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Are at least 80 percent of the people in Country X

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Are at least 80 percent of the people in Country X [#permalink] New post 30 Apr 2012, 17:18
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Are at least 80 percent of the people in Country X who are 25 years old or younger full-time students?

(1) In Country X, 32 percent of the population is 25 years old or younger.

(2) In Country X, of the population 25 years old or younger, 90 percent of the women and 75 percent of the men are full-time students.

I think that the typical approach of the table to solve the set problems is not useful in this question. It seems there are more than two categories. Please, your help.
Also, please confirm whether it is a 700+ question according to your experience. Thanks!


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[Reveal] Spoiler: OA

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Re: Are at least 80 percent of the people in Country X [#permalink] New post 30 Apr 2012, 19:09
metallicafan wrote:
Are at least 80 percent of the people in Country X who are 25 years old or younger full-time students?

(1) In Country X, 32 percent of the population is 25 years old or younger.

(2) In Country X, of the population 25 years old or younger, 90 percent of the women and 75 percent of the men are full-time students.

I think that the typical approach of the table to solve the set problems is not useful in this question. It seems there are more than two categories. Please, your help.
Also, please confirm whether it is a 700+ question according to your experience. Thanks!


Source: http://www.gmathacks.com


Statement 1) The most this can give us is that 32% of the population is 25 years or younger

Statement 2) This gives us the fact that 90% of the women and 75% of men 25 years or younger are students

Combined) Now we can calculate the total population which in fact equals one because we know that 32% are younger than 25. and 68% are older.

Now we can see if it works out. Percentage women who are 25 and younger and are students= (.10)(.9)=9%

Percentage of men 25> who are students= (.25)(.75)=18.75%

Think it should be Not Sufficient therefor E

I would would complete the prob but no use

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Re: Are at least 80 percent of the people in Country X [#permalink] New post 30 Apr 2012, 23:10
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Are at least 80 percent of the people in Country X who are 25 years old or younger full-time students?

Question asks whether 80% of some particular group are students.

(1) In Country X, 32 percent of the population is 25 years old or younger. We are given the size of this particular group. Not sufficient.

(2) In Country X, of the population 25 years old or younger, 90 percent of the women and 75 percent of the men are full-time students. Of this particular group 90% of the women and 75% of the men are students --> since the weighted average of 2 individual averages (90% and 75%) must lie between these individual averages, then the average percent of students in this particular group is between 75% and 90%, so it may or may not be more than 80%. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

Answer: E.

Similar question to practice: at-least-10-percent-of-the-people-in-country-x-who-are-122734.html

P.S. I wouldn't rate this problem as 700 level.

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Re: Are at least 80 percent of the people in Country X [#permalink] New post 01 May 2012, 15:26
Thank you Bunuel.
You are right. Definitely, not a 700+ question.

Sometimes we are so used to some approachs that we don't see other ways to solve a problem. Thanks again.

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Re: Are at least 80 percent of the people in Country X [#permalink] New post 11 Jun 2013, 06:28
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

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Re: Are at least 80 percent of the people in Country X [#permalink] New post 05 Jun 2014, 00:52
Bunuel please correct me :
I approached this question with Venn Diagram
<= 25 years ::: >25 years ::: Total
Full Time ::
Not Full T ::
Total ::
According to Statement 1 :
<= 25 years ::: >25 years ::: Total
Full Time ::
Not Full T ::
Total :: 32%

Since its given the percentage of students under or of 25 years is 32% , this states that the percentage can never be more than 32%.

Please correct me where I am making mistake.
The second statement though uses the weighted average concept : hence the total average will be between 57% and 90% -- not sufficient.

Also, this is contradicting the two statements. Please mention what I am missing.

Thanks
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Re: Are at least 80 percent of the people in Country X [#permalink] New post 05 Jun 2014, 01:15
Expert's post
GmatDestroyer2013 wrote:
Bunuel please correct me :
I approached this question with Venn Diagram
<= 25 years ::: >25 years ::: Total
Full Time ::
Not Full T ::
Total ::
According to Statement 1 :
<= 25 years ::: >25 years ::: Total
Full Time ::
Not Full T ::
Total :: 32%

Since its given the percentage of students under or of 25 years is 32% , this states that the percentage can never be more than 32%.

Please correct me where I am making mistake.
The second statement though uses the weighted average concept : hence the total average will be between 57% and 90% -- not sufficient.

Also, this is contradicting the two statements. Please mention what I am missing.

Thanks


Yes, from (1) we have that 32% of the population is 25 years old or younger. Now, the question asks whether 80% of those 32% are full-time students, not 80% of the whole population.

Does this make sense?

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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Are at least 80 percent of the people in Country X [#permalink] New post 06 Jun 2014, 03:18
Hi Bunuel,

yes it does.

now I am clear from statement 1 - we can't say it may or may not
from statement 2 - the proportion will lie between the 90% and 75% which can be more than 80%.but nothing definitive hence not sufficient.

Combining 1 and 2 : still not sufficient. Hence E .. thanks a lot
Re: Are at least 80 percent of the people in Country X   [#permalink] 06 Jun 2014, 03:18
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