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100 people are attending a conference

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by gmatdriller » Fri Jan 13, 2012 5:08 pm
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 B16 C 17 D 33 E84

Appreciate if you could use vennn diagram.
In solving the problem, kindly emphasize on the difference between
"editors" vs "only editors" or "writers" vs "non-writers"

Source ManhattanGmat cat6.

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by GMATGuruNY » Fri Jan 13, 2012 6:02 pm
gmatdriller 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 B16 C 17 D 33 E84

Appreciate if you could use vennn diagram.
In solving the problem, kindly emphasize on the difference between
"editors" vs "only editors" or "writers" vs "non-writers"

Source ManhattanGmat cat6.

OAB
The quickest approach is to use the following formula:

Total = writers + editors - both + neither.

The big idea is to SUBTRACT the overlap.
When we count the total number of writers and the total number of editors, the OVERLAP -- everyone who is BOTH a writer and an editor -- is counted TWICE.
Thus, the people who are in BOTH groups must be subtracted from the total so that they are not double-counted.

In the equation above:
Total = 100.
Writers = 45.
Both = x.
Neither = 2x.

Plugging these values into the equation:
100 = 45 + editors - x + 2x
55 = editors + x.

In order to MAXIMIZE x, we need to MINIMIZE the number of editors.
Since more than 38 of the people are editors, the minimum number of editors = 39:
55 = 39 + x
x = 16.

The correct answer is B.
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by Anurag@Gurome » Fri Jan 13, 2012 6:10 pm
Image

The correct answer is B.
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by Neo Anderson » Fri Jan 13, 2012 6:17 pm
An alternate method:
Image

now you have 55-X > 38
=> X < 17 => Max value X can take is 16 hence B
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by gmatdriller » Sat Jan 14, 2012 9:03 am
i got it clearly, especially from the first two contributions.

Got confused as to how to represent "Editors" on the diagram, but the
ven diagram has explained it.

Thanks.
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by avigaggy » