Question

What is the greatest common divisor of x and y

Answer 1

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4 --> clearly insufficient: of course 4 itself could be the GCD but it's also possible that x and y share some other common factor more than 4, for example 5 (in this case both will be divisible by 20), or 8, or 4,000,000 ... so GCD could be more than 4 as well. Though from this statement we know that GCD cannot possibly be less than 4.

(2) x - y = 4 --> according to the property #2: GCD(x,y)≤4

GCD(x,y)≤4, but still insufficient.

(1)+(2) From (1) GCD≥4

GCD≥4 and from (2) GCD≤4

GCD≤4 --> GCD=4

GCD=4 Sufficient.

Answer: C.