In a certain class, percentage of students who increased their average grade during spring term compared to that of the fall term was recorded between 6.9% and 7.1%. What could be the least possible number of students in that class?
To determine the least possible number of students in the class, we need to consider the boundaries of the given range (6.9% to 7.1%) and calculate the number of students for each boundary. Let's assume the class has "x" students.
To determine the minimum number of students, let's consider the lower boundary of 6.9%:
6.9% of x = (6.9/100) * x = 0.069x
Since the number of students must be a whole number, we can round up the result to the nearest integer:
Minimum number of students = ceil(0.069x)
Next, let's consider the upper boundary of 7.1%:
7.1% of x = (7.1/100) * x = 0.071x
Again, we round up this result to the nearest whole number:
Maximum number of students = ceil(0.071x)
To determine the least possible number of students, we want to find the smallest integer value that satisfies both the minimum and maximum number of students. In other words, we need to find the least common multiple (LCM) of ceil(0.069x) and ceil(0.071x).
By calculating the LCM, we can find the smallest number that is divisible by both ceil(0.069x) and ceil(0.071x). This number will represent the least possible number of students in the class.
Please note that the calculation for the LCM may involve trial and error, as there is no direct formula. Additionally, since the question does not provide an exact value or range for the number of students, we can only determine the minimum possible number based on the given percentage range.