Question 1

Study the following statements and determine whether the data provided is sufficient to answer the question.

Question: Is Rajesh taller than Priya?

Statement I: Rajesh is taller than Amit, and Amit is taller than Priya.
Statement II: Priya is shorter than Rajesh.

Which of the following is correct?
(A) Statement I alone is sufficient, but Statement II alone is not sufficient.
(B) Statement II alone is sufficient, but Statement I alone is not sufficient.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Either statement alone is sufficient.

Accepted Answer

To answer 'Is Rajesh taller than Priya?', we need a direct or chain comparison establishing Rajesh's height relative to Priya's.

Statement I: 'Rajesh is taller than Amit, and Amit is taller than Priya.' This creates a chain: Rajesh > Amit > Priya. By transitivity, Rajesh > Priya. This directly answers the question as YES. Statement I alone is sufficient.

Statement II: 'Priya is shorter than Rajesh.' This directly states Rajesh > Priya (since 'Priya is shorter than Rajesh' means Rajesh is taller than Priya). This directly answers the question as YES. Statement II alone is sufficient.

Since both Statement I and Statement II independently answer the question with certainty, either statement alone is sufficient. Therefore, the answer is Option D.

Question 2

Is Ramesh older than Priya?

Statement I: Ramesh is 5 years older than Suresh, and Suresh is 3 years older than Priya.
Statement II: The sum of Ramesh's and Priya's ages is 54 years, and their age difference is 8 years.

Accepted Answer

To determine if Ramesh is older than Priya, we need to establish their relative ages.

Statement I Analysis:
- Ramesh = Suresh + 5
- Suresh = Priya + 3
- Therefore: Ramesh = (Priya + 3) + 5 = Priya + 8
- This clearly shows Ramesh is 8 years older than Priya
- Statement I ALONE is SUFFICIENT to answer YES

Statement II Analysis:
- Ramesh + Priya = 54 (sum condition)
- |Ramesh - Priya| = 8 (difference condition)
- From the difference: Either Ramesh = Priya + 8 OR Priya = Ramesh + 8
- If Ramesh = Priya + 8: Then (Priya + 8) + Priya = 54 → 2Priya = 46 → Priya = 23, Ramesh = 31 ✓
- If Priya = Ramesh + 8: Then Ramesh + (Ramesh + 8) = 54 → 2Ramesh = 46 → Ramesh = 23, Priya = 31 (This contradicts the assumption)
- The valid solution shows Ramesh is 31 and Priya is 23, so Ramesh is older
- Statement II ALONE is SUFFICIENT to answer YES

Since both statements independently provide sufficient information to answer the question with certainty, the answer is that either statement alone is sufficient.

Question 3

Five friends—Anil, Bina, Chetan, Diya, and Esha—sit in a row facing North. Statement I: Anil sits immediately to the left of Bina. Statement II: Chetan sits at one of the ends. Statement III: Diya and Esha are not adjacent to each other. Is it possible to determine the exact seating arrangement of all five friends using these statements?

Accepted Answer

To determine if the seating arrangement can be uniquely established, we must check if the three statements together provide sufficient constraints. Statement I fixes Anil-Bina as a consecutive pair (AB or BA). Statement II places Chetan at position 1 or 5. Statement III prevents Diya and Esha from sitting adjacent. However, even with all three statements: if Chetan is at position 1, the pair AB can occupy positions (2,3), (3,4), or (4,5), leaving multiple valid arrangements for Diya and Esha that satisfy the non-adjacency constraint. For example: C-A-B-D-E (Diya and Esha adjacent—violates III), C-A-B-E-D (valid), C-D-A-B-E (valid), etc. Similarly, if Chetan is at position 5, multiple arrangements exist. Since multiple distinct seating arrangements satisfy all three statements simultaneously, the exact arrangement cannot be uniquely determined. Therefore, the data is insufficient.

