CAT 2005 — QA Question 21
Domain & RangeEasy
In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is
Answer & solution
Correct answer: 16
- A
8
- B
12
16
- D
20
Solution
|x + y| + |x – y| = 4 … (i)
Consider the case when x and y are both positive. This is the area of quadrant I.
In this case, two cases are possible.
Case I: x > y
In this case, expression (i) becomes:
x + y + x – y = 4
∴ 2x = 4
∴ x = 2
Case II: x < y
In this case, expression (i) becomes:
x + y + y – x = 4
∴ 2y = 4
∴ y = 2
∴ The area for the first quadrant is as shown in the figure.
Extending the same logic to other quadrants, we get the area as shown in the above diagram.
∴ Its area = 4 × 4 = 16 sq. units
Hence, option (c).