IMO C

A. cartographers' most common design of maps that only measure distance
wrong comparison.. maps to cartographers'
B. cartographers and their most common design of maps that only measure distance
wrong comparison.. maps to cartographers
C. the most common maps designed by cartographers that only measure distance
looks good
D. the most commonly designed maps of cartographers that only measure distance
"maps of cartographers" changes meaning.
E. the most commonly used maps and only measuring distance
unnecessarily removes cartographers.

IMO C

How D changes the meaning?
A says common design of maps...D says commonly designed maps..

OE:

The original sentence incorrectly compares design with contour maps. Choice (C) corrects the lack of parallelism by comparing common maps to contour maps. Incorrect choice (B) compares cartographers and design to the contour maps. While (D) does compare maps to maps, the phrase "maps of cartographers" is redundant and wordy. Choice (E) incorrectly compares measuring distance to a map.

In contrast to X, Y

C rightly shows the correct usage.

adi_800 wrote:How D changes the meaning?
A says common design of maps...D says commonly designed maps..

'Common design of maps' lays emphasis on design while 'commonly designed maps' lays emphasis on maps. Moreover the maps were not of cartographers but by them.