6. From the 11 integers 1 to 11, if any 6 numbers are taken, then the following conclusions that are correct are ( ) in number.
(1) There must be two numbers that are coprime;
(2) There must be one number that is a multiple of another number;
(3) There must be one number whose double is a multiple of another number.
A. 3
B. 2
C. 1
D. 0
Analysis: Pigeonhole Principle
(1) 1 is coprime with any other natural number greater than 1, and any two consecutive natural numbers are coprime. From 1 to 11, there are 5 even numbers. If you select one more number, there must be two numbers that are consecutive, and thus, there must be two numbers that are coprime.
(2) (1) $(2,4,8)(3,6)(5,10)(7)(11)(9)$, clearly, taking $4, 5, 6, 7, 9, 11$, no number is a multiple of another.
(3) $(4,8)(3,6,9)(5,10)(7)(11)$, taking one number from each group, taking 5 numbers (not taking $4,6$ at the same time), it can be guaranteed that no number is twice another. However, if you take 1, 2, or any other number within each group, there must be a number that is twice another.
Therefore, there are 2 correct answers, the answer is B.