CAT 2017 Quantitative Ability

Question : 19 of 34

Marks: +1, -0

What is the area

| x -2| + |y + 4| < 5 ?

$25/2$ sq units
25 sq units
50 sq units
$25/4$ sq units

Validate

Solution:

Let us take

X = x - 2

and

V = y + 4

Now, let us draw

|x| +|y|< 5

.
When

y = 0. |X| < 5 \text " i.e.", -5 < X < 5

.
When

X = 0, |y| < 5 \text " i.e.", -5 < Y < 5

Now, try to think of how the graph of | x - 2|+ | y + 4| <5 would look, 'x - 2' indicates a shift along the X-axis, 2 unit to the right and 'y + 4' indicates a shift along the y-axis, 4 units to the bottom

We can observe that shifting the origin has no impact on the area of the figure. This essentially means that area computed using |x-2| + |y+4| <5 has to be same as the area computed using | x| + | y| < 5.
Required Area =

4×\;\;{1}/{2}×5×5=50\;\text"squnits"\;

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