Should be E.

Use inversion and you will see the structure
If X then Y would happen.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

That is a great way of solving the problem. But, in the light of what is discussed on the 48th page of MGMAT
ie. would and could (although he doesn't mention should) NEVER appear in the if clause,
how do you justify this?

Although, the E choice looks like a subjunctive mood to me.. comments?

Yes you are right about this:
would and could (although he doesn't mention should) NEVER appear in the if clause.
MAKE NOTE: There is nothing wrong in using SHOULD in the if clause.

Here are the usage notes from
http://dictionary.reference.com/search?q=should

should:
aux.v. Past tense of shall

1. Used to express obligation or duty: You should send her a note.
2. Used to express probability or expectation: They should arrive at noon.
3. Used to express conditionality or contingency: If she should fall, then so would I.
4. Used to moderate the directness or bluntness of a statement: I should think he would like to go.

Usage Note: Like the rules governing the use of shall and will on which they are based, the traditional rules governing the use of should and would are largely ignored in modern American practice. Either should or would can now be used in the first person to express conditional futurity: If I had known that, I would (or somewhat more formally, should) have answered differently. But in the second and third persons only would is used: If he had known that, he would (not should) have answered differently. Would cannot always be substituted for should, however. Should is used in all three persons in a conditional clause: if I (or you or he) should decide to go. Should is also used in all three persons to express duty or obligation (the equivalent of ought to): I (or you or he) should go. On the other hand, would is used to express volition or promise: I agreed that I would do it. Either would or should is possible as an auxiliary with like, be inclined, be glad, prefer, and related verbs: I would (or should) like to call your attention to an oversight. Here would was acceptable on all levels to a large majority of the Usage Panel in an earlier survey and is more common in American usage than should. ·Should have is sometimes incorrectly written should of by writers who have mistaken the source of the spoken contraction should've.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Nice explanation ps_dahiya. I went for C, but clearly, its E.

just to add to the rules by ps_dahiya...

WILL never appears in IF clause as well

E is the only one that logically completes the sentence.