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When n and k are positive integers, what is the greatest common diviso [#permalink]

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13 Apr 2017, 23:22

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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

St I n=2 if k is odd say 1 then n+k = 3 and n = 2 and the GCD(n+k,n)=1 but if K is even say 2 n+k = 4 and n = 2 and the GCD(n+k,n)=2 ----------Insufficient

St II k = 1 if n is odd say 1 then n+k = 2 and k = 1 and the GCD(n+k,n)=1 but if n is even say 2 n+k = 3 and k = 2 and the GCD(n+k,n)=1 so no matter what the value of n is, since k = 1 the GCD(n+k,n) will always be 1 (n+k and n will be consecutive integers) ----------Sufficient

Hence option B is correct Hit Kudos if you liked it

==> In the original condition, there are 2 variables, and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get n+k=2+1=3 and n=2, and GCD(3,2)=1, hence it is unique and sufficient. Therefore, the answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), k is unknown hence it is not sufficient. For con 2), if k=1, n+k(=n+1) and n becomes 2 consecutive integers, so always GCD=1, hence it is unique and sufficient.

Therefore, the answer is B, not C. Answer: B
_________________

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