Practice GMAT Data Sufficiency Question
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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
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.
 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  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  Substitute into the equation from the top:
Equation from top: 5*Mean = w + x + y + z + 10
5*Mean = 20 + 10 = 30
Mean = 6  Statement (1) alone is SUFFICIENT.
 Translate each piece of information into algebra:

Evaluate Statement (2) alone.
 Simplify the algebra:
[z  y x  w] = 20
z + y + x + w = 20  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  Statement (2) alone is SUFFICIENT.
 Simplify the algebra:
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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