Problem Solving

In a recent anonymous poll of a certain private community, 22 percent of its 2500 residents reported that they were suffering from depression. Of this group of depressed people, 20 percent were at least sixty years old. If 25 percent of all the people are at least sixty years old, how many people over the age of sixty did not report that they were suffering from depression?

Answer is 515.

Thank you in advance.

22% of 2500 people are suffering from depression

=> 22*2500/100 = 550 people are suffering from depression.

Out of these 550 people, 20% are at least 60 yrs old

=> 20*550/100 = 110 people are at least 60 yrs and suffering from depression.

Now, 25% of total population is at least 60 yrs old

=> 25*2500/100 = 625 people are at least 60 yrs old.

So, people who are at least 60 and not suffering from depression = 625-110 = 515.

shanice wrote:In a recent anonymous poll of a certain private community, 22 percent of its 2500 residents reported that they were suffering from depression. Of this group of depressed people, 20 percent were at least sixty years old. If 25 percent of all the people are at least sixty years old, how many people over the age of sixty did not report that they were suffering from depression?

This is an EITHER/OR group question.
Every resident EITHER suffers from depression OR does not.
Every resident EITHER is at least 60 years old OR is not.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let D = depressed, ND = not depressed.
Here's the grid, with the following percentages inserted:
Total = 100.
Total D = 22.
D + at least sixty years old = .2(22) = 4.4.
Total at least 60 = 25.

_______________D________ND_______Total

≥60:__________4.4_________________25

<60:________________________________

total:__________22_________________100

The values in each row and column must add up to the total.
Thus, ND + at least 60 = 20.6%:

_______________D______ND_______Total

≥60:__________4.4____20.6________25

<60:________________________________

total:__________22________________100

Thus, 20.6% of the 2500 people are not depressed and at least 60:
.206(2500) = 515.

Hi BirottamDutta & GMATGuruNY,

Thanks for your help.But I'm confused with the question being asked.Please look at the sentence below:-

If 25 percent of all the people are at least sixty years old, how many people over the age of sixty did not report that they were suffering from depression?

Confusion: are they asking us to find the no of people over the age of sixty(above 60 years old)or just 60 years old that did not report they were suffering from depression? Is the question stated correctly?

Thank you.

Hi, can anyone please reply?

shanice wrote:In a recent anonymous poll of a certain private community, 22 percent of its 2500 residents reported that they were suffering from depression. Of this group of depressed people, 20 percent were at least sixty years old this means that 20% (of the depressed people, 550) were 60 or older. If 25 percent of all the people are at least sixty years old this means that 25% of the whole population (2500) are over 60 years old, how many people over the age of sixty did not report that they were suffering from depression?

Now to solve the problem set up a chart.
Does this answer your question?

yes,alex.gellately.You've answered my question.

Thank you very much.