(A) 3: ababab is divisible by 3 because the sum of its digits is 3(a + b), a multiple of 3 for any

integers a and b.

(B) 4: An integer is divisible by 4 if its last two digits represent a two-digit number that is itself

divisible by 4. It is uncertain whether the two-digit integer ab is divisible by 4.

(C) 5: An integer is divisible by 5 if the last digit is 0 or 5. It is uncertain whether the positive

integer b is 5.

(D) 6: An integer is divisible by 6 if it is even and divisible by 3. We already established that ababab is divisible by 3, but it is uncertain whether the last digit b is even, a requirement for ababab to be even.

Alternatively, we can tackle this problem by thinking about the place values of the unknowns. If we had a two-digit number ab, we could express it as 10a + 1b. By similar logic, ababab can be expressed as follows:

ababab = 100,000a + 10,000b + 1,000a + 100b + 10a + b

If we combine like terms, we get the following:

ababab = 101,010a + 10,101b

At this point, we can spot a common term: each term is a multiple of 10,101. If we factor 10,101 from each term, the expression can be written as follows:

ababab = 10,101(10a + b), where a and b are individual digits.

Or simply:

ababab = 10,101(ab), where ab is a two-digit number.

Since we don't know the value of the two-digit number ab, we cannot know what its factors are. To find a known factor of ababab, our only option is to find a factor of 10,101.

At this point, we can recognize that 10,101 is a multiple of 3 (the sum of the digits is 3). Therefore, ababab must be a multiple of 3.

The correct answer is A.

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Thanks & Regards,

Anaira Mitch