CAT 1997 | Question: 132

Question

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 square, counting from the innermost square.

• A. $10^{2}$ 
• B. $30$ 
• C. $35^{2}$ 
• D. None of these

Answer 1

Area of first square = 2 sq. units

Area of second square = 8 sq. units

Area of third square = 18 sq. units

Area of fourth square = 32 sq. units

Area of fifth square = 50 sq. units

Area of sixth square = 72 sq. units

Area of seventh square = 98 sq. units

Area of eighth square = 128 sq. units

Difference between areas of eighth and seventh square is 128 - 98 = 30 sq. units (Option B)