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by phoenix9801 » Thu May 31, 2012 10:39 pm
At a family reunion, the ratio of the number of women to the number of children is 5 to 2 and the number of women at the reunion is less than 30. The ratio of the number of children to the number of men is 5 to 11.Then What is the number of men at the reunion??????
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by Anurag@Gurome » Thu May 31, 2012 11:00 pm
phoenix9801 wrote:At a family reunion, the ratio of the number of women to the number of children is 5 to 2 and the number of women at the reunion is less than 30. The ratio of the number of children to the number of men is 5 to 11.Then What is the number of men at the reunion?
As the ratio of the number of women to the number of children is 5:2, the number of women must be a multiple of 5. As the number of women is less than 30, possible number of women are : 5, 10, 15, 20, and 25.

Hence, possible number of children are : 2, 4, 6, 8, and 10

Now, the ratio of the number of men to the number of children is 11:5, the number of children must be a multiple of 5. Therefore, only possible number of children is 10.

Hence, number of men at the reunion = 11*(10/5) = 22
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by Birottam Dutta » Thu May 31, 2012 11:04 pm
Let number of women be W, children C and men M.

Now, C/W = 2/5. Again, let the number of women be 5X and the number of children be 2X, X being a natural number.

We know that number of women is less than 30, so, if W=5X, we have the possible values of W as 5 (X=1), 10(x=2), 15 (X=3), 20 (X=4) and 25 (X=5).

Corresponding to these, the possible number of children can be 2, 4, 6, 8 and 10.---- (1)

Coming to the second piece of information, C/M= 5/11. From this, we know that C has to be a multiple of 5.

From (1), we see that only 10 is the option which is a multiple of 5.

Therefore, number of children = 10.

Number of men = (11/5)*10 = 22.

So, this is the required answer.
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by GMATGuruNY » Fri Jun 01, 2012 2:08 am
phoenix9801 wrote:At a family reunion, the ratio of the number of women to the number of children is 5 to 2 and the number of women at the reunion is less than 30. The ratio of the number of children to the number of men is 5 to 11.Then What is the number of men at the reunion??????
W/C * C/M = W/M.

Since W/C = 5/2 and C/M = 5/11, we get:
5/2 * 5/11 = W/M
25/22 = W/M.

The resulting ratio implies that the number of women is a multiple of 25.
Since the number of women is less than 30, there must be 25 women, implying that there are 22 men.
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