Hi nidhis.1408:

We are given that y and n are positive integers, and need to find whether y*n is divisible by 7.

Let's look at the statements:

(1)n^2- 14n+49=0
This reduces to n^2- 14n+49 = (n-7)^2.
Since n^2- 14n+49=0, n-7=0 so n=7. Hence yn is divisible. sufficient.

(2) n + 2 is the first of three consecutive integers
whose product is 990.
Here we have (n+2)*(n+3)*(n+4) = 990. A quick breakdown of 990 reveals that 990 = 9*10*11.
Hence (n+2)*(n+3)*(n+4) = 9*10*11. Hence n+2=9 or n=7. Again sufficient.

The final answer is, therefore, D.

Let me know if this helps

I forgot to do n+2 = 9. i took n as 9!
thanks a lot!

, if the product of 3 consecutive integers is 990, then there can be only 3 consecutive integers that satisfy this condition. In other words, there is only one possible value for the first of those three consecutive integers.

Brent, you seem to be doing generalization here. for what types of number it is true ?