Very confusing A B C D If then question

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dotnetuncle
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Topic: Very confusing A B C D If then question
PostSun Nov 15, 2009 5:54 am
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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.

This is driving me nuts. Whats the explanation?
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PostSun Nov 15, 2009 11:28 pm
dotnetuncle wrote:
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.

This is driving me nuts. Whats the explanation?
This is a formal reasoning question.. IMHO not very likely on the GMAT but this is so basic, that it might be asked..
The solution is based on 2 concepts. 1) If A, then B and if B, then C. Then one can infer " If A, then C"
2) Contrapositive: ie. If A, then B. Its contrapositive is "if Not B then Not A". Using this concept u can easily conclude
If A then D (by Concept 1). Now using Concept 2, If Not D then Not A.
Choice C is the answer.
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PostSun Nov 15, 2009 11:52 pm
Yes, the answer to this question is definitely C.

But, no, this question would definitely not be on the GMAT or even the LSAT for that matter. On a standardized test, the test-maker won't use just letters in an argument!

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

A--->D

Therefore, if no D, then no A (because if there was A, there would be D).

If you are in Toronto (A)--->you are in Canada (D)
If you are NOT in Canada (no D)--->you are NOT in Toronto (no A)
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PostTue Nov 17, 2009 11:40 pm
IMO C

If D did not happen => C definitely did not happen (because C => D)
Similarly, if C did not happen => B definitely did not happen (because B => C)
and hence if B did not happen => A definitely did not happen (because A => B)
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