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yashikaaggarwal
(1) In-country X, among the population over the age of 25, 26 per cent of the male population and 16 per cent of the female population possess college diplomas.
What if only 5% of the total population is over 25?
We don't know what percentage of the total population is over 25.
(Not Sufficient)

(2) In-country X, women account for 55 per cent of the total population.
We don't know what percentage of the total population is over 25.
(Not Sufficient)

Combining both,
We still don't know what percentage of the total population is over 25.
(Not Sufficient)

Answer is E

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Hello: we don’t need to know the size of the population of 25 year olds to be able to solve this question.
St 1: because the age among the population over 25years old is between 16 and 26 then that implies that the percentage of people over 25 years can be 17 0r 25 . Which is any number between 16 and 26 . Hence insufficient


St 2 : all we have is the proportion of male to female in the total population insufficient

1+2 : if we had the proportion of male to female in the population over 25 years then we could go ahead and solve this . But we don’t that so insufficient. We only have their proportions in the total population.
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Shouldn't the answer be A? The question clearly asks if 20% of population over the age of 25 possess college diploma, the first statement even though doesn't tell us the percentage that belongs to that age group, it does tell us that 26% male and 16% female from that age group has a diploma which will be greater than or equal to 20% of population of over 25
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Do at least 20 percent of the people in country X who are over the age of 25 possess a college diploma?

(1) In country X, among the population over the age of 25, 26 percent of the male population and 16 percent of the female population possess college diplomas.

The overall percent over age 25 with diplomas depends on the male/female share among those over age 25. It could be as low as 16 percent (if all are female) or as high as 26 percent (if all are male), so we cannot determine whether it is at least 20 percent. Not sufficient.

(2) In country X, women account for 55 percent of the total population.

It gives the female share of the total population, but says nothing about diploma rates or the gender split among those over age 25. Not sufficient.

(1)+(2) We still do not know the male/female split among the over 25 group, which is what we need to combine the 26 percent and 16 percent from statement (1). Not sufficient.

Answer: E.
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facerevitae
Shouldn't the answer be A? The question clearly asks if 20% of population over the age of 25 possess college diploma, the first statement even though doesn't tell us the percentage that belongs to that age group, it does tell us that 26% male and 16% female from that age group has a diploma which will be greater than or equal to 20% of population of over 25
No. From (1), the overall over 25 diploma rate is a weighted average of 26% (males) and 16% (females). A weighted average can be anywhere between 16% and 26%, depending on the male female split among those over 25. For example, if the over 25 group is mostly female, the overall could be below 20%. So (1) alone is not sufficient, and the answer is not A.

For more, check the solution above. Hope it helps.
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