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

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03 Dec 2004, 05:50

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A

B

C

D

E

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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.

I didn't get this one, please give the reasoning as well.

The idea here is just notice the two sentences:
---- if A then B
----- if A only then B.

the first statement tell , if A occurs B will definetly occur, but doesn't say B cannot occur without A.

the second statement tells. if A occurs B will definetly occur, and also B cannot occur without A.

now among the answer choices:
1. if D then A: it might not necessarily be true.

2. If not B, then not C: again C can occur without B.

3. If not D, then not A. : perfect, because, if A wud have happened, B will happen, thereby C and subsequently D. so if D dint occur, then A wouldn't have

4. If D, then E. : out of score, E is no where in picture.

5. If not A, then not D. : again this is not necessarily true, because D can occur without C, or B or A.

The idea here is just notice the two sentences: ---- if A then B ----- if A only then B.

the first statement tell , if A occurs B will definetly occur, but doesn't say B cannot occur without A.

the second statement tells. if A occurs B will definetly occur, and also B cannot occur without A.

now among the answer choices: 1. if D then A: it might not necessarily be true.

2. If not B, then not C: again C can occur without B.

3. If not D, then not A. : perfect, because, if A wud have happened, B will happen, thereby C and subsequently D. so if D dint occur, then A wouldn't have

4. If D, then E. : out of score, E is no where in picture.

5. If not A, then not D. : again this is not necessarily true, because D can occur without C, or B or A.

Didnt you say that D can happen even if C doesnt happen, C can happen even without B happening; and B can happen without A happening?? Then how can you say that if D didnt happen, then A also didnt happen??

Read your explanations for C and E... i think you are mixing the reasoning.. and contradicting yourself... In choice E , you say---"If not A, then not D. : again this is not necessarily true, because D can occur without C, or B or A"

And In C you say----If not D, then not A. : perfect, because, if A wud have happened, B will happen, thereby C and subsequently D. so if D dint occur, then A wouldn't have..

Just to simplify things take 2 events say A and B. and lets say A means: it is raining, B means 'i will work from home.

So if A then B... means: if it raining, then I will work from home.
However, this doesn't mean that i will work from home only if it is raining, i can work from home, even on a very hot day... !! (i am a bit lazy person

At the same time, If i am not working from home... it means it is not raining. because, if it wud have been raining, I would have been working from home. (as stated in the statement above). Isn't it?

SO if 'A then B' means--- if 'not B then not A'.

Extend this logic to 4 events as in the original question stem. A---> B--->C-->D. so if D dint happen, C wudn't have, and if C dint happen B wudn't have, and finally if B dint happen then A wudnot have.

Hope this answers your query.

Further the answer choice 'E' is wrong becasue.... for the two events (A and B) it will lead to if not A then not B. so in my example, if it is not raining .. i will not work from home... and as i said earlier, i can work from home, because of any other reasons, say it is very hot today/ or i am a lazy person, or i hate my boss...

If D did not happen then C did not happen, because if C had happened D would have followed.
If C did not happen then B did not happen (same logic as above)
So, if B did not happen then A did not happen.

I will go with â€˜Câ€™
According to the statements if A =>B => C => D, so in other words whenever â€˜Aâ€™ occurs â€˜Dâ€™ is bound to happen, so if â€˜Dâ€™ did not happen, we can conclude that â€˜Aâ€™ did not happen as well because if â€˜Aâ€™ had happened â€˜Dâ€™ would have too.

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