Bunuel wrote:

T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?

I. 9

II. 15

III. 27

A. I only

B. II only

C. I and II only

D. I and III only

E. I, II, and III

Ans: C

Solution:

T->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3

means x must contain 3^2 and 5^2

so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25

but 27 is not a divisor because it can't divide 9*25 fully.

so Ans : C

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