Practice GMAT Data Sufficiency Question
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What is the value of x?
 The average (arithmetic mean) of 5, x^{2}, 2, 10x, and 3 is 3.
 The median of 109, 32, 30, 208, 15, x, 10, 43, 7 is 5.
Correct Answer: D

Evaluate Statement (1) alone.
 Based upon the formula for the average, you know that:
(5 + x^{2} + 2 + 10x + 3)/5 = 3
x^{2} + 10x + 5 + 2 + 3 = 15
x^{2} + 10x + 5 + 2 + 3 + 15 = 0
x^{2} + 10x + 25 = 0
(x + 5)^{2} = 0
x = 5  Statement (1) alone is SUFFICIENT.
 Based upon the formula for the average, you know that:

Evaluate Statement (2) alone.
 Order the numbers in ascending order without x:
43, 32, 30, 15, 10, 7, 109, 208  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.  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.
 Statement (2) alone is SUFFICIENT.
 Order the numbers in ascending order without x:
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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