Very confusing A B C D If then question

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dotnetuncle: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Nov 14, 2009 9:17 am; Location: gurgaon, delhi

by dotnetuncle » Sun Nov 15, 2009 4:54 am

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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Source: Beat The GMAT — Critical Reasoning | Sun Nov 15, 2009 4:54 am

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Sun Nov 15, 2009 10:28 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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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Sun Nov 15, 2009 10:52 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)

Kaplan Teacher in Toronto

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f2006198: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Nov 17, 2009 8:38 pm; Location: India

by f2006198 » Tue Nov 17, 2009 10:40 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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james33: Master | Next Rank: 500 Posts; Posts: 200; Joined: Sat Aug 22, 2015 10:27 am

by james33 » Sun May 15, 2016 10:02 pm

Well I feel C is the answer. I guess I'm right. If some expert could

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