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CAT 2003 Slot 2 — QA Question 47

Basics of QuadrilateralsEasy
Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

  1. The first letter is any vowel.
  2. The second letter is m, n or p.
  3. If the second letter is m, then the third letter is any vowel which is different from the first letter.
  4. If the second letter is n, then the third letter is e or u.
    1. If the second letter is p, then the third letter is the same as the first letter.

Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1, A2, A3... are the areas and P1, P2, P3... are the perimeters of S1, S2, S3... respectively,

then the ratio P1+P2+P3+.....A1+A2+A3+... equals:

Answer & solution

  • A

    2(1+2)a

  • B

    2(2-2)a

  • 2(2+2)a

  • D

    2(1+22)a

Solution

Area and perimeter of square S1 is a2, 4a respectively.

Now, the side of S2 will be a22=a2

Thus, the area and perimeter of S2 = a22,4a2

The side of S3 will be a22×2=a2

Thus, area and perimeter of S3 = a24,4a(2)2

Similarly, the area and perimeter of S4 = a28,4a(2)3

∴ The required ratio

=4a+4a2+4a(2)2+4a(2)3+⋯a2+a22+a24+a28+⋯=4a(1+12+1(2)2+1(2)3…)a2(1+12+14+18…)=4a(11−12)a2(11−12)=4a(22−1)a2×2=4a×2(2+1)2a2=2(2+2)a

Hence, option (c).

CAT 2003 Slot 2 QA Q47: Let S 1 be a square of side a . Another square S 2 is formed by joining the mid-points of the sides of S 1 . T — Solution | TheCATExam