Data Sufficiency: Relations, Directions, Ranks, Numbers, Days and Ages
Data Sufficiency: Relations, Directions, Ranks, Numbers, Days and Ages
Data sufficiency does not ask for the answer itself; it asks which statements are enough to find a single, definite answer. Test statement I alone, then II alone, then both together (and with three statements, the needed combination). Stop as soon as you know whether a unique answer exists; you do not have to finish the calculation.
1. Answer Options and the Testing Order
| Option | Meaning |
|---|---|
| (a) | Statement I alone is sufficient, II alone is not |
| (b) | Statement II alone is sufficient, I alone is not |
| (c) | Either I alone or II alone is sufficient |
| (d) | Neither alone; both together are sufficient |
| (e) | Even both together are not sufficient |
Order: I alone → II alone → both together
"Sufficient" means exactly one answer. Two possible answers (x = 5 or −5) means not sufficient
With three statements, find the smallest set that fixes the answer
| Topic | What usually completes the data |
|---|---|
| Blood relation | A link through a common person and the gender of the person asked about |
| Direction | Both points tied to a common reference point |
| Rank or order | A complete chain from top to bottom, or a total |
| Number | A value or condition that leaves one number |
| Day or date | An anchor day plus an offset, or two overlapping ranges |
| Age | One present age plus a gap |
✗ x² = 25 gives x = 5, so II alone is sufficient | ✓ x could be 5 or −5; one answer is required
✗ Both statements together give the answer, so option (d) | ✓ First check that neither statement works alone
हिंदी नोट: आँकड़ों की पर्याप्तता में उत्तर निकालना ज़रूरी नहीं; बस देखना है कि एक ही निश्चित उत्तर मिलता है या नहीं। क्रम: केवल I, केवल II, फिर दोनों साथ। दो संभावित उत्तर का अर्थ है अपर्याप्त।
Exam Pointer: Verified NTPC patterns: a blood relation with three statements (June 2022 CBT-2), heights and ages from statements (October 2025 Graduate CBT-2), the value of a number from range clues (June 2022 CBT-2) and a weekday from two people's memories (May 2022 CBT-2). Direction data sufficiency had no verified NTPC shift and is tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Blood relations
[PYQ: NTPC CBT-2 14-Jun-2022 Shift-1]
EXAM LEVEL
Q. How is P related to Q? I. P is the brother of R. II. R is the daughter of Q.
I alone does not mention Q, and II alone does not mention P. Together, P is a male sibling of Q's daughter, so P is Q's son.
Answer: (d) Both together
EXAMATLAS LEVEL
Q. How is M related to N? I. M is the son of L. II. N is the daughter of K. III. K is the wife of L. Which statements are needed?
I and II together give no link between L and K. III links them: L and K are a couple, M is L's son and N is K's daughter, so (taking them as children of the couple, as these questions do) M is N's brother. No pair of statements alone connects M to N.
Answer: All three statements
Pattern 2: Directions and distances
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. In which direction is P from Q? I. P is 5 km east of R. II. Q is 5 km south of R.
Each statement alone involves only one of P and Q. Together, with R at (0, 0): P (5, 0) and Q (0, −5), so P is north-east of Q.
Answer: (d) Both together
EXAMATLAS LEVEL
Q. How far is A from B, and in which direction? I. A is 3 km north of C. II. B is 4 km east of C.
Together, with C at (0, 0): A (0, 3) and B (4, 0). The distance is √(9 + 16) = 5 km, and A is north-west of B. Neither statement alone places both points.
Answer: (d) Both together; 5 km, north-west
Pattern 3: Ranks and ordering
[PYQ: NTPC Graduate CBT-2 13-Oct-2025 Shift-1]
EXAM LEVEL
Q. Who is the shortest among A, B, C, D and E? I. A is taller than B and C but shorter than D. II. C is shorter than B, and E is taller than D.
I alone leaves B and C unordered. II alone says nothing about A. Together: E > D > A > B > C, so C is the shortest.
Answer: (d) Both together
EXAMATLAS LEVEL
Q. In a class of 40, what is Ravi's rank from the top? I. Ravi is 5 ranks above Mohan. II. Mohan is 21st from the bottom.
II alone gives Mohan 40 − 21 + 1 = 20th from the top but says nothing of Ravi; I alone gives only a gap. Together, Ravi is 15th from the top.
Answer: (d) Both together; 15th
Pattern 4: Value of a number
[PYQ: NTPC CBT-2 15-Jun-2022 Shift-2]
EXAM LEVEL
Q. What is the value of the integer x? I. 3x + 2 = 17. II. x² = 25.
I gives x = 5 alone. II gives x = 5 or −5, two answers.
Answer: (a) I alone
EXAMATLAS LEVEL
Q. How many pages does a book have? I. More than 100 and fewer than 130. II. The number of pages is a perfect cube.
I allows 29 values. II allows 1, 8, 27, 64, 125 and so on. Together, the only cube between 100 and 130 is 125.
Answer: (d) Both together; 125
Pattern 5: Day or date
[PYQ: NTPC CBT-2 9-May-2022 Shift-2]
EXAM LEVEL
Q. On which day of the week was Mohan born? I. He was born two days after his brother. II. His brother was born on a Tuesday.
I gives only an offset and II only the brother's day. Together: Thursday.
Answer: (d) Both together
EXAMATLAS LEVEL
Q. On which date in March is Priya's birthday? I. Her mother remembers it is after the 14th but before the 18th. II. Her father remembers it is after the 16th but before the 20th.
I allows the 15th, 16th and 17th; II allows the 17th, 18th and 19th. Only the 17th fits both.
Answer: (d) Both together; 17 March
Pattern 6: Ages
[PYQ: NTPC Graduate CBT-2 13-Oct-2025 Shift-1]
EXAM LEVEL
Q. What is Rahul's present age? I. Rahul is 4 years younger than his sister. II. His sister will be 20 in 3 years.
II gives the sister's age (17) but nothing about Rahul; I gives only a gap. Together, Rahul is 13.
Answer: (d) Both together
EXAMATLAS LEVEL
Q. What is a father's present age? I. The father was 28 when his son was born. II. The son is 4 years older than his daughter, who is 9 now.
II gives the son's age, 13, and I the gap of 28 years. Together the father is 41; neither alone gives it.
Answer: (d) Both together; 41
60-Second Revision
- Test I alone, II alone, then both.
- Sufficient means one definite answer.
- Each topic needs a link: a common person, a common point or an anchor value.
- Do not finish the calculation once sufficiency is clear.
Next Step: Data Sufficiency done. Practise the statement-based set in the ExamAtlas RRB NTPC 2026 mock tests; mark I alone and II alone before you even try them together.