In a Certain Population, There are 3 Times as Many People Aged Twenty-One or Under GMAT Problem Solving

Question - In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is

1. 1 to 2
2. 1 to 3
3. 1 to 4
4. 2 to 3
5. 3 to 4

‘In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one.' - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 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

Approach Solution 1

 It is asked In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. What is The ratio of those twenty-one or under to the total population is

Picking a few numbers that fit the requirements is a quick solution.
Evaluating further –
Suppose there is just one individual over the age of twenty-one.
There must be three individuals under the age of twenty-one if there are three times as many underage individuals as overage individuals.
Thus, the TOTAL population is equal to 1 + 3 + 4

The proportion of people under twenty-one to the entire population is 3 to 4.

The answer is E which is 3 to 4.

Correct Answer: E

Approach Solution 2

There is another approach to answering this question which is fast.
It is asked In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. What is The ratio of those twenty-one or under to the total population iis

Let x represent the proportion of adults above 21.

Given that the proportion of people under 21 is four times higher
hence total population = 4x
The necessary ratio is 3x : 4x, or 3:4.
The available options are (E) 3 to 4.

The answer is E which is 3 to 4

Correct Answer: E

Approach Solution 3

This problem can be solved qucikly followed by the given below method:

Let us consider x be the number of people who are over 21 years old. So, the number of people who are 21 or below be 3x.

Hence, the total population becomes (x+3x)= 4x. Therefore, the ratio of below 21 year old or below to the total population is:
3x : 4x = 3 : 4

Correct Answer: E

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