Find the fraction (in lowest terms): If 1 is added to the denominator of a fraction, the value becomes 1/2; and if 1 is added to the numerator, the value becomes exactly 1. What is the original fraction?

Introduction / Context:
This problem asks you to determine a rational number (a fraction) from two simple transformations. When 1 is added to the denominator, the fraction equals 1/2. When 1 is added to the numerator, the fraction equals 1. Translating each verbal condition into an equation and solving the resulting system is a classic aptitude skill.

Given Data / Assumptions:

• The fraction is x / y with x and y as positive integers and y ≠ 0.
• Condition A: x / (y + 1) = 1/2.
• Condition B: (x + 1) / y = 1.
• We seek the simplest form of the fraction.

Concept / Approach:
Convert each sentence into an algebraic equation, then solve simultaneously. From Condition B, (x + 1) / y = 1 implies y = x + 1. Substitute this into Condition A to find x. Once x is known, compute y and write the fraction x / y in lowest terms.

Step-by-Step Solution:

Verification / Alternative check:
Add 1 to the denominator: 2 / (3 + 1) = 2/4 = 1/2 (matches). Add 1 to the numerator: (2 + 1) / 3 = 3/3 = 1 (matches). Everything is consistent.

Why Other Options Are Wrong:
4/7, 5/9, 10/11, and 3/5 do not satisfy both conditions; testing either condition fails for each distractor.

Common Pitfalls:
Mixing up which operation (adding 1) applies to the numerator versus the denominator; forgetting to substitute y = x + 1 correctly; or reducing too early and losing track of variables.

Final Answer:
2/3