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.