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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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Math Expert
Joined: 02 Sep 2009
Posts: 43335

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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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27 Dec 2017, 23:43
00:00

Difficulty:

35% (medium)

Question Stats:

79% (00:47) correct 21% (01:05) wrong based on 41 sessions

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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
[Reveal] Spoiler: OA

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Kudos [?]: 139575 [0], given: 12794

Intern
Joined: 10 Apr 2017
Posts: 37

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Schools: Kelley '20
Re: If 70% of the women in a room are over 50 years old and 80% of the peo [#permalink]

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28 Dec 2017, 02:33
1
KUDOS
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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Manager
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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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28 Dec 2017, 16:36
1
KUDOS
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 $$\frac{Woman<50}{Men}=\frac{0.3*80}{20}=\frac{24}{20}=6:5$$

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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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30 Dec 2017, 21:46
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

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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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30 Dec 2017, 22:06
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 . 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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If 70% of the women in a room are over 50 years old and 80% of the peo   [#permalink] 30 Dec 2017, 22:06
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