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.

If there are only 10 men in the group and 70% of them are married and no woman in the group is married, then there will be only 7 people married in the group, so less than 75.
If all 250 people are men, then there will be at least 250*0.65=~163 people married in the group, so more than 75.

Not sufficient.

(2) At least 30 percent of the women in the group are married. Basically the same here:

If there are only 10 women in the group and 30% of them are married and no man in the group is married, then there will be only 3 people married in the group, so less than 75.
If all 250 people are women, then there will be at least 250*0.3=75 people married in the group.

Not sufficient.

(1)+(2) At least 30 percent of the women and at least 65 percent of the men in the group are married. This means that the percent of married people cannot be less than 30% (the overall percent of married people cannot be less than individual percent of married people in each group). So, at least 0.3*250 = 75 people are married. Sufficient.

Answer: C.
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my response
Total member (M+F) = 250
IS MARRIED PERSONS >=75 [NOT NECESSARY with other gp mem]
S1
65% of 250 >75 --YES
s2
30%250 =75 ---Yes

"D"

A is insufficient as 65% of men are married.IDK the no. of men in 250.
if 100 of 250 are men then ....at least 65 people are married.
However if 200 are men then ,,atleast 75 are married.
Hence Insufficient..

B..if 100 women are there that implies at least 30 are married
if all are women then at least 75 are married...Hence insufficient

combining ...if all women then True
if we keep on reducing women the 65% of men will always make it >=75

D

combining
case all men ---True
all women --True
100 men,150 women
True

(1) At least 65 percent of the men in the group are married.
(2) At least 30 percent of the women in the group are married.


Statement 1 - Not sufficient

If Men are 20 out of 250, married number = 13
Women would be 230, assume married % is 10, married women = 23
Total married = 36

If married % of women is higher, say 50%, total married is in excess of 75.

So, we have both the possibilities. Eliminate A and D

Statement 2 - Not sufficient
Women have 30% married.
Assume women number = 250, Total married = 75. Answer to Q in stem is YES
Assume women number = 100, total married = 30; Men =150. Married % of men could be anything from 0 to 100. So answer to q in stem in could be NO.

Eliminate B.

Remaining choices C and E.

Lets combine the two statements.

Women have 30% married. If women = 250, married = 75
Start replacing women with men and we'll have the following addition to married population (0.65 - 0.3) since men have more % married. Since replacement causes a net addition, therefore, combining the two statements will always yield a YES to the question in stem.

C is sufficient.
Wome

Option A - We do not know the number of men, so we cannot determine the number of married people
Hence, Insufficient

Option B - We do not know the number of women, so we cannot determine the number of married people
Hence, Insufficient

Option C - Combining both

Let no. of men = x
So. no. of married people = \(0.65*x + 0.30*(250-x)\) = \(75 + 0.35*x\) -> this implies that no. of married people are atleast 75

Hence, we can say that the number of married people will always be 75 or greater

The correct answer should be C

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.
No info. about women
Not sufficient

(2) At least 30 percent of the women in the group are married.
No info. about men
Not sufficient

(1) + (2)
If only women are there in the group, then at least 30% of 250 or 75 people in the group are married.
If only men are there in the group, then at least 65% of 250 or 163 people in the group are married.
If some women and the other are men, we get a value between 75 and 163
Sufficient

Option C

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Hope it helps.
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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.
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