Here's a hypothetical scenario that fits these statements:

total population of Townville: 10,000
# of tennis players: 1,000 --> non-tennis-players: 9,000
# of smokers: 500 --> non-smokers: 9,500
# of tennis-playing smokers: 400 (80% of all smokers --> "most smokers play tennis")
# of tennis-playing non-smokers: 100 (barely over 1% of nonsmokers --> "most nonsmokers do not play tennis")
percentage of tennis players who smoke: 400/100 --> 40%

In this hypothetical, the conclusion was false. Fewer than half of the tennis players smoked.

So, the flaw in this argument is the same one that you made: proportions within overlapping categories are not transferable. Consider: "most winners of the Westport Dog Show are terriers." Would it follow that "most terriers have won the Westport Dog Show?" Oh course not - the # of dog show winners is far smaller than the # of dogs within a particular breed type, so one proportion would not tell you about the other.

To answer a question about Pattern of Reasoning**, try to abstract the argument into variables:

Most people in category X are also in category Y, and most not in X are not in Y. Therefore, most people in category Y are also in category X.

Now, similarly abstract the information in the answer choices:

A. In Townville, most Lions Club members were born in Townville, and most of the residents who are not Lions Club members were not born in Townville. Therefore, most of the residents who were born in Townville are Lions Club members.

"Most X were Y, and most not-X were not Y. Therefore, most Y are X." --> This is exactly what we're looking for.

B. In Townville, most of the people who live west of Main Street own a GPS live east of Main Street. Therefore, most of the people in Townville own a GPS.

... I think this one is missing half a sentence. It doesn't make sense.

C. In Townville, most cat owners own exactly one dog, and most dog owners own more than one dog. Therefore, most of the people in Townville who own more than one dog do not own any cats.

"Most people who are in category X (owning any cats) are in a subset of category Y (just one dog), and most in Y are in a different subset of Y..." Already this is different. Wrong.

D. In Townville, most tennis players play golf, but not every golfer plays tennis. Therefore, in Townville, there are more tennis players than golfers.

"Most in category X are also in category Y, but not every Y is in X." Different logic structure.

E. In Townville, most of the houses are painted red, and most of the houses have a pool. Therefore, in Townville, most of the houses are painted red and have a pool.

"Most in category X (houses) are also in category Y (red), and most in X (houses) are also in Z (pool)." Different structure.

The answer (assuming it's not B, which we can't read fully) is A.


**Nota bene: this question type are VERY rare on the GMAT, and perhaps no longer being asked. We haven't seen them in an OG since OG11.