In Garfield School, 250 students participate in debate or

Yes, I see your point but it's not so: there is no need for {neither} in the formula {250}={Debate}+{Government}-{40}, means that among those 250 students there are no student who do not participate in either debate or government, but it doesn't mean that such students doesn't exist at all. Statement (2) says that there is such a group of 150 people apart of the group of 250.

Hope it's clear.

"80 of the students... " refer to 250 students mentioned in the stem.

Here it is for the first statement:

Numbers in black are given and in red are calculated.

Hope it helps.

Thanks for the explanation bunnel. I think second option is contradicting question stem where you have pointed out "(notice that 250 students participate in debate or government or both, so no need of the group {neither} here)"
but neither is given in the second option.

Thanks Bunnel. Now I got it.

marked A,

but bunuel explanation rocks
+1

Because St1 did not state that 80 students belong to the group of 250 students, I'm arriving at the below
{Debate} + {Neither} - {Both} = 80
{Debate} + {Neither} - 40 = 80
{Neither} could be some non-zero number.

{Niether} = 0, only if St1 says that these 80 students belong to the group of 250 students.
As a result, I'm still unable to understand how you arrived at A.

why is the answer A when in the stem it is not mentioned that total number of students is 250.
It just says that govt+debate+both is 250 ???

What is the OA ??

I believe the wording of this question is not clear.

We can assume 80 "of the students" as "80 of the 250 students".
We can also assume 80 "of the students" as "80 of the school students".

I probably would have picked A if stmt 2 did not raise a possibility of those students who picked neither.

Hi Bunuel,
Is it possible to solve the problem using double-sided matrix as I am having hard-time setting it up correctly.
Thanks your help!

Hi Bunuel! Could you please explain how you got 0 in "No Debate / No SG" cell? It seems there is nothing being said about this in both options. Thank you in advance!

Check the highlighted text above.

We are told that 250 students participate in debate or student government or both. Thus there was no one, out of those 250, who did not participate in either debate or student government.

Hope it's clear.

Now it's clear, thank you!

Since 40 students participate in both activities, and 250 participate in one or both, we can subtract these numbers to get 210, the number of students who participate in one activity alone. If we can figure out how many students participate in debate, we can simply subtract that number from 210 to get the number of students who do not participate in debate.

Statement 1: This gives us how many students do not participate in student government (80). Therefore, these 80 students must participate in debate. We could then subtract 80 from 210 (as the 210 includes only those students who participate in one activity or the other, but not both) to get the number of students who do not participate in debate (i.e., they only participate in student government). Sufficient.

Statement 2: This gives us the number of students who do not participate in either activity. Since the question is asking about "these students", referring to the 250 students first mentioned, this information is irrelevant. We still have no way of knowing how many of the 210 students that participate in one activity alone do not participate in debate. Insufficient.

250 students participate in debate or student government of both needs to be 250 students participate in debate or student government or both.

Can someone explain how to write statement 2 as equation form??

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