4.4 Reasoning Data Sufficiency

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

1. Statement I alone is sufficient, but Statement II alone is not.
2. Statement II alone is sufficient, but Statement I alone is not.
3. Either Statement I alone or Statement II alone is sufficient.
4. Neither Statement I nor Statement II is sufficient, even together.
5. Both statements together are necessary.

The Four-Step Protocol

1. Fix the target: Note exactly what must be established—a relationship, a direction, a rank, a code.
2. Test Statement I alone: Ignore Statement II completely.
3. Test Statement II alone: Forget everything Statement I said.
4. Combine only if both fail: Check whether the two together leave exactly one possibility.

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Topic Rules That Decide Sufficiency

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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.

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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.

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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.