Critical Reasoning

Every political philosopher of the early twentieth century who was either a socialist or a communist was influenced by Rosa Luxemburg. No one who was influenced by Rosa Luxemburg advocated a totalitarian state.
If the statements above are true, which one of the following must on the basis of them also is true?
(A) No early-twentieth-century socialist political philosopher advocated a totalitarian state.
(B) Every early-twentieth-century political philosopher who did not advocate a totalitarian state was influenced by Rosa Luxemburg.
(C) Rosa Luxemburg was the only person to influence every early-twentieth-century political philosopher who was either socialist or communist.
(D) Every early-twentieth-century political philosopher who was influenced by Rosa Luxemburg and was not a socialist was a communist.
(E) Every early-twentieth-century political philosopher who did not advocate a totalitarian state was either socialist or communist.


[spoiler]Answer: A[/spoiler]
I did it by Venn diagram, without which it was kind of impossible to me. Anybody with any better (faster) way?

~Binit.

binit wrote:Every political philosopher of the early twentieth century who was either a socialist or a communist was influenced by Rosa Luxemburg. No one who was influenced by Rosa Luxemburg advocated a totalitarian state.
If the statements above are true, which one of the following must on the basis of them also is true?
(A) No early-twentieth-century socialist political philosopher advocated a totalitarian state.
(B) Every early-twentieth-century political philosopher who did not advocate a totalitarian state was influenced by Rosa Luxemburg.
(C) Rosa Luxemburg was the only person to influence every early-twentieth-century political philosopher who was either socialist or communist.
(D) Every early-twentieth-century political philosopher who was influenced by Rosa Luxemburg and was not a socialist was a communist.
(E) Every early-twentieth-century political philosopher who did not advocate a totalitarian state was either socialist or communist.

Every A is B ---> If A, then B.
No B is a C ---> If B, then not C.
Since A implies B, and B implies not C, we get:
If A, then not C.

Rephrase the information in the passage as if-then statements.

Every political philosopher of the early twentieth century who was either a socialist or a communist was influenced by Rosa Luxemburg.
Rephrased as if A, then B:
If a political philosopher of the early twentieth-century was a socialist or a communist, then he was influenced by Rosa Luxemburg.

No one who was influenced by Rosa Luxemburg advocated a totalitarian state.
Rephrased as if B, then not C:
If a person was influenced by Rosa Luxemburg, then he did not advocate a totalitarian state.

Since A implies B, and B implies not C, we get:
If a political philosopher of the early twentieth century was a socialist or a communist, then he did not advocate a totalitarian state.

This statement supports answer choice A:
No early-twentieth-century socialist political philosopher advocated a totalitarian state.
Rephrased as an if-then statement:
If a person in the early twentieth-century was a socialist political philosopher, then he did not advocate a totalitarian state.

The correct answer is A.

Awesome Mitch, that's a really fast approach toward A.
But, I was just wondering if I have to evaluate the other answer choices i.e. B,C,D and E using your method.. I am finding it tough. Pls help me evaluating, cos answer choices cud be jumbled up in any order.

~Binit.

binit wrote:Awesome Mitch, that's a really fast approach toward A.
But, I was just wondering if I have to evaluate the other answer choices i.e. B,C,D and E using your method.. I am finding it tough. Pls help me evaluating, cos answer choices cud be jumbled up in any order.

~Binit.

True: If John is IN TIMES SQUARE, then John is IN NEW YORK.
Given this true statement, which of the following must also be true?

Not necessarily true: If John is NOT IN TIMES SQUARE, then John is NOT IN NEW YORK.
Not necessarily true: If John is IN NEW YORK, then John is IN TIMES SQUARE.
Must be true: If John is NOT IN NEW YORK, then John is NOT IN TIMES SQUARE.

Only the option in red must be true.
This option is known as the CONTRAPOSITIVE.
To yield the contrapositive of an if-then statement, FLIP AND NEGATE.
Original statement: If A, then B.
Contrapositive: If not B, then not A.
Only the contrapositive of an if-then statement MUST be true.

From my post above:

If a political philosopher of the early twentieth-century was a socialist or a communist, then he was influenced by Rosa Luxemburg.
If a person was influenced by Rosa Luxemburg, then he did not advocate a totalitarian state.

Contrapositives:
If a person was NOT influenced by Rosa Luxemburg, then he was NOT a socialist or communist twentieth-century political philosopher.
If a person DID advocate a totalitarian state, then he was NOT influenced by Rosa Luxemberg.

