Practice GMAT Data Sufficiency Question

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What is the average (arithmetic mean) of w, x, y, z, and 10?
  1. the average (arithmetic mean) of w and y is 7.5; the average (arithmetic mean) of x and z is 2.5
  2. -[-z - y -x - w] = 20
Correct Answer: D
  1. 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
  2. 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.
  3. 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.
  4. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.

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