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
From the given data,
P increases in the series of 20P ,21P, 22P, 23P,... and so on
2034 is 15 years after 2019. So, the first part of the value would be 215 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(20 + 21 + 22)
In 2034, the value of the second part would be 3 (20 + 21 + 22 +.... +214 )
On simplifying using Geometric progression we get, 3 () = 3 (
Total population = 215p +3 (
Substituting p = 1000,
Total population = (215 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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