A fraction is greater than twice its reciprocal by 7/15. What is the value of this fraction?

Introduction / Context:
This question again uses a relationship between a fraction and its reciprocal, but this time the fraction is greater than twice its reciprocal. It is a typical algebraic aptitude question that requires setting up and solving a quadratic equation.

Given Data / Assumptions:

• Let the fraction be x (non-zero).
• Its reciprocal is 1/x.
• The statement says x - 2 * (1/x) = 7/15.
• We must determine the correct value of x from the options.

Concept / Approach:
We convert the verbal statement into an algebraic equation and clear denominators. The result is a quadratic equation. Solving the quadratic and matching with the choices yields the correct fraction.

Step-by-Step Solution:

Verification / Alternative check:
Check x = 5/3: 5/3 - 2 * (3/5) = 5/3 - 6/5 = (25 - 18)/15 = 7/15, so 5/3 satisfies the original condition. The other root x = -6/5 also satisfies the algebraic equation, but it is negative and not listed among the choices. The options suggest a positive fraction, so we select 5/3.

Why Other Options Are Wrong:
Substituting 3/5, 3/4 or 4/3 into x - 2/x does not yield 7/15. For example, 3/5 - 2 * (5/3) is negative and far from 7/15. Therefore these values cannot be correct.

Common Pitfalls:
Errors often occur when multiplying by the common denominator or simplifying the quadratic. Some candidates forget to test the roots back in the original equation. Others ignore the sign of the fraction and choose a negative value even when the context points to a positive answer.

Final Answer:
The fraction satisfying the given condition is 5/3.