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# In a certain group of people, the average weight of the males is 170

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Math Expert
Joined: 02 Sep 2009
Posts: 42574

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In a certain group of people, the average weight of the males is 170 [#permalink]

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21 Aug 2017, 23:16
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Difficulty:

45% (medium)

Question Stats:

58% (00:45) correct 42% (02:42) wrong based on 36 sessions

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In a certain group of people, the average weight of the males is 170 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 15 more females than males.
[Reveal] Spoiler: OA

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In a certain group of people, the average weight of the males is 170 [#permalink]

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21 Aug 2017, 23:25
Given data:
Average weight(Male) = 170 pounds
Average weight(Female) = 120 pounds
Let the number of females be F, and the number of males be M

1. The group contains twice as many females as males.
If the number of females is twice the number of males F:M = 2:1
Using this ratio, we can determine the average weight of the group
Average weight = $$\frac{(170*2 + 120)}{3} = \frac{460}{3}$$(Sufficient)

2. The group contains 15 more females than males.
F = M + 15
Based on the number of M, F will change and give us different averages
for every different value of M.(Insufficient)(Option A)
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Re: In a certain group of people, the average weight of the males is 170 [#permalink]

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22 Aug 2017, 03:39
Bunuel wrote:
In a certain group of people, the average weight of the males is 170 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 15 more females than males.

Average weight males = 170, so $$170*m = sum of the male's weight$$.
Average weight females = 120, so $$120*f = sum of the females' weight$$.
Average total = $$\frac{[(170*m)+(120*f)]}{(m+f)}$$

So, if we know m and m, we can calculate the average weight.

Statement 1.
- F = 2M
- Plugin into equation = $$\frac{(170m + 240m)}{3m}$$. We can eliminate the m and get the absolute number.
SUFFICIENT.

Statement 2.
- F = 15+M
- Plugin into equation = $$\frac{[(170m) + 120 (15+M)]}{(m+m+15)}$$. We still get "m" in our equation, no absolute value.
INSUFFICIENT.

A.
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Re: In a certain group of people, the average weight of the males is 170   [#permalink] 22 Aug 2017, 03:39
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