Let a 1- p and b 1- q where p and q are positive quantities- Define a n - pb n -1 and b n - qb n -1- for even n -1and a n - pa n -1- bn - qa n -1- for odd n -1-If p -1-3 and q -2-3- then what is the smallest odd n such that a n - b n -0-01 - CAT2007 A- 11B- 13C- 9D- 15E- 7

The correct option is C 9Soln:c. If p= 1/3 and q= 2/3, then p+q =1 and pq =2/9 a_1 +b_1 = p+q =1 a_3 + b_3 = p^2 q +pq^2 = pq(p+q) = 2/9. a_5 + b_5 = p^3q^2 +p ...

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Quantitative Aptitude

Functions

Let a 1= p an...

Question

Let $a_{1} = p$ and $b_{1} = q$ where p and q are positive quantities. Define $a_{n} = p b_{n - 1}$ and $b_{n} = q b_{n - 1}$ , for even $n > 1$
and $a_{n} = p a_{n - 1}, b n = q a_{n - 1}$ , for odd $n > 1$ .If $p = \frac{1}{3}$ and $q = \frac{2}{3}$ , then what is the smallest odd n such that $a_{n} + b_{n} < 0.01 ?$ (CAT 2007)

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Solution

The correct option is C 9
Soln:c.
If $p = \frac{1}{3}$ and $q = \frac{2}{3}$ , then $p + q = 1$ and $p q = \frac{2}{9}$
$a_{1} + b_{1} = p + q = 1$
$a_{3} + b_{3} = p^{2} q + p q^{2} = p q (p + q) = \frac{2}{9} .$
$a_{5} + b_{5} = p^{3} q^{2} + p^{2} q^{3} = p^{2} q^{2} (p + q) = \frac{4}{81} .$
So, in general, for odd 'n' we can write
$a_{n} + b_{n} = {(\frac{2}{9})}^{(\frac{n - 1}{2})}$ ; we need to find least value of n such that ${(\frac{2}{9})}^{(\frac{n - 1}{2})} < 0.01$
Using the options given, if $n = 7, a_{7} + b_{7} = {(\frac{2}{9})}^{3} > 0.01;$ if $n = 9, a_{9} + b_{9} = {(\frac{2}{9})}^{4} < 0.01$

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Let a1=p and b1=q where p and q are positive quantities. Define an=pbn−1 and bn=qbn−1, for even n>1 and an=pan−1,bn=qan−1, for odd n>1 .If p=13 and q=23, then what is the smallest odd n such that an+bn<0.01? (CAT 2007)