Hi carlos.lara.7,

This DS question is really just about translating the words into 'math' (and in this case, that means creating two inequalities). We're asked how many people attended Susanne's party.

1) If, in addition to all those who attended, the 3 friends who take bass classes with her had come, there would have been at least 20 people at the party.

This Fact tells us that IF 3 more people attended, then the total would have been AT LEAST 20 people. This translates into....

X = total number of people at the party

X + 3 >= 20
X >= 17

So we know that there were AT LEAST 17 people at the party, but we don't know exactly how many.
Fact 1 is INSUFFICIENT

2) If no other person had attended and the 3 friends who live in another town had NOT made it to the party, then the attendance would have been below 15 people.

This Fact tells us that IF 3 people who attended had NOT attended, then the total would have been BELOW 15 people. This translates into....

X - 3 < 15
X < 18

So we know that there were LESS THAN 18 people at the party, but we don't know exactly how many.
Fact 2 is INSUFFICIENT

Combined, we know the digit is...
X >=17 and X < 18
Thus, X MUST be 17
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich