题目信息
What is the median of the data set S that consists of the integers 17, 29, 10, 26, 15, and x ?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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已选答案：
正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Arithmetic Statistics
Since the average of the six numbers is 17, it follows that the sum of the six numbers is 6(17). Therefore, 17 + 29 + 10 + 26 + 15 + x = 6(17), which can be solved for a unique value of x, after which the median can be determined; SUFFICIENT. The range of the numbers when x is not included is 29 − 10 = 19. Therefore, if x = 29 + 5 = 34, then the range of the seven numbers (10, 15, 17, 26, 29, 34) is 34 − 10 = 24 and the median of the seven numbers is
= 21.5.
However, if x = 10 − 5 = 5, then the range of the seven numbers (5, 10, 15, 17, 26, 29) is 29 − 5 = 24 and the median of the seven numbers is
= 16; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Since the average of the six numbers is 17, it follows that the sum of the six numbers is 6(17). Therefore, 17 + 29 + 10 + 26 + 15 + x = 6(17), which can be solved for a unique value of x, after which the median can be determined; SUFFICIENT. The range of the numbers when x is not included is 29 − 10 = 19. Therefore, if x = 29 + 5 = 34, then the range of the seven numbers (10, 15, 17, 26, 29, 34) is 34 − 10 = 24 and the median of the seven numbers is
= 21.5.However, if x = 10 − 5 = 5, then the range of the seven numbers (5, 10, 15, 17, 26, 29) is 29 − 5 = 24 and the median of the seven numbers is
= 16; NOT sufficient.The correct answer is A;statement 1 alone is sufficient.
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