x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median Q of x, y, and z?
I. 9
II. 10
III. 11	Choose the correct choice from the following choices.
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
Average gives us an idea that 3 nos. are close to 10.   so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.   Let us see options.   If 9 has to be median.   1st term has to less than 9 or equal to 9. (also maintain z-x = 3)   9 9 12 --&gt; satisfies all conditions so 9 can be a median value.   If 11 has to be a median   3rd term has to be 11 or more than 11. (also maintain z-x = 3)   8 11 11 --&gt;satisfies all conditions so 9 can be a median value.   Now for 10 to be median Q.   z+ x = 20 and z-x = 3, we wont have integer values of z.   10 cannot be a median   I and III only is the answer.
<result>E</result>
x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median Q of x, y, and z?
I. 9
II. 10
III. 11