A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number
sold was 96. What was the ratio of the number of male members to the number of female members in the club?
(A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 (E) 3 : 1
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Jim@StratusPrep
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(84x + 96y)/(x+y) = 92
84x + 96y = 92x + 92y
4y = 8x
4/8 = x/y = 1/2
Answer is B
84x + 96y = 92x + 92y
4y = 8x
4/8 = x/y = 1/2
Answer is B
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We can plug in the answers, which represent the ratio of men to women.klaud wrote:A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number
sold was 96. What was the ratio of the number of male members to the number of female members in the club?
(A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 (E) 3 : 1
The average for the whole club (92) is closer to the average for the men (96) than to the average for the women (84).
Thus, there must be MORE MEN than women.
Eliminate A, B and C.
Answer choice D: M:W = 2:1.
If there are two men and 1 woman, the total number of tickets sold = 2(96) + 1(84) = 276.
Average sold by all 3 members = 276/3 = 92.
Success!
The correct answer is D.
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By the algebraic method:klaud wrote:A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number
sold was 96. What was the ratio of the number of male members to the number of female members in the club?
(A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 (E) 3 : 1
Let the number of females = F and number of males = M
(84F + 96M)/(F + M) = 92
4M = 8F
M : F = 8 : 4
M : F = [spoiler]2 : 1[/spoiler]
The correct answer is D.
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We are given that a club sold an average (arithmetic mean) of 92 raffle tickets per member, that among the female members, the average number sold was 84, and that among the male members, the average number sold was 96. We can let f = the number of females and m = the number of males, and we can create the following weighted average equation:klaud wrote:A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number
sold was 96. What was the ratio of the number of male members to the number of female members in the club?
(A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 (E) 3 : 1
92 = (84f + 96m)/(m + f)
92m + 92f = 84f + 96m
8f = 4m
2f = m
2 = m/f
Answer: D
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