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Double set matrix problem

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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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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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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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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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