byRituparna Nath Content Writer at Study Abroad Exams
Question: 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
- \((997)2^{14}-3\)
- \((997)2^{14}+3\)
- \((1003)2^{15}−3\)
- (997)^15−3
- (1003)^15+6
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’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
The population at the beginning of 2019 is 1000
After 1 year, Population =
3+2∗1000
=3+2(1003−3)
=2(1003)−3
After 2 years, Population =
3+2[2(1003)−3)]
=\(3+2^2(1003)−6\)
=\(2^2(1003)−3\)
After 3 years, Population =
3+2[2^2(1003)−3)]
=3+2^3(1003)−6
=2^3(1003)−3
After n years, Population =
\(2^n(1003)−3\)
In 2034, i.e, after 15 years,
Population =
\(2^{15}(1003)−3\)
Hence, we can rearrange and state this as \(2^{15}(1003)−3\)
The correct answer is C.
Correct Answer: C
Model Answer 2
Explanation:
This problem can be solved by analyzing patterns in the progressions.
As per the question, the Population increases as follows:
Let us consider the population is P
Year-0 (2019): P
Year-1 (2020): 2P+3
Year-2 (2021): 4P+9
Year-3 (2022): 8P+21
Year-4 (2023): 16P+45
Year-5 (2024): 32P+93
From the above the progression we see there are two parts (a) a Power of a 2 and (b) multiples of 3
Every subsequent year the (a) increases by 2^(n). That is in year 5 the part (a) is 2^5
So, for Year-15 (2034) the part (a) will 2^15P
We see similar patterns in the part (b),
Year 1: 3 = 3X1 = 3X(2^1 -1)
Year 2: 9 = 3X3 = 3X(2^2 -1)
Year 3: 21 = 3X7 = 3X(2^3 -1)
So, for Year 15 or 2034: 3X(2^15-1)
combining (a)+(b), we get
= 2^15P + 3X(2^15 -1)
= 2^15P + 3*2^15 - 3
= 2^15(P+3) - 3
As per the question, we know P=1000 in 2019,
Hence,
=2^15(1000+3) - 3
=2^15(1003) - 3
The correct answer is C.
Correct Answer: C
Approach Solution 3
Population 2019 --> 10001000
After 1 year, Population = 3+2∗1000=3+2(1003−3)=2(1003)−33+2∗1000=3+2(1003−3)=2(1003)−3
After 2 years, Population = 3+2[2(1003)−3)]=3+22(1003)−6=22(1003)−33+2[2(1003)−3)]=3+22(1003)−6=22(1003)−3
After 3 years, Population = 3+2[22(1003)−3)]=3+23(1003)−6=23(1003)−33+2[22(1003)−3)]=3+23(1003)−6=23(1003)−3
After n years, Population = 2n(1003)−32n(1003)−3
In 2034, i.e, after 15 years, so the Population becomes 215(1003)−3215(1003)−3
The correct answer is C.
Correct Answer: C
Suggested GMAT Problem Solving Questions
- The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
- If tu=xytu=xyand ty=uxty=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving
- A Farm has Chickens, Cows and Sheep GMAT Problem Solving
- In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving
- If 4 People are Selected from a Group of 6 Married Couples GMAT Problem Solving
- If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
- If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
- A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
- A Conference Room is Equipped with a Total of 45 Metal or Wooden Chairs.GMAT Problem Solving
- A Welder Received an Order to Make a 1 Million Litre Cube-Shaped Tank. GMAT Problem Solving
- Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours. GMAT Problem Solving
- What is the Value of k if the Sum of Consecutive Odd Integers From 1 to k Equals 441? GMAT Problem Solving
- A Circle with a Radius R is Inscribed into a Square with a Side K. GMAT Problem Solving
- Machine A can do a Certain Job in 12 Days Working 2 Full Shifts GMAT Problem Solving
- The square of 5√252 =? GMAT Problem Solving
- After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving
- If 12 Ounces of a Strong Vinegar Solution are Diluted with 50 Ounces GMAT Problem Solving
- A Contractor Estimated that his 10-Man Crew GMAT Problem Solving
- A Circle is Inscribed in a Square with the Diagonal of 4 Centimeters. GMAT Problem Solving
- At a Dog Competition, a Dog is Awarded 10 Points if it Runs GMAT Problem Solving
Comments