WoundedTiger wrote:

A repunit is a positive integer that contains only the digit 1. If the integer r is a repunit, is r prime?

(1) The number of digits in r is a multiple of 3.

(2) 0 < r < 1200

Target question: Is r prime? Given: Integer r is a repunit So, some possible values of r include: 1, 11, 111, 1111, 111111111111111111, etc

Statement 1: The number of digits in r is a multiple of 3. So, r could equal 111 or 111,111 or 111,111,111 or 111,111,111,111 etc

We know that, if the sum of the digits in a number is divisible by 3, then that number is also divisible by 3

For example, since the digits in 111 add to 3 (and 3 is divisible by 3), we know that 111 is divisible by 3, which means 111 is NOT prime.

Likewise, since the digits in 111,111 add to 6 (and 6 is divisible by 3), we know that 111,111 is divisible by 3, which means 111,111 is NOT prime.

And, since the digits in 111,111,111 add to 9 (and 9 is divisible by 3), we know that 111,111,111 is divisible by 3, which means 111,111,111 is NOT prime.

As we can see, if the number of digits in r is a multiple of 3, then the sum of r's digits will be divisible by 3.

So, the answer to the target question is

NO, r is NOT primeSince we can answer the

target question with certainty, statement 1 is SUFFICIENT

Statement 2: 0 < r < 1200There are 4 possible values of r: 1 or 11 or 111 or 1111

Case a: If r = 11, then

r IS primeCase b:If r = 111, then

r is NOT primeSince we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,

Brent

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