g.c. divisor (29)

[marianha]

29.If g is the greatest common divisor of k+7 and n, where n and k are integers. g=?

1) n=20891

2) n=k+6

 

i guesed its

b

but please throw some light

[rajatmeh]

(1) is clearly not sufficient.

 

Using (2)

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n=k+6 ==> two numbers are k+7 and k+6 i.e these are two consecutive integers.

For any two consecutive integers the GCM can only be 1.

Alternative explanation

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Also you can write 2 consecutive integers as p, p+1

Any factor of p when divides p+1 and the resultant is an integer can only happen when that factor is 1.

 

p/(factor) = some integer

 

(p+1)/(factor) = p/factor + 1/factor = some integer + 1/factor

1/factor can be integer only when factor is 1

 

Hence sufficient, (B).

[raza]

Choice B