Carcass wrote:
Of the total number of students enrolled at University U in the fall of 2008, \(\frac{3}{8}\) were sophomores and \(\frac{1}{50}\) were biology majors. Which of the following could be the total number of students enrolled at University U in the fall of 2008?
Indicate all such numbers.
A. 7,000
B. 7,040
C. 7,050
D. 7,100
E. 7,125
F. 7,200
Kudos for the right answer and explanation
The key property here is that, since this is a real world question involving students, the number of students must always be an INTEGER. For example, were told that 3/8 of the students were sophomores.
If we let N = the total number of students, then the number of sophomores = (3/8)(N) = 3N/8
In order for 3N/8 to be an INTEGER, it must be the case that
N is divisible by 8Likewise, since 1/50 of the students were biology majors, the number of biology majors = (1/50)(N) = N/50.
In order for N/50 to be an INTEGER, it must be the case that
N is divisible by 50In order for N to be divisible by 8 AND by 50, then N must be divisible by 200 (which is the least common multiple of 8 and 50)
So, we're looking for values of N that are divisible by 200.
Answer: A and F