how to treat this kind of question

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NSNguyen: Master | Next Rank: 500 Posts; Posts: 401; Joined: Fri May 04, 2007 9:21 am; Thanked: 3 times; Followed by:1 members

how to treat this kind of question

by NSNguyen » Sat Jul 05, 2008 10:58 pm

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.

Please share your idea and your reasoning

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Source: Beat The GMAT — Critical Reasoning | Sat Jul 05, 2008 10:58 pm

abhishingwekar: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Tue May 20, 2008 10:00 pm

by abhishingwekar » Mon Jul 07, 2008 3:05 am

In case you are stuck up in this kind of question look into answer choices....

I am not sure, but I think the answer is E.What's the OA??

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Mon Jul 07, 2008 5:15 am

Have never seen a real GMAT question like this- this is a question in mathematical logic. Whenever you know "If A, then B", you can always conclude the contrapositive is true: "If not B, then not A". You cannot conclude the 'converse' ("If B, then A"), or the 'inverse' ('If not A, then not B').

You can try this with a mathematical statement:

A could be 'x = 2', and B could be 'x^2 = 4'.

Then If A is true, B is true ('If A, then B'). But, if B is true, A is not necessarily true; x could be -2. That is, the converse is not a legitimate deduction to make. The contrapositive is always a legitimate deduction: if B is false, then A must be false. That is, if x^2 is not equal to 4, then it's certainly true that x is not equal to 2.

Back to the question: If A implies B, B implies C, and C implies D, then A implies D. We know "If A, then D". The contrapositive of this must also be true: "If not D, then not A". So the answer is C.

It can be useful to understand contrapositives for CR questions, but you will never see a question presented like the above on the GMAT; instead you'll see a problem with some kind of argument about a real-world situation.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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newera: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Wed Jun 18, 2008 4:26 pm; Thanked: 10 times

by newera » Mon Jul 07, 2008 5:45 am

I think the answer is C.

The stimulus tells us
A-->B
B-->C
C-->D

which is the same as A-->D. In logic, we cannot reverse this to say that D-->A, this is not always the case. However, we can say that Not D-->Not A.
Its the only trick I remember from that class!