Data Sufficiency — Identify the Three-Digit Number What is the three-digit number? I. Two-fifths of the number equals half of 204. II. 20% of the number equals 51.

Introduction / Context:
We need only determine whether the number is uniquely fixed from each statement; computing it explicitly is fine as a check but not required by the DS format.

Given Data / Assumptions:

• Let the number be N (three-digit).
• Statement I: (2/5)*N = 204/2 = 102.
• Statement II: 20% of N = 51.

Concept / Approach:
Each linear relation directly yields a unique N. If either statement gives a unique integer N in the three-digit range, it is sufficient alone.

Step-by-Step Solution:

Verification / Alternative check:
Both statements independently return N = 255, which is a valid three-digit number, confirming sufficiency of each alone.

Why Other Options Are Wrong:

• I alone sufficient or II alone sufficient: Each is true, but the best choice is “Either alone is sufficient”.
• Both together needed: Not necessary.
• Even both not sufficient: False; either one suffices.

Common Pitfalls:
Mistaking “two-fifths” as “two-fourths,” or misapplying percentages. Always convert carefully.

Final Answer:
Either statement I alone or statement II alone is sufficient.