Difficulty: Easy
Correct Answer: 1
Explanation:
Introduction / Context: We first transform the given ratio into a simple parametric form for x and y, then compute the target expression. This tests algebraic manipulation with ratios.
Given Data / Assumptions: x/(2y) = 6/7 ⇒ x/y = 12/7.
Concept / Approach: Parameterize x and y as a common multiple of the ratio, compute (x − y)/(x + y), and then add 14/19.
Step-by-Step Solution: Let x = 12t and y = 7t. (x − y)/(x + y) = (12t − 7t)/(12t + 7t) = 5t/19t = 5/19. Add 14/19 ⇒ 5/19 + 14/19 = 19/19 = 1.
Verification / Alternative check: Substitute t = 1: x = 12, y = 7 ⇒ (12 − 7)/(12 + 7) + 14/19 = 5/19 + 14/19 = 1.
Why Other Options Are Wrong: 5, 4, 3, 2 are not equal to the simplified sum; they ignore the fractional addition step.
Common Pitfalls: Forgetting to reduce the fraction (x − y)/(x + y) properly or misadding numerator terms.
Final Answer: 1
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