Data Sufficiency

This is another DS word problem of RATIO.

I did not get the answer for this. My choice was E but the OA is C.

Now I am trying to work my way through it. Here are my steps to solve this.

From the problem its given that w/c = 5/2 ----let say I
where w is the number of women
c is the number of children
m is the number of men = ?

Now from 1) you c/m = 5/11 ==> c = 5/11(m)
From I c = 2/5(w) so if we equate the above 2 eqns

2/5(w) = 5/11(m)

I get w = 25/22(m)

Since m is unknown cancel answer choices A and D

From 2) its given w < 30
From this we cannot find m so cancel answer choice B.

Now from 1) and 2) together we have .
w = 25/22(m) , Eqn I and w < 30.

from I and w < 30 we have
w/c = 10/4 or 25/10 both gives us the ration of 5/2

But w = 25/22 (m) which should yield an integer

Therefore m = 22 and w = 25.

Is this the right solution. Can the value of w have a decimal and then we can round it off or the value of w should be simply an integer.

I am confused about this. Can someone please reflect on this and propose their own solution.

Again thanks in advance.