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100 people are attending a newspaper conference. 45 of them

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calreg11
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100 people are attending a newspaper conference. 45 of them [#permalink] New post   Updated on: 16 Feb 2012, 21:52
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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
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B

Originally posted by calreg11 on 16 Feb 2012, 21:34.
Last edited by Bunuel on 16 Feb 2012, 21:52, edited 1 time in total.
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100 people are attending a newspaper conference. 45 of them [#permalink] New post   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.

Answer: B.

Hope it's clear.
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Re: 100 people are attending a newspaper conference. 45 of them [#permalink] New post   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
when.jpg [ 15.88 KiB | Viewed 71014 times ]

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

Thus, x = 16.

Answer (B)

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Re: 100 people are attending a newspaper conference. 45 of them [#permalink] New post   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?
answer-
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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Re: 100 people are attending a newspaper conference. 45 of them [#permalink] New post   20 Jul 2012, 00:13
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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] New post   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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100 people are attending a newspaper conference. 45 of them [#permalink] New post   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] New post   11 Apr 2014, 02:32
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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?

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] New post   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.

Answer: B.

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] New post   12 Aug 2014, 09:50
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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.

Answer: B.

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] New post   28 Sep 2023, 07:50
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Given: 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.

Asked: What is the largest possible number of people who are both writers and editors?


Writers~WritersTotal
Editorsxy-xy>38
~Editors100-y-2x2x100-y<62
Total4555100


x + (100-y-2x) = 45
55 = x+y
y = 55-x > 38
x < 17
Maximum value of x = 16


Writers~WritersTotal
Editorsx55-2x55-x
~Editors45-x2x45+x
Total4555100


IMO B
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100 people are attending a newspaper conference. 45 of them [#permalink] New post   01 Jan 2024, 21:39
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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?

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


Here is a video solution to this question:

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Re: 100 people are attending a newspaper conference. 45 of them [#permalink] New post   06 Apr 2024, 07:22
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.

Answer: B.

Hope it's clear.

­Great approach w/ Venn Diagram. I thought of doing this way and made a silly mistake. Chose C at first. Anyhow, here is my solution.

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