CAT 1997 — QA Question 32
Direction: Answer the questions based on the following information.
For these questions the following functions have been defined.
la(x, y, z) = min(x + y, y + z)
le(x, y, z) = max (x − y, y − z)
ma(x, y, z) = [le(x, y, z) + la(x, y, z)]
The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh squares, counting from the innermost square.
Answer & solution
- A
10√2 sq. units
30 sq. units
- C
35√2 sq. units
- D
None of these
The diagonal of the innermost square is 2 units. The diagonal of every successive square would increase by 2 units (since corners are one unit apart). So the diagonal of the 7th square = 14 units and that of the 8th square = 16 units. Areas of the 7th square = (14)2 and that of 8th square = (16)2, and 128 respectively. Hence, the difference in their areas = (128 – 98) = 30 sq.units.