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Students at a school were on average 180 cm tall. The averag

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Students at a school were on average 180 cm tall. The averag  [#permalink]

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New post 08 Jan 2014, 14:33
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Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio of men to women?

(A) 5:2
(B) 5:1
(C) 4:3
(D) 4:1
(E) 3:1

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Re: Ratio of men to women  [#permalink]

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New post 08 Jan 2014, 16:49
enigma123 wrote:
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio of men to women?

(A) 5:2
(B) 5:1
(C) 4:3
(D) 4:1
(E) 3:1

Can someone please help me with this question. I understand its a weighted average concept, but struggling to solve this.


------------------------------------------------------------------------------------------------------------------------------------------------------------------

(A) 184 x 5 + 170 x 2 = 1260
1260/7 = 180
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Re: Ratio of men to women  [#permalink]

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New post 08 Jan 2014, 22:41
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enigma123 wrote:
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio of men to women?

(A) 5:2
(B) 5:1
(C) 4:3
(D) 4:1
(E) 3:1

Can someone please help me with this question. I understand its a weighted average concept, but struggling to solve this.


avg height is 180
avg height of female=170
avg height of male=184
ratio of men to women= 180-170:184-180=5:2
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Re: Ratio of men to women  [#permalink]

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New post 09 Jan 2014, 03:34
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Quote:
Can someone please help me with this question. I understand its a weighted average concept, but struggling to solve this.

avg height is 180
avg height of female=170
avg height of male=184
ratio of men to women= 180-170:184-180=5:2


It isn't 180-170 and 184-180 = 10:4 reducing into 5:2

Lets state it like this, since we already know the answer.

There are seven students in the class, 5 boys and 2 girls.
The 5 boys each weigh 184 pounds, with a collective weight of 920 pounds.
Both girls weigh 170 pounds.
What is the collective average weight of the class?

(184*5) + (170*2) = 1260/7
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Re: Students at a school were on average 180 cm tall. The averag  [#permalink]

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New post 27 Apr 2015, 00:40
1
I worked this out like this

170 ---------180---184

There is 4 in between the men and the average and 10 in between the woman and the average. 10/4 --> 5/2

This gave me the answer pretty quickly. I was unsure at first but it was right. yay! (this is almost like a mixture problem)
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Re: Students at a school were on average 180 cm tall. The averag  [#permalink]

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New post 27 Apr 2015, 17:02
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Hi All,

This prompt is a "weighted average" question, so it can be solved in a variety of different ways. Here's an approach that uses the Weighted Average Formula:

We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 184cm
3) The average of the GROUP is 180cm

We're asked for the RATIO of men to women.

W = number of Women
M = number of Men

(170W + 184M)/(W+M) = 180

170W + 184M = 180W + 180M
4M = 10W
2M = 5W

M/W = 5/2

The ratio of men to women is 5 to 2.

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Re: Students at a school were on average 180 cm tall. The averag  [#permalink]

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New post 19 Jun 2017, 10:22
enigma123 wrote:
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio of men to women?

(A) 5:2
(B) 5:1
(C) 4:3
(D) 4:1
(E) 3:1


We can treat this question like a statistics question

180 = Total # of Male and Female Heights/ # Females (F) + # Males (M)

170 = total of female heights/ F

170F= total female heights

184= total of male heights/ M

184M = total of male heights

180 = 184(M) + 170(F) / M + F

180(M + F) = 184(M) + 170(F)
180M + 180F= 184M + 170F
4M = 10F

5:2

Thus
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Re: Students at a school were on average 180 cm tall. The averag  [#permalink]

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New post 06 Jul 2017, 16:51
enigma123 wrote:
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio of men to women?

(A) 5:2
(B) 5:1
(C) 4:3
(D) 4:1
(E) 3:1


We can create the following weighted average equation in which m = the number of men and w = the number of women. We need to determine m/w.

180 = (184m + 170w)/(m + w)

180m + 180w = 184m + 170w

10w = 4m

5w = 2m

5/2 = m/w

Answer: A
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Re: Students at a school were on average 180 cm tall. The averag  [#permalink]

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New post 06 Jul 2017, 17:29
\(\frac{180-170}{184-180} = \frac{10}{4} = \frac{5}{2}\). Ans - A.
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Re: Students at a school were on average 180 cm tall. The averag  [#permalink]

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