ardz24 wrote:When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6

If, when b is divided by 13, the remainder is 6, then that means b = 13q + 6 for some integer q. Let's analyze each answer choice to see whether the given expression can produce an integer.

A) 13b/52

We need to see if 13(13q + 6)/52 = (13q + 6)/4 could equal an integer for some integer value of q. We can choose q = 2. If q = 2, then 13q + 6 = 32, which is is divisible by 4; hence 13(32)/52 is an integer.

B) b/26

Could (13q + 6)/26 result in an integer for some integer value of q? Notice that 26 is exactly 2 times 13. So, for any integer value of q, 13q will either be divisible by 26 (if q is even) or produce a remainder of 13 (if q is odd). Adding 6 to 13q, the expression will either produce a remainder of 6 or 19, but will never produce a remainder of zero. Therefore, (13q + 6)/26 = b/26 can never equal an integer.

Answer: B