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# 100 people are attending a newspaper conference. 45 of them

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100 people are attending a newspaper conference. 45 of them [#permalink]

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16 Feb 2012, 21:34
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Difficulty:

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Question Stats:

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100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?

A. 6
B. 16
C. 17
D. 33
E. 84
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Feb 2012, 21:52, edited 1 time in total.
Edited the question
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100 people are attending a newspaper conference. 45 of them [#permalink]

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16 Feb 2012, 21:51
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calreg11 wrote:
100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
6
16
17
33
84

{Total} = {Writers} + {Editors} - {Both} + {Neither}.

{Total} = 100;
{Writers} = 45;
{Editors} > 38;
{Both} = x;
{Neither} = 2x;

100 = 45 + {Editors} - x + 2x
x = 55 - {Editors}.

We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus:
x = {Both} = 55 - 39 = 16.

Hope it's clear.
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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19 Jul 2012, 20:08
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Hi,

In the below diagram,
x = People who are both writers and editors,
2x = People who are neither writers or editors.
& y = number of editors (>38)
Attachment:

when.jpg [ 15.88 KiB | Viewed 25506 times ]

100 = 45 + y - x + 2x
or y = 55 - x > 38
or x < 17

Thus, x = 16.

Regards,
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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05 Mar 2012, 13:25
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question stem
total=100
W=45
E= more than 38
W-and-E=x
Neither=2x
x?
100=45+39+2x-x (to maximize x we need to minimize E. that is why E=39 the least value)
x=16
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Manager
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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20 Jul 2012, 00:13
5
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Don't know if fundamentally different from other answers but here's how I got it:

E: editor
/E: not editor
W: writer
/W: not writer

E(W) = X
E(W)+E(/W)=Y>38
E(/W)=Y-X
/E(/W)=2X
hence /W=Y+X
total: 100=Y+X+45
hence Y+X=55
least value of Y=39 for a maximized X

Hence X=16
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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10 Apr 2014, 23:44
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MelanieMa wrote:
I also get x<17.
But how do I know that x is 16 and not 6?

Hi,

The question asks for the highest possible value of x.
So it is 16 not 6

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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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09 Nov 2013, 06:03
Its easy if we assume minimum possible number of editors=39.
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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22 Jan 2014, 06:57
100-2x = 45+E-x
x=55-E
Max x will occur at min E. min E is 39. so max x = 55-39 = 16. Ans B.
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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22 Jan 2014, 08:57
100-2x=45+39-x
X=16
Ans.B

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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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10 Apr 2014, 18:29
I also get x<17.
But how do I know that x is 16 and not 6?
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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11 Apr 2014, 02:32
calreg11 wrote:
100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?

A. 6
B. 16
C. 17
D. 33
E. 84

W + E - Both + Neither = 100

45 + E - (x) + 2x = 100

45 + E + x = 100

Now let us plug in answer options:

We cannot plug in 84 as E will become negative
If we plug in x = 33 then E = 22 (Wrong as there are more than 38 editors)
If we plug in x = 17 then E = 38 (Wrong as there are more than 38 editors)
Hence answer is x= 16
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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03 Aug 2014, 17:32
Bunuel wrote:
calreg11 wrote:
100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
6
16
17
33
84

{Total}={Writers}+{Editors}-{Both}+{Neither}.

{Total}=100;
{Writers}=45;
{Editors}>38;
{Both}=x;
{Neither}=2x;

100=45+{Editors}-x+2x --> x=55-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=55-39=16.

Hope it's clear.

Hi Bunuel,

Can you please explain "100=45+{Editors}-x+2x --> x=55-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=55-39=16."

I understand the concept that when we want to maximize something, we want to minimize the other, but why do we want to minimize editors? Aren't we trying to find the greatest number of editors AND writers? Shouldn't we want to MAXIMIZE Editors AND Writers?

Thanks
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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03 Aug 2014, 20:14
This would be my approach,

there are 45 writers.. let that be; now lets say there are 38 editors, 'x' of whom are also writers, who are already accounted for as writers in that 45. So the number of editors who are not writers is (38-x).

Now the number of people who are neither writers or editors is 100 - [( No.of writers) + (No.of Editors who are not writers)], and we know this is 2x

100 - [ 45 + ( 38 -x ) ] = 2x
x= 17
but since number of editors is MORE than 38, 'x' has to be less than 17,
so if we assume no.of editors is just 1 more at 39, then x=16.
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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12 Aug 2014, 09:50
russ9 wrote:
Bunuel wrote:
calreg11 wrote:
100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
6
16
17
33
84

{Total}={Writers}+{Editors}-{Both}+{Neither}.

{Total}=100;
{Writers}=45;
{Editors}>38;
{Both}=x;
{Neither}=2x;

100=45+{Editors}-x+2x --> x=55-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=55-39=16.

Hope it's clear.

Hi Bunuel,

Can you please explain "100=45+{Editors}-x+2x --> x=55-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=55-39=16."

I understand the concept that when we want to maximize something, we want to minimize the other, but why do we want to minimize editors? Aren't we trying to find the greatest number of editors AND writers? Shouldn't we want to MAXIMIZE Editors AND Writers?

Thanks

We want to maximize x, which is {both writers and editors}. To maximize x, we need to minimize {Editors} because x = 55 - {Editors}.

Does this make sense?
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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29 Oct 2014, 09:00
Completely missed the more than 38 part for the editors... Doi!
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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30 Jan 2017, 09:18
wow totally missed the more than clause in the question stem. Great question cause this is exactly what I need to focus on. Small mistakes such as this are killing me
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink]

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22 May 2017, 20:16
calreg11 wrote:
100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?

A. 6
B. 16
C. 17
D. 33
E. 84

The trick of this problem is that you will read it too quickly. It states that more than 38 are editors, so you have to introduce an inequality into your table. Once you have > 38 as the total number of editors and x as the number of both writers and editors, then the number of editor non-writers is 55-2x. 55-2x + x > 38 or x<17. The max integer value less than 17 is 16.
Re: 100 people are attending a newspaper conference. 45 of them   [#permalink] 22 May 2017, 20:16
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# 100 people are attending a newspaper conference. 45 of them

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