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Re: Of the total number of students enrolled [#permalink]
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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


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The question clearly states that

1. Sophomores are 3/8th of total so total should be multiple of 8

2. Biology majors are 1/50th of total so total should be a multiple of 50

Therefore total should be a common multiple of 8 and 50 i.e. multiple of 200 (LCM of 8 and 50)

Therefore option A (7000) and option F (7200) are correct
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Re: Of the total number of students enrolled [#permalink]
1
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 8

Likewise, 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 50

In 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
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Re: Of the total number of students enrolled [#permalink]
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