fahim123456
One-third, one-fourth, one-fifth, and one-seventh of the human population of Island X, which has fewer than 5,000 human inhabitants, are all whole numbers and the sum is exactly the population of Y. What is the population of Island Y?
4200
4279
4581
4800
Can not be determined
Certainly, let’s go through it cleanly with the correct variables and setup.
Problem Recap
We know:
• Island X has a population, , which is less than 5,000.
• One-third, one-fourth, one-fifth, and one-seventh of  are all whole numbers.
• The sum of these fractional parts equals the population of Island Y, which we’ll call .
We need to find , the population of Island Y.
Step-by-Step Solution
1. Set Up the Equation for :
Since the sum of the fractional parts of  equals , we have:

2. Find the Sum of the Fractions:
To add these fractions, let’s find a common denominator.

So, we can rewrite  as:

3. Determine Requirements for :
Since  must be divisible by 3, 4, 5, and 7 to make each fraction a whole number,  needs to be a multiple of the least common multiple (LCM) of these numbers.
• 
So  must be a multiple of 420 and less than 5,000.
4. List Possible Values of :
The possible values for  under 5,000 are:

5. Calculate  for :
Testing :

6. Conclusion:
Thus, if , then . This matches an answer choice.
Final Answer: The population of Island Y is 4,200.
my bad it didn’t show the calculations lol