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On a certain sight-seeing tour, the ratio of the number

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On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.

Official Answer

1 Answer

We have to find out no of men on the tour, and we are give the ration Woman to Children. If we find out the ratio of one of these entities to Men and the total of number of Woman or Children, we are done. 
Let us assign some nomenclature to the problem W : women, C : children, Men : M
We already know W:C = 5:2
Using Condition 1)
This  tells us C:M = 5 : 11
Hence we get W:C:M = 25:10:33
However, this does not suffice to answer the question. INSUFFICIENT
Using Condition 2) 
The number of woman < 30. This also does not tell anything. 
Let us try to combine both the conditions
if the woman are < 30,and number of woman have to be a +ve integer & we also know the ratio of W:C:M as 25:10:33, this can only be possible if # of W = 25, hence the number of Men = 33
Answer is C. Combining the statements is SUFFICIENT to answer the question.
answered Jul 11, 2014 by Senior Associate (475 points)
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