Tricky CR question to solve

[ildude02]

I have copied the CR question below. I wanted to see what you guys think is the answer. What I "strongly" thought would be the answer wasn't the one. I will post the correct answer choice after a little while since I don't want to spoil the fun of solving it. I'd appreciate if any of you could pick the answer and may be explain why you chose it.



If A, then B.
If B, then C.
If C, then D.
If all of the statements above are true, which of the following must also be true?
(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

[Stuart@KaplanGMAT]

The correct answer is (C).

I'm not sure where you got this question, but it's much more similar to a (fairly low level) LSAT question than a GMAT question, since it's testing the rules of formal logic. Formal logic is rarely, if ever, tested on the GMAT.

From any if-then statement, we can form what's called the contrapositive of the statement by reversing the terms and negating them.

For example, let's examine the statement "if something is a dog, then it's a mammal".

Using shorthand, we get:

If Dog, then Mammal

To form the contrapositive, we reverse and negate, to get:

If not a mammal, then not a dog

(which is of course true in the real world, just as the original statement was true).

The contrapositive is just a different way of expressing the original statement.

So, if we look at the question you posted:

If A, then B
If B, then C
If C, then D.

We can create a long chain of logic:

A --> B --> C --> D

To see that If A, then D is also true.

Now, if we take the contrapositive of "If A, then D", we get:

If not D, then not A

which is the answer to the question.

To put the symbols into a real world example:

If in Dallas, then in Texas
If in Texas, then in USA
If in USA, then in North America

The equivalent to the correct answer would be:

If not in North America, then not in Dallas

which is, of course, true.

You can try the other answer choices (subbing Dallas for "A", Texas for "B", USA for "C" and North America for "D") to see that they don't have to be true.

[ildude02]

Thanks for your response. I got this question from the 1000CR.

I chose choice (e) and my reasoning for that was,

Since it's given that A->B>C->D , I would think without A, there wouldn't be D.

As for choice C, I'm not sure about the reasoning that without D, there is no A , especially since there is no dependency of A on D and if there is one, it's vice versa. But I should say that your example with "Dallas" made sense in the reasoning behind your choice.

[Stuart@KaplanGMAT]

Just sub in the terms that I suggested and it will all make more sense.

Just because it's true that "If someone is in Dallas, they're in North America", that doesn't make it true that "if someone is in North America, they're in Dallas".

[khanshainur]

I would choose C