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The area of the quadrilateral bounded by the Y-axis, the line x=5, and the lines |x−y|−|x−5|=2, is:

CAT · 2023 · Quant Slot 2
Question:
The area of the quadrilateral bounded by the Y-axis, the line x=5, and the lines |x−y|−|x−5|=2, is:

Options

90
45
120
none
Answer: 45

Explanation:
Analyze the equation |x−y|−|x−5|=2 by considering different cases based on the signs of (x−y) and (x−5). Plot the lines and find the vertices of the quadrilateral, then calculate area using coordinate geometry.

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