Which one of the following fractions is greater than 1/2?

Introduction / Context:
This question checks your ability to compare simple fractions with the benchmark value 1/2. Being comfortable with comparing fractions is very important in aptitude tests because it appears in ratio, proportion and data interpretation questions as well.

Given Data / Assumptions:
- The fractions to compare are 2/5, 4/7, 4/9 and 5/11.
- We need to decide which single fraction is greater than 1/2.
- All fractions are positive proper fractions.

Concept / Approach:
To compare a fraction a/b with 1/2, a fast method is to compare 2a with b. If 2a is greater than b, then a/b is greater than 1/2. If 2a is less than b, then the fraction is less than 1/2. This avoids converting to decimals and saves time in exams.

Step-by-Step Solution:
Step 1: For 2/5, compute 2 * 2 = 4 and compare with 5. Since 4 < 5, 2/5 is less than 1/2. Step 2: For 4/7, compute 2 * 4 = 8 and compare with 7. Since 8 > 7, 4/7 is greater than 1/2. Step 3: For 4/9, compute 2 * 4 = 8 and compare with 9. Since 8 < 9, 4/9 is less than 1/2. Step 4: For 5/11, compute 2 * 5 = 10 and compare with 11. Since 10 < 11, 5/11 is less than 1/2. Step 5: Among the given options, only 4/7 satisfies the condition of being greater than 1/2.

Verification / Alternative check:
You can also approximate the fractions as decimals. 2/5 = 0.4, 4/7 is about 0.571, 4/9 is around 0.444, and 5/11 is about 0.455. Only 0.571 is greater than 0.5, confirming that 4/7 is the correct choice.

Why Other Options Are Wrong:
- Option 2/5: Its decimal value is 0.4, clearly less than 0.5.
- Option 4/9: Its value is approximately 0.444, still below 0.5.
- Option 5/11: This is about 0.455, again less than 0.5, so it cannot be greater than 1/2.

Common Pitfalls:
A frequent mistake is to compare only numerators or only denominators, which does not work for fractions with different denominators. Another error is to assume that the fraction with the largest numerator or smallest denominator is the largest. Using the simple 2a versus b trick is a reliable and fast way to compare with 1/2.

Final Answer:
The only fraction greater than 1/2 is 4/7.