pappueshwar wrote:If the remainder is 7 when 85 is divided by n and the remainder is n+7 when 85 is divided by 2n, then what is the value of n?
A. 13 B. 20 C. 23 D. 26 E. 27


OA IS D

The remainder is 7 when 85 is divided by n means that 85 is 7 more than a multiple of n:
85 = kn + 7.

Thus, kn = 78.
Thus, n is a FACTOR of 78.
78 = 2*3*13.
The only answer choices that are factors of 78 are A (n=13) and D (n=26).
Eliminate B, C and E.

Answer choice A: n=13
If n=13, then 2n=26.
Since 2n must yield a remainder of n+7, n=13 cannot be correct:
As we noted above, since 26 is a factor of 78, it will yield a remainder of 7.
Eliminate A.

The correct answer is D.

The remainder is n+7 when 85 is divided by 2n means that 85 is n+7 more than a multiple of 2n:
85 = k(2n) + (n+7).

Thus:
78 = k(2n) + n
78 = n(2k+1).

78 is even.
Since 2k+1 is an odd integer, and odd*odd = odd, n must be EVEN.
Thus, n=13 is not possible.