Critical Reasoning

Not surprisingly, there are no professors under the age of eighteen. And as is well known, no one under eighteen can vote legally. Finally some brilliant people are professors, some are legal voters, and some are under eighteen.
If the statements above are true, then on the basis of them which one of the following must also be true?
(A) No professors are eighteen-year-olds.
(B) All brilliant people are either professors, legal voters, or under eighteen.
(C) Some legal voters are not professors.
(D) Some professors are neither legal voters nor brilliant people.
(E) Some brilliant people are neither professors nor legal voters.

Can we solve this problem by using venn diagram?
And conclude that E is the correct answer? Would you please explain why answer choice A is wrong?

P=Professor,
UA=Under the age of 18,
VL=Vote legally.

Hi Talaangoshtari,

Question Analysis:

Professors cannot be aged less than 18 years.
People aged under 18 cannot vote => All professors are legal voters.
Out of all brilliant people some are professors, some are legal voters and some are under 18 (not professors or legal voters).

A) This cannot be true because as mentioned professor aren't aged LESS THAN 18 years => professors age can be 18 or more.

B) Question stem clearly states SOME not ALL. So, cannot be true.

D) Professor has to be a legal voter. So, cannot be true.

I am stuck between C and E!

C) Legal voters can be both Professors and non professors unless question stem restricts our discussion only to professors.

E) Straight .. this can be true.

Can someone please help me eliminate option C?

Not surprisingly, there are no professors under the age of eighteen. And as is well known, no one under eighteen can vote legally. Finally some brilliant people are professors, some are legal voters, and some are under eighteen.
If the statements above are true, then on the basis of them which one of the following must also be true?
(A) No professors are eighteen-year-olds.
(B) All brilliant people are either professors, legal voters, or under eighteen.
(C) Some legal voters are not professors.
(D) Some professors are neither legal voters nor brilliant people.
(E) Some brilliant people are neither professors nor legal voters.

There are no professors under the age of eighteen.
not 18 --> not a professor.

No one under eighteen can vote legally.
not 18 --> can't vote.

Thus:
not 18 --> not a professor and can't vote.

Some brilliant people are professors, some are legal voters, and some are under eighteen.
Some brilliant --> professors.
Some brilliant --> can vote.
Some brilliant --> not 18.

Linking together the statements in red, we get:
Some brilliant --> not 18 --> not a professor and can't vote.
Some brilliant --> not a professor and can't vote.
Thus, E must be true:
Some brilliant people are neither professors nor legal voters.

The correct answer is E.

C: Some legal voters are not professors.
All legal voters must be at least 18 years of age.
Nothing in the passage prevents all legal voters from being professors.
Since it is possible that all legal voters are professors, C does not have to be true.
Eliminate C.

Hi talaangoshtari,

This Venn diagram may help u. Note: since nothing is said about Legal Voters' relationship with Professors, any pencil-drawn figure could represent LV, provided it has to be outside U18.

We can easily eliminate all but choice E, I think.


~Binit.