windofchange wrote:
What is the remainder when the positive integer n is divided by 12?
(1) When n is divided by 6, the remainder is 1.
(2) When n is divided by 12, the remainder is greater than 5.
We need to determine the remainder when n is divided by 12.
Statement One Alone:
When n is divided by 6, the remainder is 1.
The information in statement one is not sufficient to answer the question. We see that when n = 7, 7/12 has a remainder of 7; however when n = 13, 13/12 has a remainder of 1.
Statement Two Alone:
When n is divided by 12, the remainder is greater than 5.
The information in statement two is not sufficient to answer the question, since when n is divided by 12, it can be any one of these possible remainders: 6, 7, 8, 9, 10, and 11.
Statements One and Two Together:
Using the information from statements one, we see that n can be values such as:
7, 13, 19, 25, …..
We also see that when we divide these values by 12, we get a pattern of remainders:
7/12 has a remainder of 7
13/12 has a remainder of 1
19/12 has a reminder of 7
25/12 has a remainder of 1
Since we have found a pattern, we do not have to test any further numbers. Furthermore, since statement two tells us that the remainder when N is divided by 12 is greater than 5, the only possible remainder is 7.
Answer: C
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