¡¡¡¡7. The set S of numbers has the following properties£º
¡¡¡¡I£© If x is in S£¬ then 1/x is in S.
¡¡¡¡II£© If both x and y are in S£¬ then so is x + y.
¡¡¡¡Is 3 in S£¿
¡¡¡¡£¨1£© 1/3 is in S.
¡¡¡¡£¨2£© 1 is in S.
¡¡¡¡Consider £¨1£© alone. Since 1/3 is in S£¬ we know from Property I that 1/£¨1/3£©
¡¡¡¡= 3 is in S. Hence£¬ £¨1£© is sufficient.
¡¡¡¡Consider £¨2£© alone. Since 1 is in S£¬ we know from Property II that 1 + 1 = 2
¡¡¡¡£¨Note£¬ nothing in Property II prevents x and y from standing for the same n
¡¡¡¡umber. In this case both stand for 1.£© is in S. Applying Property II again s
¡¡¡¡hows that 1 + 2 = 3 is in S. Hence£¬ £¨2£© is also sufficient. The answer is D.
¡¡¡¡8. What is the area of the triangle above£¿
¡¡¡¡£¨1£© a = x£¬ b = 2x£¬ and c = 3x.
¡¡¡¡£¨2£© The side opposite a is 4 and the side opposite b is 3.
¡¡¡¡From £¨1£© we can determine the measures of the angles£º a + b + c = x + 2x + 3
¡¡¡¡x = 6x = 180
¡¡¡¡Dividing the last equation by 6 gives£º x = 30
¡¡¡¡Hence£¬ a = 30£¬ b = 60£¬ and c = 90. However£¬ different size triangles can hav
¡¡¡¡e these angle measures£¬ as the diagram below illus
