Greatest common divisor

[mehravikas]

S13-25 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.

[g_beatthegmat]

Answer should be (B).

(A) is insufficient as it doesn't tell us about 'n'. m could be a prime number, but n could be a multiple of m.

(B) is sufficient as it tells us that m and n are consecutive numbers. In such a case, the numbers cannot not have any common factors, thus GCF is 1.
Eg: 2, 3.
10, 11.
48, 49
etc.

Hope it helps.

[mehravikas]

Thanks, it does help. OA is 'B'

Answer should be (B).

(A) is insufficient as it doesn't tell us about 'n'. m could be a prime number, but n could be a multiple of m.

(B) is sufficient as it tells us that m and n are consecutive numbers. In such a case, the numbers cannot not have any common factors, thus GCF is 1.
Eg: 2, 3.
10, 11.
48, 49
etc.

Hope it helps.

[helviolc]

(I) alone is insufficient because the GCD can be m only if n is a multiple of m - all other cases will lead to no commom divider. This leads to two possible answers so therefore Insufficient.

(2) alone is insufficient because you can have more than one number combination that satisfies the equation but gives you a different GCD: To test, plug m=2 , n=7 (no commom divider) or m=6 , n=21 (3 as a commom divider)

(1) and (2) together satisfy the question. The only prime number for m that satisfies equation (2) is 2, stating that the numbers do not have a commom divider, as n will be equal to 7, another prime number.

So, answer is C.

[mehravikas]

Sorry but the answer is B

As per statement 2, m and n are consecutive integers.

(I) alone is insufficient because the GCD can be m only if n is a multiple of m - all other cases will lead to no commom divider. This leads to two possible answers so therefore Insufficient.

(2) alone is insufficient because you can have more than one number combination that satisfies the equation but gives you a different GCD: To test, plug m=2 , n=7 (no commom divider) or m=6 , n=21 (3 as a commom divider)

(1) and (2) together satisfy the question. The only prime number for m that satisfies equation (2) is 2, stating that the numbers do not have a commom divider, as n will be equal to 7, another prime number.

So, answer is C.