Set A= (4/7), 1, (5/2), 4, (11/2), 7

Set B= (4/7), (7/4), 4, 7

If n is a member of both Set A and Set B above which of the following must be true?

I. n is an integer
II. 4n is an integer
III. n=4

B) II only
C) I and II only
D) I and III only
E) I, II, and III

There are 3 numbers that are members of both sets: \dfrac{4}{7}, 4, and 7. The question asks which of those conditions must be true. I doesn’t have to be true—\dfrac{4}{7} isn’t an integer. II also doesn’t have to be true, because 4\times\dfrac{4}{7} is still not an integer. III also doesn’t have to be true—neither \dfrac{4}{7} nor 7 are equal to 4.

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