What is the greatest common factor of the positive integers j and k?

Question

(1) k = j + 1 
(2) jk is divisible by 5.

14101992 · Accepted Answer

Statement 1: k = j + 1

It means j and k are consecutive positive integers. All pairs of consecutive positive integers have greatest common factor as 1.
So, Statement 1 is sufficient!

Statement 2: jk is divisible by 5

Let us take an example of jk=50 which is divisible by 5.
j and k can be 2 and 25 respectively. Here we have the greatest common factor as 1.
But if j and k are 5 and 10 respectively then we will have the greatest common factor as 5.

Hence, Statement 2 is insufficient.

Answer will be A.

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mahawarchirag · Answer

Answer - A 
Statement 1 - For any positive integer suppose j=5 then K=6 , the G.C.F. is 1 , every such no. will occur in pair of odd and even . so any pair of odd and even no. with difference 1 has G.C.F 1. Sufficient

Statement 2- JK divisible by 5 . It is possible that only j is divisible by 5 or only k is divisible by 5 or both are divisible by 5 .Thus statement 2 is Insufficient.

hsbinfy · Answer

A

1) the first statement states that j and k are co primes. and co-primes don't share any other factor than 1.suff
2)product of j and k is divisible by 5. this does not mean there aren't any other factors.not suff

stonecold · Answer

Here is my approach => 
WE need to get the GCD of J and K
Statement 1 => J=K+! => J and K are coprimes 
Hence GCD = 1 => Suff
Statement 2 => J=5,K=10=> GCD=5
J=5,K=6 => GCD =1 => Hence using the "TEST CASE Approach" => not suff
SMASH THAT A

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What is the greatest common factor of the positive integers j and k?

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