Akansha wrote:On a certain sight-seeing tour, the ratio of the number of women to the number of children is 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.

No. of men=m; No. of women= w; No. of children= C;

given; w/c=5/2; w=(5/2)c;

1) c/m=5/11;
m=(11/5)c;
which clearly is not sufficient to answer the question.

2)No. womens are less than 30; also we know that w=(5/2)c; since no. of men,women and children should be an integer therefore; c should be even;
c=10; w=25;
c=8; w=20;
c=6; w=15;
c=4; w=10;
c=2; w=5;

since we don't have the information about no. of men, therefore 2 alone is also not sufficient to answer the question.

combining 1 and 2;

only value of c, for which both m and w becomes integer is 10;
therefore c=10; m=(11/5)*10=22; w=25;

hence answer should be C

Akansha wrote:On a certain sight-seeing tour, the ratio of the number of women to the number of children is 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.

This question is restricted to positive integers because it is about people. We can't have 2/3 of a child.

Given info is W:C = 5:2.

Question: M?

Statement 1: C:M = 5:11.
To combine this ratio with the first ratio, the common element (C) must be represented by the same value in each ratio.
W:C = 5:2 = 25:10
C:M = 5:11 = 10:22
Thus, W:C:M = 25:10:22.
Since we know only the ratio, no way to determine the actual value of M.
Insufficient.

Statement 2: W<30.
No way to determine M.
Insufficient.

Statements 1 and 2 together:
Given that W:C:M = 25:10:22 and W<30, we know that W=25 (because if we use a multiple of the ratio, the number of women will be at least 2*25 = 50).
Since W=25 and W:C:M = 25:10:22, M=22.
Sufficient.

The correct answer is C.