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If m and n are positive integers and r is the remained when

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If m and n are positive integers and r is the remained when

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If m and n are positive integers and r is the remained when 5(10^n) + m is divided by 3, what is the value of r?

1) n=10
2) m=1

OA B

Source: GMAT Prep

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BTGmoderatorDC wrote:
If m and n are positive integers and r is the remained when 5(10^n) + m is divided by 3, what is the value of r?

1) n=10
2) m=1
5(10^n) = 5 followed by n zeros.
If n=1, then 5(10^n) = 5*10¹ = 5 followed by 1 zero = 50
If n=2, then 5(10^n) = 5*10² = 5 followed by 2 zeros = 500
If n=3, then 5(10^n) = 5*10³ = 5 followed by 3 zeros = 5000

Rule:
An integer whose digits sum to a multiple of 3 is itself a multiple of 3.
An integer whose digits do not sum to a multiple of 3 is NOT a multiple of 3.

Statement 1:
Case 1: n=10 and m=1
In this case, 5(10^n) + m = (5 followed by 10 zeros) + 1
Sum of the digits = 5 + (10*0) + 1 = 6
Since the sum of the digits is a multiple of 3, the yielded integer is a multiple of 3.
Implication:
Dividing by 3 will yield a remainder of 0.

Case 2: n=10 and m=2
In this case, 5(10^n) + m = (5 followed by 10 zeros) + 2
Sum of the digits = 5 + (10*0) + 2 = 7
Since the sum of the digits is not a multiple of 3, the yielded integer is NOT a multiple of 3.
Implication:
Dividing by 3 will NOT yield a remainder of 0.

Since the remainder can be different values, INSUFFICIENT.

Statement 2:
In this case, 5(10^n) + m = (5 followed by n zeros) + 1
Sum of the digits = 5 + (n*0) + 1 = 6
Since the sum of the digits is a multiple of 3, the yielded integer is a multiple of 3.
Implication:
Dividing by 3 will yield a remainder of 0.
SUFFICIENT.

The correct answer is B.

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