KLMN rectangles ratios

Obviously you figured out that neither statement alone is sufficient, so let's look at the 2 statements together.

Notice that the number of children has to be a multiple of 10. Its ratio to number of women is 2 to 5, and its ratio to number of men is 5 to 11. This means that it needs to be evenly divided by both 2 and 5, which makes it a multiple of 10. If there are 10 children, there will be 25 women. If there are 20 children, then there will be 50 women, which is greater than 30 as per statement 2. Therefore, the number of children has to be 10, and from this you can calculate the exact numbers of women and men.

madeline wrote:Obviously you figured out that neither statement alone is sufficient, so let's look at the 2 statements together.

Notice that the number of children has to be a multiple of 10. Its ratio to number of women is 2 to 5, and its ratio to number of men is 5 to 11. This means that it needs to be evenly divided by both 2 and 5, which makes it a multiple of 10. If there are 10 children, there will be 25 women. If there are 20 children, then there will be 50 women, which is greater than 30 as per statement 2. Therefore, the number of children has to be 10, and from this you can calculate the exact numbers of women and men.

OA please??

Thanks Madeline. Nice work.
OA is C