In a group of 250 adults, is the number of married (not necessarily to other group members) people at least 75?
(1) At least 65 percent of the men in the group are married.
Let there be 100 men, so 65 are married. Surely, it is less than 75 but we also don't know about women who might be married or unmarried. Additionally, more than 75 men can also be married.
INSUFFICIENT.
(2) At least 30 percent of the women in the group are married.
Let there be 100 women, so 30 are married. Surely, it is less than 75 but we also don't know about men who might be married or unmarried. Additionally, more than 75 women can also be married.
INSUFFICIENT.
Together 1 and 2.
Using 2x2 matrix, we can have 2 equations:
1. 0.65x + 0.35x = x where x is the number of men.
2. 0.30y + 0.70y = y where y is the number of women.
Also, x + y = 250 &
0.65x + 0.30y >= 75,
0.35x + 0.70y <= 175
We can now solve for the x and y for many values and here's the catch.
As the question mentions 'not necessarily to other group members', it is true that two men or two women aren't married together(i.e. they are married to people outside this group of 250) in which case the answer might change, most likely to E.
So the least married people are 30% women if there are no men.
30% * 250 = 75
Hence, more women might be married.
SUFFICIENT.
Answer C.
NOTE: Had these men and women were married together within this group of 250 together, then following cases arise.
A. For men and women are married together 0.65x = 0.30y and x + y = 250.
\(\frac{x}{y} = \frac{6}{13}\) which gives us x >= 80 and y <= 170. So, we need to find a cases where x and y are in such a ratio that married women equals married men. For example: \(\frac{x}{y} = \frac{2}{3}\) gives x = 100, y = 150 where in 60% women are married to 90% men.
B. For men married to men and women married to women and some men married to women.
This would be ridiculously difficult without further inputs.
C. Slight more difficult would be when some are married within the group and some are married outside. _________________