In Garfield School, 250 students participate in debate or

Question

In Garfield School, 250 students participate in debate or student government or both. If 40 of these students participate in both debate and student government, how many of these students do not participate in debate?

(1) 80 of the students do not participate in student government.
(2) In Garfield School, 150 students do not participate in either debate or student government.

Scratching my head. Just lost the touch on these questions. Need help. :cry:

Show Answer

Official Answer

A

Bunuel · Answer

In Garfield School, 250 students participate in debate or student government or both. If 40 of these students participate in both debate and student government, how many of these students do not participate in debate?

Given: {250}={Debate}+{Government}-{40}, (notice that 250 students participate in  debate  or  government  or  both , so no need of the group {neither} here).

Question: how many of these students do not participate in debate? Which means how many participate in government ONLY: {Government}-{40}=? So basically we need to find the value of {Government}.

(1) 80 of the students do not participate in student government --> {Debate}-{40}=80. We know {Debate}, we can get {Government}. Sufficient.

(2) In Garfield School, 150 students do not participate in either debate or student government. Useless info. Not sufficient.

Answer: A.

shadabkhaniet · Answer

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.

Bunuel · Answer

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.

shadabkhaniet · Answer

Thanks Bunnel. Now I got it.

kraizada84 · Answer

marked A,

but bunuel explanation rocks
+1

some2none · Answer

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.

Bunuel · Answer

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

shikhar · Answer

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 ??

Bunuel · Answer

OA is given under the spoiler in the first post.

Your question is answered in the posts above: entire question is about those 250 students who participate in debate or student government or both. Statement (1) also talks about 80 of the 250 students who do not participate in student government.

gmatprav · Answer

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.

khanym · Answer

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! :-D

Bunuel · Answer

Here it is for the first statement: https://gmatclub.com/forum/download/file.php?id=24460 Numbers in black are given and in red are calculated. Hope it helps. Untitled.png

Viktoriaa · Answer

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!

Bunuel · Answer

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.

Viktoriaa · Answer

Now it's clear, thank you!

azooktutor · Answer

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.

AjiteshArun · Answer

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

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In Garfield School, 250 students participate in debate or

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