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The ratio of the number of women to the number of men to the [#permalink]
28 Apr 2008, 12:24

2

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D

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Difficulty:

45% (medium)

Question Stats:

60% (01:46) correct
40% (00:45) wrong based on 315 sessions

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. _________________

Re: The ratio of the number of women to the number of men to the [#permalink]
24 Sep 2013, 06:36

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]
15 Nov 2013, 19:26

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?

Re: The ratio of the number of women to the number of men to the [#permalink]
16 Nov 2013, 10:11

1

This post received KUDOS

Expert's post

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. _________________

Re: The ratio of the number of women to the number of men to the [#permalink]
30 Jan 2014, 01:42

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.

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