MathRevolution 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 1Case 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 2Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k = 1There'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 1Since we can answer the

target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com