GMAT Problem Solving - Initial Population of a Town was 8000 People

Question: Initial population of a town was 8000 people. In one year male population increased by 10% and the female population increased by 8%. The total increase in population was 9%. How many males were there initially ?

1. 3600
2. 4000
3. 5000
4. 6000
5. 7200

“Initial population of a town was 8000 people” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. 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

This model answer has only 1 approach to solve the problem.

The given scenario of the case identifies that the initial population of a town was 8000 people. In one year the population of males increased by 10% and the population of females increased by 8%. The total increase in population was 9%.

The problem requires finding the number of males within the town which in terms of the initial population can be considered as x. Accordingly, the total population has been designated as 8000

Therefore, with male population being x, the rest can be the female population. Hence, 8000 - x.

Considering that there have been an increase in the total population by 9%, this implies that the new population data is

9% of 8000
=> 9/100 * 8000 = 720

Accordingly, an increase in the male population has been given to be 10%. So this implies -

Increase in population of male = 10% of x = 10/100 * x

Increase in the female population stands at 8%. This implies that -

Increase in female population = 8% of (8000 - x)

Thus, the number of male population can be evaluated by solving the equation:

= 10% of x + 8% of (8000 - x) = 720 which is the increase in the number of population
= 10/100 * x + 8/100 * (8000 - x)

By solving the equation, the answer stands as
x= 4000

Hence, the male population stands at 4000 in the town after an increase of 10%, and thus, option B is the right answer.

Correct Answer: B

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