题目信息
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?
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：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra Applied problems; Statistics
Let M and F, respectively, be the number of males and females in the group. Also, let
and 
, respectively, be the total weight, in pounds, of the males and females in the group. We are given that 
= 180 and 
= 120. What is the value of 
?
Given that F = 2M (equivalently, M =
), it follows that 
= 
= 
; SUFFICIENT.
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.
Tip In data sufficiency problems it is often helpful to consider contrasting extreme scenarios when they exist. If a variable can be any positive real number, then consider the scenario when the variable is very close to 0 and the scenario when the variable is very large. If a quadrilateral can be any rectangle, then consider the scenario when the rectangle is a square and the scenario when the rectangle is very long with a small width.
Alternatively,
, and by long division (takes one step), this can be written as 150 − 
, which can clearly vary when the value of M varies; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Let M and F, respectively, be the number of males and females in the group. Also, let
and , respectively, be the total weight, in pounds, of the males and females in the group. We are given that = 180 and = 120. What is the value of ?Given that F = 2M (equivalently, M =
), it follows that = = ; SUFFICIENT.
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.Tip In data sufficiency problems it is often helpful to consider contrasting extreme scenarios when they exist. If a variable can be any positive real number, then consider the scenario when the variable is very close to 0 and the scenario when the variable is very large. If a quadrilateral can be any rectangle, then consider the scenario when the rectangle is a square and the scenario when the rectangle is very long with a small width.
Alternatively,
, and by long division (takes one step), this can be written as 150 − , 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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