swerve wrote:\(N\) is a positive integer which can be expressed as \(57 \cdot 10^p\), where \(p\) is a positive integer. What is the remainder when \(N\) is divided by 9?
A. 0
B. 3
C. 4
D. 6
E. 7
The OA is B
Source: e-GMAT
If p = 1, we have N = 570 and 570/9 = 63 R 3.
Alternate solution:
The remainder when a positive integer is divided by 9 is the same as when the sum of the digits of that integer is divided by 9. Since N = 57 x 10^p, where p is a positive integer, N is the integer 57 followed by p zeros. Therefore, the sum of the digits of N is 5 + 7 + p x 0 = 12, and since 12 has a remainder of 3 when it's divided by 9, N also has a remainder of 3 when it's divided by 9.
Answer: B
