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rss GMAT Practice Question (One of Hundreds)
What is the value of x?
  1. The average (arithmetic mean) of 5, x2, 2, 10x, and 3 is -3.
  2. The median of 109, -32, -30, 208, -15, x, 10, -43, 7 is -5.
Correct Answer: D
Write out the average formula, rearrange the numbers in an equation format, and solve for x.
  1. Evaluate Statement (1) alone.
    1. Based upon the formula for the average, you know that:
      (5 + x2 + 2 + 10x + 3)/5 = -3
      x2 + 10x + 5 + 2 + 3 = -15
      x2 + 10x + 5 + 2 + 3 + 15 = 0
      x2 + 10x + 25 = 0
      (x + 5)2 = 0
      x = -5
    2. Statement (1) alone is SUFFICIENT.
  2. Evaluate Statement (2) alone.
    1. Order the numbers in ascending order without x:
      -43, -32, -30, -15, 10, 7, 109, 208
    2. Consider the possible placements for x and whether these would make the median equal to -5:
      Case (1): x, -43, -32, -30, -15, 10, 7, 109, 208
      Median: -15
      Not a possible case since the median is not -5.

      Case (2): -43, x, -32, -30, -15, 10, 7, 109, 208
      Median: -15
      Not a possible case since the median is not -5.

      Case (3): -43, -32, x, -30, -15, 10, 7, 109, 208
      Median: -15
      Not a possible case since the median is not -5.

      Case (4): -43, -32, -30, x, -15, 10, 7, 109, 208
      Median: -15
      Not a possible case since the median is not -5.

      Case (5): -43, -32, -30, -15, x, 10, 7, 109, 208
      Median: x
      A possible case since the median is x, which can legally be -5.
      In this case, x must be -5 in order for the median of the set to be -5, which must be according to Statement (2).

      Case (6): -43, -32, -30, -15, 10, x, 7, 109, 208
      Median: 10
      Not a possible case since the median is not -5.

      Case (7): -43, -32, -30, -15, 10, 7, x, 109, 208
      Median: 10
      Not a possible case since the median is not -5.

      Case (8): -43, -32, -30, -15, 10, 7, 109, x, 208
      Median: 10
      Not a possible case since the median is not -5.

      Case (9): -43, -32, -30, -15, 10, 7, 109, 208, x
      Median: 10
      Not a possible case since the median is not -5.
    3. Since Statement (2) tells us that the median must be -5, we know that x must be a value such that the median is -5. This can only happen in Case 5. Specifically, it can only happen when x = -5. Since the median must equal -5 and this can only happen when x = -5, we know that x = -5.
    4. Statement (2) alone is SUFFICIENT.
  3. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.