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  3. In a certain group of people, the average (arithmetic mean) weight of the males

In a certain group of people, the average (arithmetic mean) weight of the males

游客2025-02-27  10
问题 In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and of the females, 120 pounds. What is the average weight of the people in the group?
(1) The group contains twice as many females as males.
(2) The group contains 10 more females than males.
选项 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.
答案 A
解析 Let M and F, respectively, be the number of males and females in the group. Also, let ∑ M and ∑F respectively, be the total weight, in pounds, of the males and females in the group.
We are given that ∑M/M= 180 and ∑F/F = 120.                        
What is the value of (∑M+∑F) /M + F?
(1)    Given that F= 2M (equivalently, M=F/2), it follows that

SUFFICIENT.
(2)    We are given that F= M+ 10. If M= 2 and F= 12, then there are six times as many females as males, and hence the average weight of the people in the group will be strongly skewed toward the average weight of the females. However, if M= 100,000 and F= 100,010, then the ratio of females to males is close to 1, and hence the average weight of the people in the group will be close to the average of 120 and 180.
Alternatively,

and by long division (takes one step), this can be written as , which can clearly vary when the value of M varies; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
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