DS from MGMAT Adv Quant -- m=4n+9

[rishimaharaj]

Hi all,
Question 12 from WorkoutSet #2 is:

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.

In the answer explanation, there is heavy usage of scenario charts calculating the GCF for over 20 different values. I doubt this is the most efficient method of solving this problem. Anyone have any shortcuts to apply to this one?

BTW, the official answer is answer choice A.

Thanks,
--Rishi

[neerajkumar1_1]

statement 1

m = 9s.

which means that m is a multiple of 9
also m = 4n + 9

for this to be true,
since we are already adding 9 to 4n, we will have to make 4n a multiple of 9 to satisfy m=9s

hence n can take value 9, 18, so on so forth..

since n will also have to be a multiple of 9, there will be a constant GCF between the m and n as 9.
so sufficient

statement 2:
n= 4t
which makes m = 16t + 9
u will get different GCFs as there is no control on the value of t.

so insufficient..

Hence A..

I am getting back to BTG forum after a long time as I have restarted my prep..
hope my skills havnt become too rusty and this helps...

[sl750]

For statement 2,

Is it necessary to choose the same value of t for both m and n?. Otherwise, the gcf (4t,16t+9) will be 1, making statement 2 sufficient

[GmatMathPro]

gcf(4t,16t+9) will not be 1 if t is a multiple of 3.