Which of the following sentences contain an adverb clause? a. people will not get ahead if they do not study. b. doctor smith, who was once our family doctor, retired to arizona. c. because of the defensive driving lessons, i am probably a better driver today. d. at the edge of the woods, i encountered an older farmer pushing a wheelbarrow.

The correct answer is:  [A]:  

                   "People will not get ahead if they do not study." 

Explanation:

Note that one (1) feature of an "adverb clause" is that an "adverb clause" must begin with a "subordinating conjunction".

The only answer choices provided that meet this criterion are:

 Choice:  [A]:  "People will not get ahead if they do not study." 

 In this sentence, there is a "subordinating conjunction"— which is—" if ".

Choice:  [C]:  " Because of the defensive driving lessons, I am probably a better driving today ".

In this sentence, there is a "subordinating conjunction"
— which is—"Because" .

Note the other criteria for "adverb clauses" — as follows:

1)  Adverb clauses are "modifiers". 

2)  Adverb clauses contain both a subject AND a verb.

3)  Adverb clauses, on their own, do not form complete sentences.

Consider:  Choice:  [C]:  

         "Because of the defensive driving lessons, I am probably a better driving today."
 
     →  Note:  Since the particular clause beings with the "subordinating conjunction—"Because" (in this case) — consider the phrase:

    "Because of the defense driving lessons" ; 

→  This is NOT an "adverb clause".  An "adverb clause" must contain BOTH  a "noun" AND a "verb"— and this particular clause does NOT contain a "verb".

Rule out "Choice: [C] " .

Consider:
 
"Choice:  [A]:  "People will not get ahead if they do not study." 

   →  Note:  Since the particular clause beings with the "subordinating conjunction"—" if " (in this case) — consider the phrase:

     " if they do not study ." 


→  Note the following:

      1)  This clause contains BOTH a "noun" —which is:  "they" (a subject pronoun referring to "people");  AND a "verb" —which is: "do [not] study" .

      2)  This clause modifies "people" . 
 
      3)  This clause is a NOT a sentence if it stands alone.

Thus;  this very answer choice:  "Answer choice:  [A]:

       →    "People will not get ahead if they do not study." 

               →  is the only sentence — 
                     (among the answer choices provided) — 
                     that:   1)   is an "adverb clause" ; AND:               
                     that:   2)    is the correct answer.