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I'm happy to help with this.

I'm going to start by looking for a split in the answer choices --- for more on that strategy, read this post. First of all, notice the will/would split
(A) ...would....
(B) ...will....
(C) ...would...
(D) ...will...
(E) ...will...

Let's start there. Consider these two sentences.

1) Jordan never would be allowed to drive her father's car.
2) Jordan never will be allowed to drive her father's car.

The first is something we call "the subjunctive" in grammar. (If you're unfamiliar with that, read this post.) The subjunctive is used for hypothetical situations --- If Jordan were to be this completely hypothetical thing, then she never would be allowed to drive her father's car. There's nothing hypothetical about the current situation. Jordan smashed up a real car. There was a real accident, and there are real consequences. She *will* not be able to drive her father's car. That's the real consequence of a real accident.

So, "will" is correct, and "would" is incorrect. That eliminates (A)+(C).

(B) has not been allowed to drive and probably never will be allowed to drive
(D) has not and probably will never be allowed to drive
(E) has not and probably never will be allowed to drive

We have two verbs in parallel --- read this post for more about parallelism. (B) states things in a wordy way. saying all the repeated words twice, which can be done; all the verbs are correctly constructed. You are allowed to omit repeated words in parallel if the repeated words of the two parallel elements are the same. The problem with (D) and (E) is --- we can't follow "has not" with the element given in the second half of the sentence "be allowed to drive" --- "has not be allowed to drive" -- that doesn't work. The words "has not" has to be followed by "been." Because of this, both (D)+(E) are wrong. If one of the choices had been

(F) has not been and probably never will be allowed to drive

That would be correct, and superior to (B), but we simply don't get that option. GMAT SC correction is not always about the best conceivable option, but merely the best of the five.

Here, (B) is wordy, it's not how I would say it, but it contains no grammar mistakes, and the others do, so (B) is the best of the five.

Does that make sense?
Here's a free video about Sentence Correction.
http://gmat.magoosh.com/lessons/599-intro-to-sentence-correction

Let me know if you have any questions.

Mike

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Magoosh GMAT Instructor
http://gmat.magoosh.com/