if k and n are integers, is n divisible by 7?
1. n-3=2k
2. 2k-4 is divisible by 7
thank you in advance for your help
1. n-3=2k
2. 2k-4 is divisible by 7
thank you in advance for your help
Statement 1:
n-3=2k
-> n=2k+3
if k = 2, n = 7 YES
if k = 3, n = 9 NO
Insufficient
Statement 2:
2k-4 is divisible by 7
Insufficient since we don't learn anything about n.
Together:
n=2k+3 and 2k-4 is divisible by 7
Now see that when we add 7 to 2k-4, we get 2k+3.
So 2k-4, which is divisible by 7, plus 7, which will also be divisible by 7, is 2k+3.
Since n = 2k+3, it will be divisible by 7.
Sufficient.
(Example: If 2k-4 = 14, then 2k+3=21 and both are divisible by 7.)
