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

abhijit_sen · Answer

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.

sidhu4u · Answer

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

gmatzac · Answer

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?

Bunuel · Answer

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

CrackverbalGMAT · Answer

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

hemantbafna · Answer

W:M:C=5:2:7= 5x:2x:7x

(1) W+C=5x+7x=12
12x=12
x=1

Total = 14x=14
 Sufficient .

(2) 2x<4= x<2
If x is less than 2, then x has to be 1, number of boys cannot be 0 or -ve.
 Sufficient.

D

Schachfreizeit · Answer

why is it not possible that we don't have any men?

MayaK · Answer

what about the option of 0 men? why don't we count the possibility that the room is empty ?

Bunuel · Answer

I tried explaining this  here .

Hope it helps.

bumpbot · Answer

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