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CAT 2003 Slot 2 — QA Question 35

Similarity of TrianglesEasy
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.

In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC and QD is parallel to CP. In ∆ARC, ∠ARC = 90°, and in ΔPQS, ∠PSQ = 90°. The length of QS is 6 cm. What is the ratio AP : PD?

Answer & solution

  • A

    10 : 3

  • B

    2 : 1

  • 7 : 3

  • D

    8 : 3

Solution

In ∆ABC, PQ is parallel to AC,

BP : AP = BQ : QC = 3 : 4

In ∆PBC, QD is parallel to CP,

BD : DP = BQ : QC = 3 : 4

The given figure may be depicted as follows:

Let AP = 4x and PB = 3x

Since DB : PD = 3 : 4,

∴ PD = 47×3x=12x7

∴ AP : PD = 4x : 12x7 = 7 : 3.

Hence, option (c).

CAT 2003 Slot 2 QA Q35: In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel t — Solution | TheCATExam