Data Sufficiency

What is the largest common factor of positive integers J & K

1) K=J + 1
2) kj is a multiple of 5

OA IS A

grandh01 wrote:What is the largest common factor of positive integers J & K

1) K=J + 1
2) kj is a multiple of 5

OA IS A

Statement 1: k = j+1
Since k is 1 more than j, j and k are CONSECUTIVE integers.
Consecutive integers are COPRIMES: they share no factors other than 1.
Thus, the greatest common factor of j and k is 1.
SUFFICIENT.

Statement 2: kj is a multiple of 5
If j=1 and k=5, the greatest common factor of j and k is 1.
If j=5 and k=5, the greatest common factor of j and k is 5.
Since the greatest common factor can be different values, INSUFFICIENT.

The correct answer is A.

grandh01 wrote:What is the largest common factor of positive integers J & K

1) K=J + 1
2) kj is a multiple of 5

The question asks for the LCF between two integers J and K. Remember that the LCF is the largest factor which goes "into" two numbers. For example the LCF of 2 and 4 is 2 because both 2 and 4 have a 2 "inside"

Now to our statements:

STATEMENT 1: Sufficient. k=j+1 suggests that j and k are consecutive integers. Two consecutive integers LCF will simply be 1. You can find this out by testing numbers. If j=2, then k=3 LCF=1 J=10 k = 11 LCF is 1

STATEMENT 1: Insufficient. This does not tell us anything about j and k. It only says that one j or k is a multiple of 5 since jk together have a 5 "inside". We cannot determine the LCF.

The correct answer should be A
Hope this helps

GMATGuruNY wrote:

grandh01 wrote:What is the largest common factor of positive integers J & K

1) K=J + 1
2) kj is a multiple of 5

OA IS A

Statement 1: k = j+1
Since k is 1 more than j, j and k are CONSECUTIVE integers.
Consecutive integers are COPRIMES: they share no factors other than 1.
Thus, the greatest common factor of j and k is 1.
SUFFICIENT.

Statement 2: kj is a multiple of 5
If j=1 and k=5, the greatest common factor of j and k is 1.
If j=5 and k=5, the greatest common factor of j and k is 5.
Since the greatest common factor can be different values, INSUFFICIENT.

The correct answer is A.

I have a doubt
Is the LCM of negative integers -1, -2 is 1