"고양이가 놀라서 뛰었어요."
Translation:The cat got surprised and jumped.
That's the case when it's connecting two sentence fragments. When it's between two or more verbs, it indicates succession. As in "and then"
Some people seem to be confused as to whether 서 should be translated as "and" or "so/because". The way I wrap my head around it is, often in English, when we say "and", we usually mean "and as a result" -- a logical cause and effect. Which, more concisely translates to "so".
So, the sentence could be:
The cat got surprised and [as a result] jumped.
The cat got surprised and [so it] jumped.
The cat got surprised and jumped.
The cat got surprised so it jumped.
Another example: I went to the store and bought some milk. 저는 가게에 가서 우유를 샀어요.
There are two clauses in this sentence: "I went to the store" and "I bought some milk". Since these two clauses are related (cause and effect), the sentence uses 서, rather than 고.
I went to the store and [so I] bought some milk.
I went to the store and [as a result I] bought some milk.
I went to the store and bought some milk.
The hint for 뛰었어요 includes 'ran' but 'the cat ran because it was surprised' is not accepted
Not really. Your sentence sounds like the cat did the two things at the same time, whereas the nuance of the sentence is that the jumping comes after the surprise and is a result of it, therefore 놀라서 뛰었어요 is the right choice.