Linking the second statement to the first, we get:
If a person DID advocate a totalitarian state, then he was NOT a socialist or communist twentieth-century political philosopher.

The remaining answer choices, rephrased as if-then statements:
B: If an early-twentieth-century political philosopher did not advocate a totalitarian state, then that philosopher was influenced by Rosa Luxemburg.
C: If a person influenced every early-twentieth-century political philosopher who was either socialist or communist, then that person was Rosa Luxemberg.
D: If an early-twentieth-century political philosopher was influenced by Rosa Luxemburg but was not a socialist, then that philosopher was a communist.
E: If an early-twentieth-century political philosopher did not advocate a totalitarian state, then that philosopher was either socialist or communist.

None of these answer choices must be true.
Eliminate B, C, D and E.

In Verbal, it is always a good idea to check all five answer choices.

Hello Mitch,

Thanks a ton for your providing such a detailed analysis. Awesome. I think I am in a better position now with IF-THEN statements.
But I think it will take me quite long before I can actually use the logical deduction your way in the real test.
Then Venn-diagram (which I actually used to solve the problem) seems faster for ME. Pls have a look at the diagram and comment on that.

Abbr. TP = political philosopher of the early twentieth-century
R = Rosa Luxemburg, Tot = advocates a totalitarian state
S = Socialist, C = Communist, 1,2,3 are other TPs

I totally see your way Mitch, and binit, awesome venn diagram.

Here's how I went about it. I ready and interpreted the paragraph really carefully so that I could picture who is in which camp. Armed with that understanding, I looked at the answer like this

-Don't know this for sure
-Leave it in

A - leave it in
B - we don't know this for sure
C - we don't know this for sure
D - we don't know this for sure
E - we don't know this for sure

Review A. Revisit the paragraph. Confirmed.

Thanks pappyvanwinkle,

I think u did exactly what I did but managed without a Venn Diagram. I am sure you have a deep understanding and great memory that is required to tackle tough CR problems.

Good luck my friend.

~Binit.

GMATGuruNY wrote:

binit wrote:Awesome Mitch, that's a really fast approach toward A.
But, I was just wondering if I have to evaluate the other answer choices i.e. B,C,D and E using your method.. I am finding it tough. Pls help me evaluating, cos answer choices cud be jumbled up in any order.

~Binit.

True: If John is IN TIMES SQUARE, then John is IN NEW YORK.
Given this true statement, which of the following must also be true?

Not necessarily true: If John is NOT IN TIMES SQUARE, then John is NOT IN NEW YORK.
Not necessarily true: If John is IN NEW YORK, then John is IN TIMES SQUARE.
Must be true: If John is NOT IN NEW YORK, then John is NOT IN TIMES SQUARE.

Only the option in red must be true.
This option is known as the CONTRAPOSITIVE.
To yield the contrapositive of an if-then statement, FLIP AND NEGATE.
Original statement: If A, then B.
Contrapositive: If not B, then not A.
Only the contrapositive of an if-then statement MUST be true.

From my post above:

If a political philosopher of the early twentieth-century was a socialist or a communist, then he was influenced by Rosa Luxemburg.
If a person was influenced by Rosa Luxemburg, then he did not advocate a totalitarian state.

Contrapositives:
If a person was NOT influenced by Rosa Luxemburg, then he was NOT a socialist or communist twentieth-century political philosopher.
If a person DID advocate a totalitarian state, then he was NOT influenced by Rosa Luxemberg.

Linking the second statement to the first, we get:
If a person DID advocate a totalitarian state, then he was NOT a socialist or communist twentieth-century political philosopher.

The remaining answer choices, rephrased as if-then statements:
B: If an early-twentieth-century political philosopher did not advocate a totalitarian state, then that philosopher was influenced by Rosa Luxemburg.
C: If a person influenced every early-twentieth-century political philosopher who was either socialist or communist, then that person was Rosa Luxemberg.
D: If an early-twentieth-century political philosopher was influenced by Rosa Luxemburg but was not a socialist, then that philosopher was a communist.
E: If an early-twentieth-century political philosopher did not advocate a totalitarian state, then that philosopher was either socialist or communist.

None of these answer choices must be true.
Eliminate B, C, D and E.

In Verbal, it is always a good idea to check all five answer choices.

Awesome stuff. Where can I find more questions with similar reasoning to practice?