Mo2men wrote:Felixity, a musician, never sings sad rock songs. Of the songs on Felixity's new album, 20 songs are not sad, and 25 songs are not rock songs. How many of the songs in Felixity's new album are neither sad nor rock songs?
(1) Of the songs on Felixity's new album, the number of rock songs that are not sad is 5 less than the number of sad songs that are not rock songs.
(2) There are 30 songs on Felixity's new album.
Use a DOUBLE-MATRIX to organize the data.
Every song is either ROCK or NOT ROCK.
Every song is either SAD or NOT SAD.
According to the prompt:
Total not sad = 20.
Total not rock = 25.
Since Felixity never sings sad rock songs, both sad and rock = 0.
The following matrix is yielded:
The question asks for the value of the CENTER BOX (neither rock nor sad).
Statement 1: Of the songs on Felixity's new album, the number of rock songs that are not sad is 5 less than the number of sad songs that are not rock songs.
Case 1: Rock but not sad = 5, sad but not rock = 10
The following matrix is yielded:
Case 2: Rock but not sad = 10. sad but not rock = 15
The following matrix is yielded:
Since the center box can be different values, INSUFFICIENT.
Statement 2: There are 30 songs on Felixity's new album.
The following matrix is yielded:
Thus, the center box = 15.
SUFFICIENT.
The correct answer is
B.
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