Probability

[BTGmoderatorRO]

A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability the piece ends no more than 7 spaces from the square numbered 49?

(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

OA is E

Can an Expert give a simple and easy way to solve this problem?

[elias.latour.apex]

Obviously if the piece falls directly on 49, regardless of which direction it moves, it will be within 7 squares of 49.
Should the piece fall on the squares 35-48 or 50-63, a total of 28 squares, it will be within 7 squares of 49 half the time. Should it move away from 49, it will not end up within 7 squares whereas if it moves towards 49, it will.

So, the answer is half of 28 (14) representing the chances for tiles 35-63 (excluding 49) and 1 additional chance for landing exactly on 49. That's a total of 15. That's answer choice D.

However, the problem seems to indicate that the "Official Answer" is E. I cannot explain it.