neeti2711 wrote:What is the greatest common divisor of positive integers m and n?

(1) m is a prime number
(2) m and n are consecutive integers

(1) m is a prime number but there is info about n; NOT sufficient.

(2) m and n are consecutive integers.
Any two consecutive positive integers are co-prime, which implies that they share 1 as the common factor.
For example: 3 and 4, 5 and 6, are consecutive integers and they share 1 as the common factor.
So, the greatest common divisor of m and n is 1; SUFFICIENT.

The correct answer is B.

neeti2711 wrote:What is the greatest common divisor of positive integers m and n?

(1) m is a prime number
(2) m and n are consecutive integers

Target question: HWhat is the greatest common divisor (GCD) of m and n?

Statement 1: m is a prime number
There are several pairs of numbers that meet this condition. Here are two:
Case a: m=3 and n=3, in which case the GCD of m and n is 3
Case b: m=3 and n=4, in which case the GCD of m and n is 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m and n are consecutive integers
Notice that consecutive integers take the form x and x+1
So, if integer d is a divisor of x (such that d does not equal 1), then d cannot be a divisor of x+1.
In other words, 1 is the only divisor that two consecutive positive integers can have in common. As such, the GCD of any two consecutive positive integers must be 1.
So, if m and n are consecutive integers, then the GCD of m and n must be 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent