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# In Garfield School, 250 students participate in debate or

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In Garfield School, 250 students participate in debate or  [#permalink]

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26 Feb 2012, 18:24
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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.

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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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26 Feb 2012, 18:43
3
1
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.

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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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18 Apr 2012, 08:41
2
shikhar wrote:
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 ??

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.
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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17 Mar 2012, 00:49
1
Bunuel wrote:
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.

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.

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.
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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18 Apr 2012, 04:01
1
some2none wrote:
Bunuel wrote:

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

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.

"80 of the students... " refer to 250 students mentioned in the stem.
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In Garfield School, 250 students participate in debate or  [#permalink]

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23 Oct 2014, 00:13
1
khanym wrote:
Bunuel wrote:
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.

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

Here it is for the first statement:

Numbers in black are given and in red are calculated.

Hope it helps.

Attachment:

Untitled.png [ 6.56 KiB | Viewed 3521 times ]

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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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17 Mar 2012, 00:19
Bunuel wrote:
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.

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.
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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17 Mar 2012, 01:50
Bunuel wrote:
Bunuel wrote:
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.

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.

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.

Thanks Bunnel. Now I got it.
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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21 Mar 2012, 23:59
marked A,

but bunuel explanation rocks
+1
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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17 Apr 2012, 23:53
Bunuel wrote:

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

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.
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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18 Apr 2012, 07:24
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 ??
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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30 Jan 2014, 06:32
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.
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In Garfield School, 250 students participate in debate or  [#permalink]

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22 Oct 2014, 18:20
Bunuel wrote:
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.

Hi Bunuel,
Is it possible to solve the problem using double-sided matrix as I am having hard-time setting it up correctly.
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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07 Mar 2016, 14:09
Bunuel wrote:
khanym wrote:
Bunuel wrote:
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.

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

Here it is for the first statement:
Attachment:
Untitled.png
Numbers in black are given and in red are calculated.

Hope it helps.

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!
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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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08 Mar 2016, 03:27
Viktoriaa wrote:
Bunuel wrote:
khanym wrote:
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.

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.
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In Garfield School, 250 students participate in debate or  [#permalink]

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08 Mar 2016, 05:47
Now it's clear, thank you!
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Re: In Garfield School, 250 students participate in debate or student gove  [#permalink]

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06 Aug 2018, 18:37
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.
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Re: In Garfield School, 250 students participate in debate or student gove  [#permalink]

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06 Aug 2018, 21:28
ArjunJag1328 wrote:
In Garfield School, 250 students participate in debate or student government of 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.
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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Re: In Garfield School, 250 students participate in debate or  [#permalink]

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23 Apr 2019, 05:46
Can someone explain how to write statement 2 as equation form??
Re: In Garfield School, 250 students participate in debate or   [#permalink] 23 Apr 2019, 05:46
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