Each of the questions given below consists of a statement and/or a question…
2025
Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.
Read both the statements and Give answer
Who is lightest among A, B, C, D?
I. A is heavier than B, and B is heavier than D
II. B is lighter than C
- A.
if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
- B.
if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
- C.
if the data in each Statement I and Statement II alone is sufficient to answer the question.
- D.
if the data in both Statements I and II together are necessary to answer the question.
Show answer & explanation
Correct answer: D
In Data Sufficiency, a statement (or a combination of statements) is sufficient only when it independently fixes the exact answer to the question asked, with no ambiguity left. When statements are combined, every fact from both must hold true at the same time.
Statement I alone gives A > B > D. Statement I says nothing about C, so C could be lighter than D or heavier than A - the lightest person cannot be fixed from Statement I alone.
Statement II alone gives C > B. It says nothing about A or D relative to B or C, so the lightest person cannot be fixed from Statement II alone either.
Combine both: from Statement I, B > D; from Statement II, C > B. Chaining C > B > D gives C > D. Together with A > B > D from Statement I, every one of A, B and C is now shown heavier than D, so D is confirmed lightest only when both statements are used together.
Check with sample weights obeying both statements, e.g. A = 40, B = 30, C = 35, D = 20: A > B, B > D and C > B all hold, and D = 20 is indeed the smallest of the four. Any assignment consistent with both statements forces the same conclusion.
Since neither statement alone fixes the lightest person, but both together do, both Statements I and II together are necessary to answer the question.