Rca wrote:
If x is a positive integer, is the remainder 0 when (3^x + 1)/10?
(1) x = 3n + 2, where n is a positive integer.
(2) x > 4
We are given that x is a positive integer and need to determine the remainder when 3^x + 1 is divided by 10. Since we know that 1/10 produces a remainder of 1, we really need to determine the remainder when 3^x is divided by 10. We should keep in mind that the remainder of any integer divided by 10 is equivalent to the units digit of that number, so we need to determine the units digit of 3^x.
Statement One Alone:x = 3n + 2, where n is a positive integer.
We see that we cannot determine the units digit of 3^n. If n = 1, then 3^x = 3^5, which has a units digit of 3, and thus a reminder of 3 when divided by 10. However, if n = 2, then 3^x = 3^8 has a units digit of 1, and thus a reminder of 1 when divided by 10. Statement one alone is not sufficient to answer the question.
Statement Two Alone:x > 4
Knowing that x is greater than 4 is not sufficient to answer the question.
Statements One and Two Together:Using the statements together, we still cannot answer the question. We can still use n = 1 and n = 2 to obtain 3^x = 3^5 and 3^x = 3^8, respectively. Since 3^5 and 3^8 have different units digits, the remainder when 3^5 + 1 is divided by 10 and the remainder when 3^8 + 1 is divided by 10 will be different.
Answer: E