To sum up the comments:
There is nothing wrong with either sentence. Both are equally valid. Both are equally terse.
The author's explanation that "answers with -ING are usually wrong" (as reported by Tᴚoɯɐuo) shows she is unclear how this style rule words. Yes, it is generally considered poor style to use the progressive form of a verb when the simple present will do, for example:
Scientists around the world are constantly working to solve the anticipated problems from global warming.
Scientists around the world constantly work to solve the anticipated problems from global warming.
The reason for this and other style rules is that young English writers often use too many unnecessary words to express themselves, and forcing them to break certain habits helps them write more clearly and concisely. However, this all depends on context. There are many occasions in which you might want to use the progressive tense to indicate concurrency.
Moreover, there is absolutely nothing wrong with using the "-ing" form of a verb as a gerund. This is a completely different animal from the progressive tense, as Ms. Melzer should know, and proper use is a good indication of English fluency.
In any case, from what I understand of the SAT essay exam, the essay is read by two scorers who then grade it from 1-4 (4 being highest) in each of four categories. In order to get a score of at least 3 in each category, you need to demonstrate the following:
A well-constructed essay (usually three to five organized paragraphs) that effectively argues one side or the other of the given question
Perfect grammar, spelling, and punctuation
That's about it. Apparently the difference between a score of 3 and a score of 4 is somewhat trivial, and may be somewhat based on luck, in that you get a favorable scorer.
It is very unlikely that your score will hinge on whether you use the gerund or the infinitive in this context. I expect the scorers are far more likely to ding you for something like the missing article in one of the sentences in your question:
But, according to the book's answer, (the) second one is correct.
Seriously, if you want to get a good score on this essay exam, first learn to write absolutely perfect spelling and grammar, as even the smallest mistake can only cost you. Then practice writing the standard 3/5-paragraph essay structure.