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?

from stem we know that the number of people in the room has to be 14*n.

statement I
If the number of women and children is 12, than we have 5 women and 7 childrens meaning two men.

statement II
since we have less than 4 men in the room, the number of men can be 1,2,3

only when the number of men is 2 ---> we will get integers for the women and childrens.

lets say men = 3 than women = 3/2*7 = 21/2

the answer is (D)