4.4 Reasoning Data Sufficiency
Key Takeaways
- A reasoning data sufficiency statement is sufficient only if it leads to one definite answer; two possible answers mean it is not sufficient.
- Test Statement I alone, then Statement II alone, and combine the statements only when both fail on their own.
- In blood-relation data sufficiency, an unknown gender usually makes the relationship impossible to fix.
- If two words always appear together in coding statements, their individual codes cannot be separated, even with both statements.
- When one statement alone is sufficient, still test the other statement to check for the 'either statement alone' option.
4.4 Reasoning Data Sufficiency
Exam Focus: Reasoning data sufficiency (DS) questions give a question and two (sometimes three) statements and ask whether the statements provide enough information to answer it. They reuse the topics of Chapters 2 to 5—blood relations, directions, ranking, seating and coding—but test judgement about information rather than a final answer. Quantitative DS is covered in Section 12.3.
The Standard Answer Options
- Statement I alone is sufficient, but Statement II alone is not.
- Statement II alone is sufficient, but Statement I alone is not.
- Either Statement I alone or Statement II alone is sufficient.
- Neither Statement I nor Statement II is sufficient, even together.
- Both statements together are necessary.
The Four-Step Protocol
- Fix the target: Note exactly what must be established—a relationship, a direction, a rank, a code.
- Test Statement I alone: Ignore Statement II completely.
- Test Statement II alone: Forget everything Statement I said.
- Combine only if both fail: Check whether the two together leave exactly one possibility.
[!IMPORTANT] "Sufficient" means one definite answer. If a statement still allows two possibilities (for example, the person could be the uncle or the aunt), it is not sufficient.
Topic Rules That Decide Sufficiency
| Topic | What must be established | Common reason a statement fails |
|---|---|---|
| Blood relations | The chain of relations and the gender of the person asked about | Gender unknown ("child", "sibling", or a name with no pronoun) |
| Direction sense | Positions of both points from a common reference | Only one leg of the path is given, or the two points are never linked |
| Ranking / comparison | The exact position asked (tallest, third heaviest) | Two people could still share the top spot |
| Seating | Positions plus facing direction | Facing direction missing, so "left" and "right" are ambiguous |
| Coding | A word that appears with only one common code | Two words always appear together, so their codes cannot be separated |
Worked Example 1: Blood Relations
Question: How is P related to Q?
- I. P is the son of R, who is the father of Q.
- II. Q is the sister of S.
Statement I alone: P and Q are both children of R, and "son" tells us P is male, so P is Q's brother. Sufficient. Statement II alone: It says nothing about P. Not sufficient. Answer: Statement I alone is sufficient, but Statement II alone is not.
Worked Example 2: Direction Sense
Question: In which direction is village M from village K?
- I. M is 5 km north of T, and T is 3 km east of K.
- II. K is 4 km west of N, and N is 5 km south of M.
Statement I alone: Place K at (0, 0). T is at (3, 0) and M at (3, 5), so M is north-east of K. Sufficient. Statement II alone: N is at (4, 0) and M at (4, 5), so M is again north-east of K. Sufficient. Answer: Either statement alone is sufficient.
Worked Example 3: Ranking
Question: Among P, Q, R, S and T, who is the tallest?
- I. P is taller than only Q and R.
- II. S is shorter than T.
Statement I alone: P is third from the bottom, so S and T are the two tallest, but we cannot tell which of them is taller. Not sufficient. Statement II alone: T is taller than S, but nobody else is placed. Not sufficient. Together: S and T are the top two and T is taller than S, so T is the tallest. Answer: Both statements together are necessary.
Worked Example 4: Row Seating
Question: How many persons sit between A and B in a row of people facing north?
- I. A is 3rd from the left end.
- II. B is 5th from the right end.
Neither statement gives the total number of people. Even together, the number between A and B depends on the length of the row (and A could even be to the right of B), so neither statement is sufficient, even together.
The Coding Trap
Question: What is the code for "cash"?
- I. "cash flow fast" is coded "le mi so", and "flow rate" is coded "mi du".
- II. "fast cash" is coded "so le".
Statement I fixes flow = mi, leaving cash and fast as {le, so} in some order. Statement II only repeats the pair {le, so}. Even together, "cash" could be "le" or "so", so neither statement is sufficient. Whenever two words always appear together, their codes cannot be separated.
Three-Statement Variants
Some sets give three statements with options such as "Only I and II together", "Any two of the three" or "All three together". Apply the same logic: find the smallest combination that gives one answer, then check whether any other combination also works.
Common Traps
- Carrying information across: Using a fact from Statement I while testing Statement II alone.
- Assuming gender from names: "Kiran" or "Sunny" does not fix gender.
- Solving more than needed: You only need to know that one answer exists.
- Stopping too early: After finding Statement I sufficient, still test Statement II for the "either" option.
Is D the grandmother of F? Statement I: D is the mother of E. Statement II: E is the father of F. Which option is correct?
What is the code for 'loan' in a certain language? Statement I: 'loan rate high' is coded 'ta ki po', and 'rate cut' is coded 'ki zu'. Statement II: 'high demand' is coded 'po ne'. Which option is correct?
Is Meena the tallest among five friends: Meena, Ravi, Anil, Tara and Joy? Statement I: Meena is taller than Ravi, and Ravi is taller than each of the other three. Statement II: Only Ravi and Meena are taller than Anil, and Meena is taller than Ravi. Which option is correct?