GATE CS 2015 Set 3 Q.8 (GA Q.8): Quantitative Aptitude

Choose the most appropriate equation for the function drawn as a thick line, in the plot below.

$x = y - |y|$

$x = -(y - |y|)$

$x = y + |y|$

$x = -(y + |y|)$

Official answer and solution

Solution

Determine the piecewise behavior of the graph across the quadrants and match with the given absolute value formulations.

Examine the thick line in the plot:

For $y \ge 0$ : The graph is a vertical ray coincident with the positive y-axis, meaning $x = 0$ .
For $y < 0$ : The graph is a straight ray passing through the origin $(0, 0)$ and the point $(2, -1)$ in the fourth quadrant.
The slope is $\frac{\Delta x}{\Delta y} = \frac{2 - 0}{-1 - 0} = -2$ , so $x = -2y$ .

Analyze Option B: $x = -(y - |y|)$ :

When $y \ge 0$ : $|y| = y$ , so $x = -(y - y) = 0$ .
When $y < 0$ : $|y| = -y$ , so $x = -(y - (-y)) = -(2y) = -2y$ .
This gives $x = 0$ for $y \ge 0$ and $x = -2y$ for $y < 0$ , perfectly reproducing the graph (at $y = -1$ , $x = -2(-1) = 2$ ).

Testing other options for comparison:

Option A: $x = y - |y| \implies x = 2y$ for $y < 0$ , giving $x = -2$ at $y = -1$ (wrong quadrant).
Option C: $x = y + |y| \implies x = 2y$ for $y \ge 0$ and $x = 0$ for $y < 0$ .
Option D: $x = -(y + |y|) \implies x = -2y$ for $y \ge 0$ and $x = 0$ for $y < 0$ .
Hence, option B is correct.

Final answer

Common trap

Confusing the sign in $-(y - |y|)$ , which gives positive $x$ coordinates for negative $y$ values.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

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