If my mother did not attend the London School of Economics

Yes, the use of "now" is a big part of it. "Have been" indicates the present perfect, and we use that to describe an achievement or something from the past that continues into the present. We could say "I might not have been born" or "I might not have been here to enjoy this day," but we can't use the present perfect to describe "now." The simple present makes much more sense.
_________________

Correct: C

(A) If my mother did not attend the London School of Economics, she might not meet my father, and I might not have been here now.
-'did not attend' in past present should be 'had not attended' in past perfect tense. We need to define chronology : attended first then met.
-'Have been' is past continuous and 'now' in present tense in same statement creates tense ambiguous. 'I might not be here now' in present tense will just do fine.

(B) If my mother did not attend the London School of Economics, she might not have meet my father, and I might not have been here now.
-both issues same as A

(C) If my mother had not attended the London School of Economics, she might not have met my father, and I might not be here now.
Correct

(D) If my mother had not attended the London School of Economics, she might not have met my father, and I might not have been here now.
-'had not attended' resolved chronology using past perfect tense.
-Been is incorrect, same issue as described in A

(E) If my mother never attended the London School of Economics, she would not have met my father, and I will not be here now.
-'Never attended' is ambiguous and having meaning error. What if mother attended LSB 2 times and second time he met father. So even if she attended LSB once, she wouldn't have met father.

All seem WRONG to me
the correct construction would be : If my mother had not ATTENDED the London School of Economics, she might not have met my father

Yes as the above poster mentioned it should be "had not attended" not "had not attend"

Also if the above typo were corrected which choice is the best between C and D

i narrowed it down to C and D but chose C

Can anyone explain?

"i might not have been here now" ----->is a present perfect, a tense used to indicate an event THAT started in past and is still in progress . this sense is wrong in this sentence

Thanks aditya

was in a hurry to answer the question

yes
simple present would suffice

kudos for pointing out the typo.
taken care of

Please explain why C is better than D ?

I think because of the "now" at the end

Can anybody explain why option E is incorrect?

I choose it because, If .. past/past perfect tense, then outcome will have.. would in it

If my mother never attended the London School of Economics, she would not have met my father, and I will not be here now.

Also, if I follow this rule why MIGHT is used in option C and D (most popular choices)?

It would be helpful, if someone can explain when can we use MIGHT?

I am bit confused with Conditional statements like IF with verb sequencing.
For example If first part is in past tense, then second part is past tense. If we go by this rule, won't that create a verb sequencing problem like above statement?

GMATNinja can you please help explain why does the correct option not follow the If-Else tense rules?
We have a past perfect in the if clause, but the else clause in the correct option does not contain "would have".

I wouldn't overthink this one. The difference between "might have" and "would have" is less about verb tense and more about meaning. For instance:

If Tim had fed his children dinner they would not have taken revenge by drawing a purple mustache on his face while he slept.

This is the classic example you're thinking of. "If Tim had done X then he would have done Y." Note that in this case, we're saying with some level of certainty that if Tim had just given his kids the macaroni and cheese they were craving, he'd be without a purple mustache today.

Contrast that with this one:

If Tim had fed his children dinner they might not have taken revenge by drawing a purple mustache on his face while he slept.

The difference now is meaning. This time, if Tim had given his kids food, he could have avoided his mustached fate. But maybe not. We don't know for sure.

Just be aware that the verb tense isn't fundamentally different here. Both sentences contain variations of HELPING VERB + HAVE, so either option seems okay. I suspect this is what the question-writer was up to in the example you cited.

The takeaway: don't be too rigid in your understanding of "rules." Tweaking a word or phrase here or there is often fine. If you're uncertain about it, don't treat the variation as an error.

I hope that clears things up!
_________________

Hello from the GMAT Club VerbalBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________