IMO: A

First, "the number of" requires a singular verb. Hence, eliminate B,C,D

Second, "likely" is prefered to "liable", thus eliminate E. Moreover, "liable" changes the meaning of the sentence.

Let me come to point
I have studied wheather is for choices and If is for condition

What is being discussed in the question?
Is it
choices or
a Condition ?

frank1 wrote:Let me come to point
I have studied wheather is for choices and If is for condition

What is being discussed in the question?
Is it
choices or
a Condition ?

OK but what is the condition here... When Lecture retired, then student decline.
If is used for Condition but the decline of students is a kind of outcome which was likely to happen when lecturer retired.
Whether is better here.

IMO A

'If' is used to introduce a conditional idea or an idea that has just one possibility whereas 'Whether' is used to introduce alternative possibilities, usually with 'or not' implied or explicitly stated in the sentence.

Here the alternative possibilities are used.

Whether the number of students was likely to decline or not.

Hope this clarify!!

selango wrote:'If' is used to introduce a conditional idea or an idea that has just one possibility whereas 'Whether' is used to introduce alternative possibilities, usually with 'or not' implied or explicitly stated in the sentence.

Here the alternative possibilities are used.

Whether the number of students was likely to decline or not.

Hope this clarify!!

Expect "if" to appear only with a "then" clause; even if the "then" is not stated, it will be clear where it could be inserted.

"Whether . . . or not" is very unlikely to appear on the GMAT with "or not", as the word "whether" already means "which of the two" (i.e. which of the two choices). Adding two words that are completely unnecessary is contrary to GMAT principles. There is nothing even remotely incorrect about it in real life, however, and people use it all the time.