This is a question where identifying which topic the question is from itself takes a minute. Of course this is from progressions. Usually there are a couple of questions around progressions in the **CAT exam**. This question tests a student's ability to convert the word problem into a mathematical problem post which is a straightforward application of the formulas . A good **CAT Preparation** would help you crack such questions.

Question 10 : If the population of a town is p in the beginning of any year then it becomes 3+2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

- (1003)
^{15}+ 6 - (977)
^{15}- 3 - (1003)2
^{15}- 3 - (977)2
^{14}+ 3

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From the given data,

Simplifying,

P increases in the series of 2^{0}P ,2^{1}P, 2^{2}P, 2^{3}P,... and so on

2034 is 15 years after 2019. So, the first part of the value would be 2^{15 }p

Now, let us observe the second pattern.

In 2021, the value increases to 2(2p + 3) + 3

On expanding, (2 x 2) +(2 x 3) + 3 = 2 x 2 + 3(1 + 2)

In 2022, the value increases to 2[2(2p+3) +3]+3

On expanding, 2((2 x 2p) + (2 x 3) + 3) + 3

= (2 x 2 x 2 x p) + (2x 2 x 3) + (2 x 3) + 3

= (2 x 2 x 2 x p) + 3(2^{0} + 2^{1} + 2^{2})

In 2034, the value of the second part would be 3 (2^{0} + 2^{1} + 2^{2 }+.... +2^{14} )

On simplifying using Geometric progression we get, 3 () = 3 (

Total population = 2^{15}p +3 (

Substituting p = 1000,

Total population = (2^{15 }x 1003) - 3

The question is **"If the population of a town is p in the beginning of any year then it becomes 3+2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be" **

**Choice C** is the correct answer.

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