Bunuel wrote:

The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6

B. x/6 - 5

C. x/7 - 5

D. x/5 - 7

E. x/5 - 6

If the equation is hard to set up, a simple A*n = S table can help.

The key is that

one occurrence of a numeric value added or subtracted to the set of numbers gets its

own row; then add column "n" to get total number and column "S" to get total sum (averages CANNOT be added).

__A__|__n__|___S____|

__x__|__y__|___xy____|

_30__|__1__|___30___|

-------

|_y+1_|_xy+30__|The new average is (x - 5). That doesn't get written in the table anywhere. It's the RHS of the equation.

LHS = \(\frac{Total Sum}{Total

Number}\)

\(\frac{(xy + 30)}{(y+1)} = (x - 5)\)

\(xy + 30 = (x - 5)(y + 1)\)

\(xy + 30 = xy + x - 5y - 5\)

\(5y = x - 35\)

\(y = \frac{x}{5} - 7\)

ANSWER D

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