Double set matrix problem

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Wed Mar 06, 2013 10:32 pm

Hello,

This is from MGMAT Strategy Guide.

40% of all high school students hate roller coasters; the rest love them. 20% of those students who love roller coasters own chinchillas. What percentage of students love roller coasters but do not own a chinchilla?

Ans: 48

In my solution, I am getting 48 out of 60 which is 80%. I am not sure if the wordings are confusing me. Can you please assist? Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Problem Solving | Wed Mar 06, 2013 10:32 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Mar 06, 2013 10:41 pm

gmattesttaker2 wrote:In my solution, I am getting 48 out of 60 which is 80%. I am not sure if the wordings are confusing me. Can you please assist? Thanks a lot.

Yes, it is 80% of 60, i.e. 80% of the students who love roller coasters.
But the question asks you to find out the same in terms of total students which is 48%.

Hope that helps.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Mar 06, 2013 10:44 pm

gmattesttaker2 wrote:40% of all high school students hate roller coasters; the rest love them. 20% of those students who love roller coasters own chinchillas. What percentage of students love roller coasters but do not own a chinchilla?

Here is a method that someone will find easier than the matrix method.

Let us assume there are 100 students in the school.
Hence, 60 of them love roller coasters.

Now, (100 - 20)% = 80% of these 60 students do not own chinchillas.
80% of 60 = 80*60/100 = 48

Hence, 48% of students love roller coasters but do not own a chinchilla.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Mar 07, 2013 3:25 am

gmattesttaker2 wrote:Hello,

This is from MGMAT Strategy Guide.

40% of all high school students hate roller coasters; the rest love them. 20% of those students who love roller coasters own chinchillas. What percentage of students love roller coasters but do not own a chinchilla?

Ans: 48

In my solution, I am getting 48 out of 60 which is 80%. I am not sure if the wordings are confusing me. Can you please assist? Thanks a lot.

Best Regards,
Sri

Your solution would be correct if the question asked the following:
What percent of THE STUDENTS WHO LOVE ROLLER COLLER COASTERS do not own a chinchilla?
Solution:
(students who love roller coasters but do not own a chinchilla)/(total students who love roller coasters) = 48/60 = 4/5 = 80%.

But the question stem here asks the following:
What percent of THE STUDENTS love roller coasters but do not own a chinchilla?
Solution:
(students who love roller coasters but do not own a chinchilla)/(total students) = 48/100 = 48%.

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