CAT 2005 — QA Question 21
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is
Answer & solution
- A
8
- B
12
16
- D
20
|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).