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CAT 2004 — QA Question 30

Basics of CirclesEasy
Passage / Data

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid-point of the line segment P0B, P2 is the mid-point of the line segment P1B and so on. Let C1, C2, C3, ... be circles with diameters P0P1, P1P2, P2P3 ... respectively. Suppose the circles C1,C2, C3, ... are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is:

Answer & solution

  • A

    8 : 9

  • B

    9 : 10

  • C

    10 : 11

  • 11 : 12

Solution

Let the radius of C be r.

Then P0P1 = r2

P1P2 = r4

P2P3 = r8

and so on.

Thus the areas of circles with diameters P0P1, P1P2, P2P3, … are 

πr216,πr264,πr2256,πr21024....

The sum of these areas = πr216×11-14=πr212

∴ Shaded area = πr212

Unshaded area = πr2  - πr212=11πr212

∴ Required ratio = 11 : 12

Hence, option (d).

CAT 2004 QA Q30: Let C be a circle with centre P 0 and AB be a diameter of C. Suppose P 1 is the mid-point of the line segment — Solution | TheCATExam