If all applicants are motivated professionals, and some professionals are unmotivated, then ...

Question

A friend of mine took an aptitude test by Deloitte. One of the questions was an interesting logical puzzle:

• All applicants are motivated professionals

• Some professionals are unmotivated

Select the correct answer:

1) engineers are unmotivated

2) some applicants are unmotivated

3) some professionals are applicants

4) none of these conclusions is logically inescapable

Thinking purely mathematically, the answer was clear to me, and so it was to my mathematics friends. However, my friend and her friends seem to interpret the question a little bit different. It's interesting to see the different approaches to this question.

Unfortunately, we were not able to see the correct answer. What do you think?

Answer 1

There's wiggle room in the statements, of course. Does "engineers are unmotivated" mean "all engineers are unmotivated" or "some engineers are unmotivated"? Is an engineer a professional or not?

But anyway, we can't say anything.

If engineers don't have to be professionals:

Consider a world with no applicants; exactly one unmotivated professional, who is not an engineer; and exactly one engineer, who is motivated. Then the preconditions hold, but none of the postconditions.

If all engineers are professionals: consider a world with no applicants, one motivated engineer, and one unmotivated non-engineer.

Answer 2

If we take the help of a Venn diagram:

Statement 1 says that: "engineers are unmotivated"
This isn't necessarily true as we cannot say anything about engineers(no information provided)

Statement 2 says that : "Some applicants are unmotivated"
This is clearly false as it can be seen in the diagram. All applicants are motivated.

Statement 3 says that: "Some professionals are applicants" This can be true as our set of applicants come under the set of motivated professionals

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Note: I have assumed that there exist applicants to begin with. (The question doesn't mention otherwise)

Answer 3

PS: I was uploading the picture when I saw the prompt answer of @sai-kartik