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# If A, then B. If B, then C. If C, then D. If all of the

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VP
Joined: 13 Jun 2004
Posts: 1111

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Location: London, UK
Schools: Tuck'08
If A, then B. If B, then C. If C, then D. If all of the [#permalink]

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20 Oct 2004, 08:47
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0% (00:00) correct 100% (00:30) wrong based on 1 sessions

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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.

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Manager
Joined: 28 Jul 2004
Posts: 179

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20 Oct 2004, 11:13
It would be nice if we can add the explanation along with the answers as well. Without the explanation, the answers sound more like guessing... Thanks

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Manager
Joined: 21 Jul 2004
Posts: 120

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20 Oct 2004, 12:28
ok, here is my explanation.

A -> B, B -> C. C->D so, A -> D

so we can negate both... so -D -> -A

this is how i came up w/ the answer.... i am not very good at explaining things...

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VP
Joined: 13 Jun 2004
Posts: 1111

Kudos [?]: 51 [0], given: 0

Location: London, UK
Schools: Tuck'08

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21 Oct 2004, 06:42
OA is C

the first time i got it wrong but now I understand it. I don't have explanation for OA but I can try to explain my vision of the OA

(A) If D, then A.-> maybe other causes for D than just A, maybe Z->D
(B) If not B, then not C. -> same idea than above, maybe X -> C
(C) If not D, then not A. -> we know that A creates D, if there is no D, there is no way there is any A. this one is the good one.
(D) If D, then E. -> we have no information
(E) If not A, then not D. -> maybe other causes so that there is no A but there is a D.

Hope you can get it even if I am not a specialist

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SVP
Joined: 16 Oct 2003
Posts: 1798

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21 Oct 2004, 07:48
Mine was more or less a guess. I cannot crack these type of questions.

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Manager
Joined: 13 Oct 2004
Posts: 50

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23 Oct 2004, 19:46
This is a good logic question, and can be easily understood by Akamaibrah diagrams

In this case we need to draw circles - Circle A inside circle B, circle B inside circle C, circle C inside circle D.

So let us check each option -
(A) If D, then A.

A is a small circle in D, so if A then D is true, but not vice versa.

(B) If not B, then not C.

Not true as B lies inside C. So if not B then it can still be C.

(C) If not D, then not A.

This is true, as D is the circle covering all other circles. So if not D then it is none of other circles.

(D) If D, then E.

Not true

(E) If not A, then not D.

Not true.

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CEO
Joined: 17 Jul 2004
Posts: 3281

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23 Oct 2004, 20:21
This appears to be a simple extension of modus tollens-

If A then D

Not D

Therefore, Not A

QED

Hjort

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23 Oct 2004, 20:21
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# If A, then B. If B, then C. If C, then D. If all of the

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