Practice GMAT Data Sufficiency Question

What is the average (arithmetic mean) of w, x, y, z, and 10?

the average (arithmetic mean) of w and y is 7.5; the average (arithmetic mean) of x and z is 2.5
-[-z - y -x - w] = 20

A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)	EACH statement ALONE is sufficient.
E)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: D

Write out the formula for the mean and arrange it in several different ways so that you can spot algebraic substitutions:
Mean = (w + x + y + z + 10)/5
5*Mean = w + x + y + z + 10
Evaluate Statement (1) alone.
1. Translate each piece of information into algebra:
  "the average (arithmetic mean) of w and y is 7.5"
  (w + y)/2 = 7.5
  w + y = 15
  
  "the average (arithmetic mean) of x and z is 2.5"
  (x + z)/2 = 2.5
  x + z = 5
2. Combine the two equations by adding them together:
  (x + z) + (w + y) = (5) + (15)
  x + z + w + y = 15 + 5
  w + x + y + z = 20
3. Substitute into the equation from the top:
  Equation from top: 5*Mean = w + x + y + z + 10
  5*Mean = 20 + 10 = 30
  Mean = 6
4. Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
1. Simplify the algebra:
  -[-z - y -x - w] = 20
  z + y + x + w = 20
2. This can be substituted into the mean formula:
  z + y + x + w = 20
  w + x + y + z = 20 {rearrange left side to make substitution easier to see}
  
  Equation from top: 5*Mean = w + x + y + z + 10
  5*Mean = (w + x + y + z) + 10
  5*Mean = 20 + 10 = 30 {substitute information from Statement (2)}
  Mean = 6
3. Statement (2) alone is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.