Which of the following is a simple sentence?

a) He ran fast but he failed to win the prize.
b) Although he ran fast he failed to win the prize.
c) In spite of running past, he failed to win the prize.
d) He failed to win the prize because he did not run fast.
Give reasons also.

A simple sentence has one subject and one verb. Which of these sentences has only one subject and one verb?

No. "He failed" is one subject and verb; "he did" is another subject and verb, are they not?

How can the answer be option a) b) C)

because I checked the definition of simple/complex/compound sentence elsewhere and noticed that compound sentences have an ordinating conjunction and complex sentences have a subordinating conjunction. In that case, wouldn't option a) be a compound sentence, and option b), c) be complex sentences?

Then it must be option c) because option a) has "he ran" and "he failed"

option b) also has "he ran" and "he failed" (2 subjects and 2 verbs)
Can you please tell me how to identify and differentiate between complex and compound sentences as well? Thank you so much for the help received so far!

A compound sentence is two thoughts that could stand on their own as complete sentences. A above is a compound sentence. "He ran fast." is a complete sentence. "He failed to win the prize." is a complete sentence.

A complex sentence contains an independent clause (a sentence all by itself) and a dependent clause that will not stand as its own sentence. "Ruth left when I arrived" is a complex sentence. It has two subjects and verbs, but "when I arrived" is not a complete sentence. It serves as an adverb clause modifying the verb "left".

Then the answer is definitely option c). Thank you so much!

And C is the correct answer here. "In spite of running fast" is an adverb phrase modifying "failed". Actually, it's two prepositional phrases, "in spite" and "of running fast". "of running fast" modifies "in spite", and together they modify "failed". It is not a clause at all, since it has no subject and no verb.

The correct answer is C.

Yes c option is right answer

Is it option d) then?