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[zagreus77]

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...

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

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


This question has a problem that I didn't focus on before, as I just assumed it was simple math. Of course, if you take half of the students from Polytechnic, the lowest percentage you could achieve would be twenty as the minimum overlap is 10 percent of 2x(the whole) which is 20 percent of x(half). But the credited answer does not specify that. It refers to the students at the Engineering Academy. We have no information that the students at the the Engineering Academy are made up entirely of this group. If there is a number of students at the Engineering Academy who are not members of the Polytech the argument does not follow. We don't know what the percentage is unless we have information about other students in the academy, or we are told that there are no other students besides the Poly students. So this question is quite flawed.

[noah]

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...

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

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


This question has a problem that I didn't focus on before, as I just assumed it was simple math. Of course, if you take half of the students from Polytechnic, the lowest percentage you could achieve would be twenty as the minimum overlap is 10 percent of 2x(the whole) which is 20 percent of x(half). But the credited answer does not specify that. It refers to the students at the Engineering Academy. We have no information that the students at the the Engineering Academy are made up entirely of this group. If there is a number of students at the Engineering Academy who are not members of the Polytech the argument does not follow. We don't know what the percentage is unless we have information about other students in the academy, or we are told that there are no other students besides the Poly students. So this question is quite flawed.

Nice catch! I'll edit that.

[ptraye]

now that the flaw has be corrected, can someone explain the answer choices please?

thanks.

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

We can infer that...

1) At least 20% of Polytechnic students who participate in sports are in the school's Engineering Academy.

2) At least 20% of Polytechnic students in the Engineering Academy participate in sports
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the correct answer is 2.

i plugged in numbers with this problem. if there are 100 students at the school, then that would be (from premise 1) 60 students participate in sports, and (from premise 2) 50 students are in the school's EA.

with answer choice 2:
AL 20% of EA are in sports at the school. so 20% of EA would be 10 (not 9 or lower).

so, 10 students from EA (minimum), plus 50 nonEA students, and you have the 60 students (60%) required to participate in sports.

if it were 9 students or fewer from the EA program, that would require 51 nonEA students, which i believe is a problem. because if there are 50% of the students (50 students in the EA), there are only 50 nonEA students left.

i think this explains why number 2 is correct, but i'm not sure, yet, how to explain why #1 is wrong.

[tommywallach]

Hey Ptraye,

If there are 100 students in the school, there would be 60 in sports and 50 in engineering.

Of the 60 in sports, there only have to be 10 that are also in engineering (the overlap), which isn't quite 20% of 60.

Hope that helps!

-t

[ptraye]

1) At least 20% of Polytechnic students who participate in sports are in the school's Engineering Academy.

2) At least 20% of Polytechnic students in the Engineering Academy participate in sports

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for answer 2, with AL 20%, that would be 20% of the 50 students in EA -- which is 10.

i think that's why it's correct.

Tommy, you put, which isn't quite 20% of 60. isn't that 20% supposed to be of 50 EA students?

also, what is the distinction between the 1st and 2nd answer choices. i think i understand #2 which is correct. AL 20% of 50 EA students participate in sports -- which is AL 10.

how does #1 break down for 100 students in the school?

[tommywallach]

I was talking about statement 1 there (you seem to think I was describing statement 2). Statement 1 describes 20% of the people in sports. There are 60 people in sports, so that would be 12 people. So 10 people wouldn't quite be 20%.

As for statement 2, we know we have 10 people of overlap, which would be 20% of the 50 people in sports. So that one is true.

Make sense?

-t

[ptraye]

yes. thanks.