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

Given that \N=(57 \cdot 10^p\), where \(p\) is a positive integer, \(N\) would be of the form 570000...

Note that the rule of the remainder when a number is divided by 9 is that "The remainder when the sum of the digits of the number is the remainder when the number is divided by 9."

Sum of digits of 570000... = 5 + 7 = 12. Remainder when 12 is divided by 9 is 3. Thus, the remainder when \(N\) is divided by 9 is 3.

The correct answer: B

Hope this helps!

-Jay
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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