Hi HG10:

We are asked if L is divisible by 27.

1. L is not a multiple of 45.
27 is not a multiple of 45, however it is divisible by 27.
Also, 1 is not a multiple of 45t, but it is not divisible by 27.
Hence not sufficient.

2. L is a multiple of 10.
10 is a multiple of 10. But 10 is not divisible by 27.
270 is a multiple of 10. But 270 is divisible by 27.
Again, insufficient.

Now let's consider them together.

L is a multiple of 10, but L is not a multiple of 45.
Now multiples of 10 that are divisible by 27 are of the form: 270*m (where m is a positive integer).
But 270*m = 3*3*3*2*5*m = 3*3*5* (2*3*m) = 45 * 6m. Clearly all multiples of 10 that are divisible by 27 are also multiples of 45. Therefore, there exists no such number L which is divisible by 27. Since we have a clear NO answer, both statements together are SUFFICIENT. Hence C.

Let me know if this helps

Thank you for the solutions!