100 people are attending a newspaper conference. 45 of them

Question

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

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

Bunuel · Accepted Answer

{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.

cyberjadugar · Answer

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 79217 times ]

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

Thus, x = 16.

Answer (B)

Regards,

LalaB · Answer

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

duriangris · Answer

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

MelanieMa · Answer

I also get x<17.
But how do I know that x is 16 and not 6?

ind23 · Answer

Hi,

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

PerfectScores · Answer

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

russ9 · Answer

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

Bunuel · Answer

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?

Kinshook · Answer

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	~Writers	Total
Editors	x	y-x	y>38
~Editors	100-y-2x	2x	100-y<62
Total	45	55	100

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

	Writers	~Writers	Total
Editors	x	55-2x	55-x
~Editors	45-x	2x	45+x
Total	45	55	100

IMO B

KarishmaB · Answer

Here is a video solution to this question:

https://www.youtube.com/watch?v=M3wJ15ZC1pY

Engineer1 · Answer

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.

bumpbot · Answer

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100 people are attending a newspaper conference. 45 of them

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