's son) → P is Q's maternal uncle.

• Statement II:

  • S is Q's brother → P is uncle of S → P is Q's uncle.
    Answer: (D) Either statement alone is sufficient (both lead to P being Q's uncle).

Question 8: A person walks 10 m south from point X, then turns left and walks 5 m. In which direction is he from his starting point?
Statements:
I. After walking 5 m, he turns right and walks 3 m.
II. His final position is southeast of X.

Explanation:

• Initial movement:

  • 10 m South → turns left (East) → 5 m.

• Statement I: Adds a right turn (South) + 3 m → Final position is Southeast.

• Statement II directly states the direction but isn't needed.
  Answer: (A) Statement I alone is sufficient.

Question 9: Is it true that "All pens are pencils"?
Statements:
I. No pencils are erasers. Some erasers are pens.
II. Some pens are pencils, and all pencils are markers.

Explanation:

• Statement I: No direct link between pens and pencils.

• Statement II: "Some pens are pencils" → "All pens are pencils" is false.
  Answer: (B) Statement II alone is sufficient to reject the conclusion.

Question 10 : Among five boxes-P, Q, R, S, T-which is the heaviest?
Statements:
I. P > Q but P < T.
II. R > S but R < Q.

Explanation:

• From Statement I: T > P > Q.

• From Statement II: Q > R > S.

• Combining: T > P > Q > R > S.
  Answer: (C) Both statements together are sufficient (T is heaviest).

Key Takeaways:

• Direction Sense: Use path + Pythagoras or direction clues.

• Syllogism: Look for direct negation or Venn diagram logic.

• Coding-Decoding: Check letter/number shifts or patterns.

• Puzzles: Combine constraints to form arrangements.

• Blood Relations: Draw family trees for clarity.