If a and b are positive integers, and a=2b+6, the greatest common divisor of a and b CANNOT be Choose the correct choice:
A) 1	B) 2	C) 3	D) 6	E) 12
since a =2b + 6,   so we can say b = (a/2 -3).   So we need to find not possible gcd values for a , (a/2 -3).   A. 1, We can easily get this value by making a = 8.   B. 2. we can again get this value as GCD by keeping a =10   C. 3 We will get this as GCD by keeping a =12   D. 6 We can get GCD 6 by keeping (a/2-3) = 6 and a as 18.   E. 12 This is not possible as for 12(2^2*3 ) to be GCD = 2^2*3 both a and a/2-3 should be divisible by 4 and 3 . So a has to be a multiple of 4 . this means a/2 has to be even and Even - odd will be odd and odd number wont be divisible by 4.   This 12 cant be the GCD.   Answer 12.
<result>E</result>
If a and b are positive integers, and a=2b+6, the greatest common divisor of a and b CANNOT be