If p and q are integers, is the number [m]10^p + q[/m] divisible by 3?

if the sum of digits of any number is divisible by 3, the number itself is divisible by 3.

1) p =5, hence the number is \(10^5 + q\) or 10000q
The sum of digits = 1+q, since value of q is not known, we cant say whether it is divisible by 3.
Not sufficient.

2) q =2, but p is not known.
if p =1, 2, 3, or any positive integer, it will be of form 1q, 10q, 100q...
Sum of digits = 1+q = 1+2 = 3. hence divisible by 3.

But Wait, it is not given that p is a positive integer, it can be negative also.
if p is negative say , p = -2.
then \(10^p + q\) will be 1/100 +2 = 2.01 which is not divisible by 3, because there is no integer which on multiplying with 3 gives 2.01.
Not sufficient.

Combining both St1 and 2, we get the \(10^p + q\) is \(10^5 + 2\) 0r 100002, hence divisible by 3.
Sufficient.

Answer C