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CAT 2003 Slot 1 — QA Question 37

Similarity of TrianglesEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90°. If AB : CD = 3 : 1, the ratio of CD : PQ is

Answer & solution

  • A

    1 : 0.69

  • 1 : 0.75

  • C

    1 : 0.72

  • D

    None of the above

Solution

Consider the figure below,  

As AB || CD and ∠ABD = ∠CDB = ∠PQD = 90°

∴ ∠BAP = ∠CDP and ∠ABP = ∠DCP

∆CPD ~ ∆BPA                                                 …(AAA test)

∴CPPB=x3x=13

If CP = y,

PB = 3y

Now, ∆CBD ~ ∆PBQ                         …(AA test)

CDPQ=CBPB=y+3y3y=43= 1 : 0.75

Hence, option (b).

CAT 2003 Slot 1 QA Q37: In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90°. If AB : CD = 3 : 1, the ratio of CD : PQ — Solution | TheCATExam