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CAT 2007 — QA Question 14

Geometric ProgressionEasy
Passage / Data

Answer the next 2 questions based on the information given below.

Let a1 = p and b1 = q, where p and q are positive quantities.

Define:
an = pbn−1     bn = qbn−1,  for even n > 1 and 
an = pan − 1   bn = qan − 1,  for odd n > 1.

Which of the following best describes an+bn for even n?

Answer & solution

  • A

    q(pq)12n-1(p+q)12n

  • q(pq)12n-1(p+q)

  • C

    qp12n-1(p+q)

  • D

    q12n(p+q)

  • E

    q12n(p+q)12n

Solution

We have the following for different values of n

​​​​​​​​​​​​​​

∴ For even n (say, n = 4),

an+bn=p2q2+pq3=pq2(p+q) 
Now consider the given options, for n = 4

Option (a) gives pq² (p + q)²

Option (b) gives pq²(p + q)

Option (c) gives pq(p + q)

Option (d) gives q²(p + q)

Option (e) gives q²(p + q)²

Hence, option (b).

CAT 2007 QA Q14: Which of the following best describes a n + b n for even n? — Solution | TheCATExam