Official Solution:
There are community leaders, as well as ex-convicts, who are successful in business. All people who are successful in business are encouraged to join the Reynard Club.
Which of the following can be concluded from the above?
A. All who are encouraged to join the Reynard Club are successful in business.
B. All who are encouraged to join the Reynard Club are community leaders or ex-convicts.
C. Some who are encouraged to join the Reynard Club are not community leaders or ex-convicts.
D. Some ex-convicts are encouraged to join the Reynard Club.
E. Some ex-convicts are not encouraged to join the Reynard Club.
Firstly, for an inference type question, the conclusion MUST BE TRUE and be derived from ONLY the facts given in the passage WITHOUT ANY ADDITIONAL ASSUMPTION. The condition “MAY BE TRUE” is not enough to deduce that the option is a conclusion. Let us say an option statement is Z - if one can derive that NOT Z may be true, then the option cannot be the answer to an inference type question. So will be our approach to eliminate each of the incorrect options.
Lets us define some groups as follows:
A = community leaders who are successful in business.
A1 = community leaders who are unsuccessful in business.
B = ex-convicts who are successful in business.
B1 = ex-convicts who are unsuccessful in business.
C = others (not community leaders or ex-convicts) who are successful in business.
C1 = others (not community leaders or ex-convicts) who are unsuccessful in business.
X = those who are successful in business.
X1 = those who are unsuccessful in business.
Y = those who are encouraged to join the club.
Y1 = those who are not encouraged to join the club.
Given in the passage:
1. Belonging to A —> must be belonging to X —> must be belonging to Y
2. Belonging to B —> must be belonging to X —> must be belonging to Y
Can be conclusively derived from the passage:
3. Belonging to A1 or B1 or C1 —> must be belonging to X1
4. Belonging to X —> cannot be belonging to Y1.
The following arguments are not incomplete / not conclusive:
5. Belonging to X1 —> belonging to Y ? Not known.
6. Belonging to X1 —> belonging to Y1? Not known.
A. Are there some X1 who are also Y? May be.
Nothing is said in the passage about the people who are not successful in business, that is, we do know whether or not they are encouraged to join the club. There MAY indeed be some unsuccessful businessmen who are encouraged to join the club, making this statement wrong because the condition “MUST BE TRUE” is not satisfied.
B. Are there some C or C1 who are also Y? May be.
Nothing is said about the people who are not community leaders or ex-convicts. There may exist some people who are NOT community leaders or ex-convicts, but are successful businessmen (group C) and hence encouraged to join Reynard club, making this conclusion wrong.
Moreover even those NOT community leaders or ex-convicts may be unsuccessful in business (group C1), but may still be encouraged to join the club, because nothing is said about the people who are unsuccessful in business (X1), that is whether or not X1 are encouraged to join the club. Thus in such a case statement B cannot be a conclusion because the condition “MUST BE TRUE” is not satisfied.
C. Are there NO C or C1 who are also Y? May be.
Nothing is said about the people who are not community leaders or ex-convicts. Such people may or may not be successful in business. It is true that if they are successful businessmen, they must be encouraged to join the club, but it is possible there exists nobody who is C, i.e. all who are NOT community leaders or ex-convicts are unsuccessful in business. if they are not successful (Group C1), they may be or may not be encouraged to join the club. Thus there is a possibility that no such people are encouraged to join the club. Therefore option C cannot be a conclusion because the condition “ MUST BE TRUE” is not satisfied.
D. Correct. Same as given in the passage as mentioned in item 2 above. The passage states that there exist ex-convicts who are successful in business and all successful businessmen are encouraged to join the club. Hence there MUST be some ex-convicts who are encouraged to join the club.
E. Are there NO B or B1 who are also Y1? Surely there is NO B who are also Y1, but there MAY BE NO B1 too who are also Y1.
It is possible that all ex-convicts are successful and hence encouraged to join the club ( i.e there exist no B1 at all), making this option wrong because the condition “MUST BE TRUE” is not satisfied.
Moreover there may exist some B1, but they may still be part of Y and not Y1 because nothing in the passage confirms that unsuccessful people are not encouraged to join the club. Therefore even in this case the option C cannot be a conclusion because the condition “MUST BE TRUE” is not satisfied.
Answer: D