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If 70% of the women in a room are over 50 years old and 80% of the peo

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If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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If 70% of the women in a room are over 50 years old and 80% of the people in the room are women, what is the ratio of the number of women 50 years old or less to the number men in the room?

A. 3 : 7
B. 4 : 1
C. 6 : 5
D. 7 : 10
E. 14 : 5

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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 28 Dec 2017, 03:33
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let, total people 100
women=80
men=20
women 50 year or less = 80*30%
---------------------------=24
so, required ratio= 24:20
-------------------= 6:5
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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 28 Dec 2017, 17:36
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Bunuel wrote:
If 70% of the women in a room are over 50 years old and 80% of the people in the room are women, what is the ratio of the number of women 50 years old or less to the number men in the room?

A. 3 : 7
B. 4 : 1
C. 6 : 5
D. 7 : 10
E. 14 : 5


Find the ratio of \(\frac{Woman<50}{Men}=\frac{0.3*80}{20}=\frac{24}{20}=6:5\)

(C) is the answer.
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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 30 Dec 2017, 22:46
Bunuel wrote:
If 70% of the women in a room are over 50 years old and 80% of the people in the room are women, what is the ratio of the number of women 50 years old or less to the number men in the room?

A. 3 : 7
B. 4 : 1
C. 6 : 5
D. 7 : 10
E. 14 : 5



Say, Total people in the room = 100

80% are women = 80 women (Given)

So, men = 100 - 80 = 20 men

70% of the women in a room are over 50 years old = 80*70/100 = 56 women

Therefore, no. of women <=50 years = 80 - 56 = 24

the ratio of the number of women 50 years old or less to the number men in the room = 24:20

Answer = 6:5 (C)
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If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 30 Dec 2017, 23:06
Bunuel wrote:
If 70% of the women in a room are over 50 years old and 80% of the people in the room are women, what is the ratio of the number of women 50 years old or less to the number men in the room?

A. 3 : 7
B. 4 : 1
C. 6 : 5
D. 7 : 10
E. 14 : 5


Very simple and straight forward solutions have been presented above :thumbup: . Here's another approach just for academic purpose ;)

Given ratio of women to men \(= 80:20=4:1\). So women forms \(4\) parts of the population.

it is given \(70\)% of WOMEN (\(4\) parts) are more than 50 years so \(30\)% of WOMEN (\(4\) parts) will be less than or equal to 50 years

Hence new ratio \(= (30\)%\(*4):1=\frac{6}{5}:1=6:5\)

Option C
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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 22 Jan 2018, 08:48
Can you please tell me why I can't get the correct answer?

Total number of people = X
Total Woman = 4X/5
Total Men = X/5

Women >50 = (4x/5)(7/10) = 28X/50
Women <50 = 22X/50

Ratio = 22X/50 / X/5 = 11/5 !!
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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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MvArrow wrote:
Can you please tell me why I can't get the correct answer?

Total number of people = X
Total Woman = 4X/5
Total Men = X/5

Women >50 = (4x/5)(7/10) = 28X/50
Women <50 = 22X/50

Ratio = 22X/50 / X/5 = 11/5 !!


Hi MvArrow

the highlighted part is incorrect

as you have calculated Women>50 as 28x/50

so women less than 50 has to be =4x/5-28x/50=12x/50

you have subtracted women>50 from the total population which is incorrect
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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 22 Jan 2018, 10:06
niks18 wrote:
MvArrow wrote:
Can you please tell me why I can't get the correct answer?

Total number of people = X
Total Woman = 4X/5
Total Men = X/5

Women >50 = (4x/5)(7/10) = 28X/50
[highlight]Women 50 as 28x/50

so women less than 50 has to be =4x/5-28x/50=12x/50

you have subtracted women>50 from the total population which is incorrect


Thanks a lot! Stupid error :) ouch! Now I fully understand :)
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Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 22 Jan 2018, 10:52
Bunuel wrote:
If 70% of the women in a room are over 50 years old and 80% of the people in the room are women, what is the ratio of the number of women 50 years old or less to the number men in the room?

A. 3 : 7
B. 4 : 1
C. 6 : 5
D. 7 : 10
E. 14 : 5
Let there be 100 People in the room.

Total women in the room is \(80\) & Total Men in the Room is \(20\)

Women in a room over 50 years old = \(56\)

Women in a room less than 50 years old is \(80 - 56\) = \(24\)

So, ratio of the number of women 50 years old or less to the number men in the room is \(24 : 20\) = \(6 : 5\), answer must be (C)
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If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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New post 22 Jan 2018, 12:14
Ratio = No. of female less than or equal to 50yrs/total No of male
If:
Total number of people = 100
Then:
Total number of female = 80
Total number of male = 20
Females who are greater than 50yrs = 70% of all females
Females who are less than or equal to 50yrs = 30% of all females = 0.3*80

So, ratio = 0.3*80/20 = 0.3*4 = 1.2 = 6/5 = hence, C
Hope it helps. :-) :-)
If 70% of the women in a room are over 50 years old and 80% of the peo   [#permalink] 22 Jan 2018, 12:14
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