CAT 2019 Question Paper | Quants Slot 1

CAT Questions

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

1. (1003)¹⁵ + 6
2. (977)¹⁵ - 3
3. (1003)2¹⁵ - 3
4. (977)2¹⁴ + 3

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Video Explanation

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Explanatory Answer

From the given data,

Simplifying,

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

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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"

Hence, the answer is (1003)2¹⁵ - 3

Choice C is the correct answer.