100 people are attending a newspaper conference. 45 of them

[rustom.hakimiyan]

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

In the MGMAT explanation, it states that we should maximize the number of editors. I'm a little confused as to why we do that and not maximize the number of writers?

It states that "x + (55 – 2x) > 38" which is what's throwing me off. Can someone please help me understand this part?

I approached it as "x + (62-2x) > 45" and this gives me x

Thanks

[HemalT607]

The question gives us a fixed number of writers that is 45, so we can't do anything with it whereas it the number of editors according to the question is more then 38 i.e not fixed. So to find the largest possible number of people who are both editors and writer we have to maximise number of editors.

Also your equation is wrong.

___________ Writers | Not Writers | Total
Editors-------| x | 55-2x | >38
_________
Not Editors--| 45-x | 2x | <62
_________
Total---------| 45 | 55 | 100

On the basis of the information in the question above we can form two equations
1) x+55-2x>38 (As given in the explanation)
2) 45-x+2x<62

Both the equation solves to x<17.
Hence the answer 16.

[jnelson0612]

Nice job, Hemal!

Another option would be to set up the double-set matrix chart (as Hemal showed) and then simply test the answer choices.