lheiannie07 wrote:When n and k are positive integers, what is the greatest common divisor of n+k and n?
1) n=2
2) k=1
Target question: What is the greatest common divisor of n+k and n?
Statement 1: n = 2
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n and k that satisfy statement 1. Here are two:
Case a: n = 2 and k = 1, in which case n+k=2+1=
3 and n=
2. Here,
the greatest common divisor of n+k and n is 1
Case b: n = 2 and k = 2, in which case n+k=2+2=
4 and n=
2. Here,
the greatest common divisor of n+k and n is 2
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: k = 1
There's a nice rule that says:
The greatest common divisor of x and x+1 is 1 (where x is a positive integer)
Since k=1, then we must find the greatest common divisor of n+1 and n
According to the above
rule, the greatest common divisor of n+1 and n is 1
So, when k=1,
the greatest common divisor of n+k and n is 1
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
B
Cheers,
Brent
