X, Y, Z are three distinct integers. Is Y the smallest of the three?…
2023
X, Y, Z are three distinct integers. Is Y the smallest of the three?
Statements:
X is greater than at least one of the two integers Y and Z.
Z is greater than at least one of the two integers X and Y.
- A.
Both statements put together are sufficient in answering the problem question
- B.
Either of the statements taken individually are sufficient in answering the problem question
- C.
Both the Statements even put together are not sufficient in answering the problem question
- D.
Any one statement alone is sufficient in answering the problem question, but the other statement alone cannot answer the question
Show answer & explanation
Correct answer: A
Concept: In Data Sufficiency, a statement (or combination of statements) is sufficient only if it forces exactly one answer to the question asked -- a statement that still leaves two or more possibilities open is not sufficient. For a three-way ordering question like this one, look for what each statement ELIMINATES from being the position in question (here, the minimum) rather than expecting it to fix the full order by itself.
Application: Statement I says X is greater than at least one of Y and Z, so X cannot itself be the minimum of the three (the minimum would have to be less than both of the others). Statement II says Z is greater than at least one of X and Y, so Z cannot be the minimum either.
Statement I eliminates X as a candidate for the minimum, but leaves both Y and Z possible -- not sufficient alone.
Statement II eliminates Z as a candidate for the minimum, but leaves both X and Y possible -- not sufficient alone.
Combining both: X is eliminated by Statement I and Z is eliminated by Statement II. Among three distinct integers exactly one must be the minimum, and with X and Z both ruled out, Y is the only integer left -- so Y must be the minimum, a single forced answer.
Cross-check: Testing with numbers confirms this holds generally, not just in one case. With X = 5, Y = 1, Z = 3: Statement I holds (X > Y) and Statement II holds (Z > Y), and Y = 1 is indeed the minimum. With X = 2, Y = 1, Z = 10: Statement I holds (X > Y) and Statement II holds (Z > X), and Y = 1 is again the minimum. Every combination satisfying both statements forces Y to be the smallest.
Since the two statements together pin down a unique answer but neither one does so by itself, the combined statements are sufficient while each statement alone is not.