The ratio of the number of women to the number of men to the

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The ratio of the number of women to the number of men to the [#permalink]

28 Apr 2008, 13:24

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The ratio of the number of women to the number of men to the number of children in a room is
5:2:7, respectively. What is the total number of people in the room?
(1) The total number of women and children in the room is 12.
(2) There are fewer than 4 men in the room.

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Re: DS - ratio [#permalink]

28 Apr 2008, 13:38

Say total number of people are = 70x
So Women = 70x*5/14 = 25x
Children = 7*70x/14 = 35x
Men = 2*70x/14 = 10x

Statement 1:
Tells us 25x + 35x = 60x = 12, so total number of people = 70/5 = 14. So you know total number of people. Question is answered.

Statement 2:
Tells us there are fewer than 4 men in room. So it can be 1, 2, or 3.
If Men = 1, then women = 5/2 *1 = 2.5 So Not Possible
If Men = 2, then Women = 5/2 * 2 = 5, and Children = 7/2 * 2 = 7
If Men = 3, then Women = 5/2 * 3 = 7.5 So Not Possible.
From this statement also we know what the total number of people is. So this also answers the question.

Answer D.

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Re: DS - ratio [#permalink]

28 Apr 2008, 20:07

saravalli wrote:

(1) There can only be 5 women and 7 children in this situation. There's no other way to satisfy the ratio and also satisfy the equation Women+Children=12. Since there are 5 women and 7 children, there must be 2 men. 5+7+2=14. SUFFICIENT, eliminate BCE.
(2) Since there are fewer than 4 men in the room, we can only have 3, 2, or 1 men. To satisfy the ratio, 3 (1.5*2) men must mean 7.5 (1.5*5) women and 10.5 (1.5*7) children. You can't have half a person, so this obviously doesn't work. As shown in (1), 2 men gives us 14 total people. 1 man would mean 2.5 women and 3.5 children. Once again, half a person makes no sense. There is only one possibility and that is 2 men for a total of 14 people in the room. SUFFICIENT.

Answer: D.
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Re: DS - ratio [#permalink]

11 Mar 2010, 05:50

5:2:7
let say common ratio is k
so 5k women 2k men and 7k children
total people in the room = 5k+2k+7k=14k

stmt1: 5k+7k = 12 => k = 1
therefore, no of people is 14*1 = 14

stmt2: fewer than 4 men means men can be 1 2 or 3

if no of men is 1 dat means k is 0.5 and women = 5 * 0.5 = 2.5 not possible
if no of men is 2 dat means k is 1 and women = 5 and children = 7 possible
if no of men is 3 dat means k is 1/3 and women = 5/3 not possible
since there is only one case so we can deduce no of people from this stmt too

so, answer is D
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Re: DS - ratio [#permalink]

11 Mar 2010, 06:04

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Please check the above post.
It was clearly mentioned to post PS and DS question in their respective subforums.
Please always read the sticky rules and follow them.
At the end it will benefit us only.
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Re: DS - ratio [#permalink] 11 Mar 2010, 06:04

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