q #2159

[michaeljanati]

Can someone explain the math here?


Thanks.

[noah]

So I'm sure I'm explaining the correct question, can you give me some of the text? Thanks.

[swwestley]

60% of all students at Polytechnic High School participate in sports, and 50% of all students at Polytechnic High School are in the Engineering Academy.

We can infer that...

(A) At least 20% of students who participate in sports are in the Engineering Academy.

(B) At least 20% of students in the Engineering Academy participate in sports.


I don't think I've seen any questions that use percentages like this on the LSAT, but then most recent preptest I've taken is #53 - are questions like these making regular appearances now?

[noah]

There have been a few percent questions - definitely not some huge trend. However, the issue does pop up consistently (1-3 questions per LSAT) in which you need to know the relationship between some and most. This vein of question is actually most helpful in making those easier, as well as reinforcing what an inference is - something that must be true.

[mcfriedrichs]

60% of all students at Polytechnic High School participate in sports, and 50% of all students at Polytechnic High School are in the Engineering Academy.

We can infer that...

(A) At least 20% of students who participate in sports are in the Engineering Academy.

(B) At least 20% of students in the Engineering Academy participate in sports.


I don't think I've seen any questions that use percentages like this on the LSAT, but then most recent preptest I've taken is #53 - are questions like these making regular appearances now?

If 60% play sports, and 50% are in Engineering, that means 10% of the total school does both (there could be more, but we're solving for the minimum because the question asks us "at least" how many students). To make this easy, let's say the school has 100 students. 60 in sports. 50 in engineering. What is 20% of 50 (engineering)? 10. The same number as the group who must play both sports and be in engineering. So the answer is B.

If we take our 10 students who play sports and also need to be in the engineering program (again, there could be more, but the question is asking "at least", so we're solving for the minimum), and we find out what percentage of the total sports students that is, we get 16.6% from dividing 10 by 60. So at least 16.6% of the sports students are also in engineering. Which makes A incorrect.

hope that helps

[noah]

Great explanation. I realize now that I totally spaced on explaining it earlier and just rambled about the question's relevance to the LSAT. Thanks!