题目信息
Each of the five divisions of a certain company sent representatives to a conference. If the numbers of representatives sent by four of the divisions were 3, 4, 5, and 5, was the range of the numbers of representatives sent by the five divisions greater than 2 ?
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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正确答案：
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Algebra Statistics
Let x be the unspecified number of representatives. By considering individual positive integer values of x, the median of the numbers is found to be 4 when x = 1, 2, 3, or 4, and the median of the numbers is found to be 5 when x ≥ 5. For example, the case in which x = 2 is shown below.
2, 3, 4, 5, 5
In terms of x, the average of the numbers is
. If x = 1, then by the remarks above the median is 4, which is greater than 
(i.e., the median is greater than the average), and the range is 5 − 1 = 4. If x = 5, then by the remarks above the median is 5, which is greater than 
(i.e., the median is greater than the average), and the range is 5 − 3 = 2; NOT sufficient.
Given the assumption that the median of the numbers is 4, it follows from the previous remarks that x can be any one of the numbers 1, 2, 3, and 4. If x = 1, then the range is 5 − 1 = 4, which is greater than 2. If x = 4, then the range is 5 − 3 = 2, which is not greater than 2; NOT sufficient.
Given (1) and (2), then from the previous remarks and (2) it follows that x must be among the numbers 1, 2, 3, and 4. From (2) it follows that 4 >
, or x < 3, and thus x is further restricted to be among the numbers 1 and 2. However, for each of these possibilities the range is greater than 2: If x = 1, then the range is 5 − 1 = 4 > 2; and if x = 2, then the range is 5 − 2 = 3 > 2.
The correct answer is C;both statements together are sufficient.
Let x be the unspecified number of representatives. By considering individual positive integer values of x, the median of the numbers is found to be 4 when x = 1, 2, 3, or 4, and the median of the numbers is found to be 5 when x ≥ 5. For example, the case in which x = 2 is shown below.
2, 3, 4, 5, 5
In terms of x, the average of the numbers is
. If x = 1, then by the remarks above the median is 4, which is greater than (i.e., the median is greater than the average), and the range is 5 − 1 = 4. If x = 5, then by the remarks above the median is 5, which is greater than (i.e., the median is greater than the average), and the range is 5 − 3 = 2; NOT sufficient.
Given the assumption that the median of the numbers is 4, it follows from the previous remarks that x can be any one of the numbers 1, 2, 3, and 4. If x = 1, then the range is 5 − 1 = 4, which is greater than 2. If x = 4, then the range is 5 − 3 = 2, which is not greater than 2; NOT sufficient.Given (1) and (2), then from the previous remarks and (2) it follows that x must be among the numbers 1, 2, 3, and 4. From (2) it follows that 4 >
, or x < 3, and thus x is further restricted to be among the numbers 1 and 2. However, for each of these possibilities the range is greater than 2: If x = 1, then the range is 5 − 1 = 4 > 2; and if x = 2, then the range is 5 − 2 = 3 > 2.The correct answer is C;both statements together are sufficient.
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