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

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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.

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.

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.

(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.

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

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

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24 Sep 2013, 07:36

Quest Statement says : w:m:c <=> 5:2:7

1) 1st statement says W+C is 12 we know W:C <=> 5:7 That clearly means w=5 and c=7 hence m=2 and total nbr of people 14 .... SUFFICIENT

2) 2nd statement says Men < 4 Which means that Men could be 3 or 2 or 1

It cant be three since the common multiplier will be 1.5 and 5*1.5 is a decimal figure and number of women cant be in decimals It cant be 1 since the common multiplier will be 0.5 and 5*0,5 is is a decimal figure and number of women cant be in decimals So we left with 2 and that tells common multiplier is 1 thus number of w / c and m = 5+2+7 = 14 ... SUFFICIENT

hence answer is D

mymba99 wrote:

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.

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

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15 Nov 2013, 20:26

Came across this in the GMAC practice exam. Should we not consider zero as an option for the number of men in statement two? When they give the ratio, we should assume there are at least some people in the room?

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.

Came across this in the GMAC practice exam. Should we not consider zero as an option for the number of men in statement two? When they give the ratio, we should assume there are at least some people in the room?

From the stem it follows that there are at least 5 women, 2 men and 7 children in the room.
_________________

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

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30 Jan 2014, 02:42

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mymba99 wrote:

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.

Let us say that there are 5x women, 2x men and 7x children

Statement I is sufficient: 12 = 5x + 7x x = 1

Statement II is sufficient: 2x < 4 and x is a positive integer Hence x has to be 1.

Answer is D
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Re: The ratio of the number of women to the number of men to the [#permalink]

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03 Jan 2016, 16:49

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

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22 Jan 2017, 19:31

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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24 Mar 2017, 15:43

Bunuel wrote:

gmatzac wrote:

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.

Came across this in the GMAC practice exam. Should we not consider zero as an option for the number of men in statement two? When they give the ratio, we should assume there are at least some people in the room?

From the stem it follows that there are at least 5 women, 2 men and 7 children in the room.

******* Me too, I fell into the "zero men" trap. However, I do not believe that it is clear from the question stem that there MUST be people in the room. Of course a ratio of 5*0:2*0:7*0 = 0:0:0 would not make much sense, but it is a possibility.

There is a better reason for eliminating the "zero men" option however: GMAT data sufficiency questions are made in a way that the 2 options NEVER result in contradictory results. This is no hard science, but in the hundreds of questions we are resolving in preparation for the test there is no single one with a conflicting data sufficiency result. Note this is my experience, if not true please send me the reference of an official DS question that illustrates else.

So, because the question stem in 1) gives us women + children = 12, there are people in the room. I am not talking about carrying over information from 1) to 2), but I am just saying that contradictory results are impossible (i.e. calculating a result for option 2 of zero people in the room, while 1) gave 14 people as a result).

1) the total number of women and children in the room is 12 2) There are fewer that 4 men in the room Hence the # of men must be a member from the set {1,2,3}. Only possibility in this question that satisfies the ratio constraint is: men = 2x = 2 so total number of people is 14. SUFFICIENT Answer D

Bunuel, if this is what you meant with "it is clear from the question stem", then I agree with you. If this is not what you meant, then this might help some people who fell into the "zero men" trap to be suspicious of a contradictory result they have calculated on a data sufficiency question.

gmatclubot

Re: The ratio of the number of women to the number of men to the
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24 Mar 2017, 15:43

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