Practice GMAT Data Sufficiency Question
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What is the value of x?
- The average (arithmetic mean) of 5, x2, 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 + 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
- Statement (1) alone is SUFFICIENT.
-
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.
- Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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