CAT Exam Model Paper 6 with solutions for free online practice

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Question : 14 of 60

Marks: +1, -0

If

\P=[1 + ( - { 1 }/ { 4 } ) ] ( 1 + ( - { 1 }/ { 4 } ) ^ { 2 } ] [ 1 + ( - { 1 } /{ 4 } ) ^ { 4 } ] [ 1 + ( - { 1 } /{ 4 } ) ^ { 8 } ] ....

then

P = $7/9$
P = $6/7$
P = $4/3$
P = $4/5$

Solution:

Let

a = ( - { 1 } /{ 4 } )

⇒ P = ( 1 + a ) ( 1 + a ^ { 2 } ) ( 1 + a ^ { 4 } ) ...

⇒ ( 1 - a ) P = ( 1 - a ) ( 1 + a ) ( 1 + a ^ { 2 } ) ( 1 + a ^ { 4 } ) ( 1 + a ^ { 8 } ) ...

⇒

( 1 - a ) P = ( 1 - a ^ { 2 } ) ( 1 + a ^ { 2 } ) ( 1 + a ^ { 4 } ) ( 1 + a ^ { 8 } ) ...

⇒

( 1 - a ) P = ( 1 - a ^ { 4 } ) ( 1 + a ^ { 4 } ) ( 1 + a ^ { 8 } ) ...

Since a is negative, as the power of a increases the value would keep getting closer to 0
So RHS = 1
⇒ (1 - a )P = 1

P = { 1 }/ { 1 - a } = { 1 } /{ 1 - ( - { 1 } / { 4 } ) } = { 1 } /{ 1 + { 1 } /{ 4 } } = { 4 } /{ 5 }

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