Data Sufficiency

if m = 4n + 9, where n is a positive integer. What is the greatest common factor of m and n?
1. m = 9s, where s is a positive integer.
2. n = 4t, where t is a positive integer.

OA is A

sana.noor wrote:if m = 4n + 9, where n is a positive integer. What is the greatest common factor of m and n?
1. m = 9s, where s is a positive integer.
2. n = 4t, where t is a positive integer.

OA is A

Statement 1:
m=9s
n=9(s-1)/4
For n to be an integer, s must be of form 4t+1
So, n = 9t and m = 9 (4t+1)
HCF of m and n will be 9*HCF of t and 4t+1.
Let x be a factor of t, so t is of form xk.
4t+1 = (4k)x+1, So, when you 4t+1 leaves remainder 1 when divided by x.,
So, there can't be an x which is a factor of both t and 4t+1
So, HCF of t and 4t+1 = 1
or
HCF of m and n = 9.
SUFFICIENT

Statement 2:
n=4t
m=16t+9

If t=1, m=25, n=4, HCF = 1
If t=9,
m and n are both divisible by 9, so HCF>1
So, INSUFFICIENT