Question 4

Five friends—Arun, Bhavna, Chitra, Deepak, and Esha—sit in a row facing North. The following conditions apply:

1. Arun sits immediately to the left of Bhavna.
2. Chitra does not sit at either end.
3. Deepak sits to the right of Esha.
4. The person second from the left is not Deepak.
5. Esha is not adjacent to Bhavna.

Statement I: Chitra sits in the middle position.
Statement II: Arun sits to the left of Esha.

Which statement(s) alone is/are sufficient to determine the complete seating arrangement?

A) Statement I alone is sufficient, but Statement II alone is not sufficient.
B) Statement II alone is sufficient, but Statement I alone is not sufficient.
C) Both statements together are sufficient, but neither alone is sufficient.
D) Neither statement alone nor both together are sufficient.

Accepted Answer

To solve this, we must test whether each statement, independently or together, uniquely determines the seating arrangement.

**Testing Statement I alone (Chitra sits in the middle position):**
Chitra is at position 3. Condition 1: Arun is immediately left of Bhavna (adjacent pair). Condition 3: Deepak is right of Esha. Condition 4: Position 2 ≠ Deepak. Condition 5: Esha not adjacent to Bhavna.

With Chitra at position 3, we have positions 1, 2, 4, 5 for Arun, Bhavna, Deepak, Esha.

Arun-Bhavna can occupy: (1,2), (4,5).

**Case 1a:** Arun at 1, Bhavna at 2. Then Deepak and Esha at 4, 5. Since Deepak > Esha (position-wise), Esha at 4, Deepak at 5. Check condition 5: Esha (4) adjacent to Bhavna (2)? No. ✓ Arrangement: Arun(1), Bhavna(2), Chitra(3), Esha(4), Deepak(5). Valid.

**Case 1b:** Arun at 4, Bhavna at 5. Then Deepak and Esha at 1, 2. Since Deepak > Esha, Esha at 1, Deepak at 2. But condition 4 says position 2 ≠ Deepak. ✗ Invalid.

Statement I yields exactly one valid arrangement. **Statement I alone is sufficient.**

**Testing Statement II alone (Arun sits to the left of Esha):**
This only constrains Arun's position relative to Esha, but does not fix absolute positions. Arun-Bhavna (adjacent) can be at (1,2), (2,3), (3,4), or (4,5). For each, Deepak and Esha must satisfy conditions 3, 4, 5.

**Case 2a:** Arun(1), Bhavna(2). Remaining: Chitra, Deepak, Esha at 3, 4, 5. Condition 2: Chitra ≠ end, so Chitra at 4. Deepak > Esha: Esha(3), Deepak(5). Condition 5: Esha(3) adjacent to Bhavna(2)? Yes. ✗ Invalid.

**Case 2b:** Arun(2), Bhavna(3). Remaining: Chitra, Deepak, Esha at 1, 4, 5. Condition 2: Chitra ≠ end, so Chitra at 4. Deepak > Esha: Esha(1), Deepak(5). Condition 4: Position 2 = Arun ≠ Deepak. ✓ Condition 5: Esha(1) adjacent to Bhavna(3)? No. ✓ Arrangement: Esha(1), Arun(2), Bhavna(3), Chitra(4), Deepak(5). Valid.

**Case 2c:** Arun(3), Bhavna(4). Remaining: Chitra, Deepak, Esha at 1, 2, 5. Condition 2: Chitra ≠ end, so Chitra at 2. Deepak > Esha: Esha(1), Deepak(5). Condition 4: Position 2 = Chitra ≠ Deepak. ✓ Condition 5: Esha(1) adjacent to Bhavna(4)? No. ✓ Arrangement: Esha(1), Chitra(2), Arun(3), Bhavna(4), Deepak(5). Valid.

Statement II yields multiple valid arrangements. **Statement II alone is not sufficient.**

**Conclusion:** Only Statement I uniquely determines the seating arrangement.

RRB Group D Data Sufficiency — Reasoning

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Data Sufficiency — Reasoning — Practice Questions

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