Data Sufficiency

GMATGuruNY wrote: 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.

GMATGuruNY wrote:

Mo2men wrote:Dear Mitch,

I have question regarding Statement 1. While you proved by plugging numbers that St 1 is insufficient, why did the algebraic solution provide otherwise as follows:
Let Rock but not sad = x
Let sad but not rock = x+5

I construct the double matrix



From the row the required box is intersection between a row and column so i can establish an equation :
20 - x = 25 - x -5........X =0 .....the required box = 20

In some question, the required box could be obtained by this method.

Where did I go wrong? What did I miss here???

Thanks

The conclusion in red is not justified.
If we solve the equation for the center box, we get:
20 - x = 25 - (x+5)
20 - x = 25 - x - 5
20 - x = 20 - x
0 = 0.

The resulting equation in blue tells us nothing about the value of x.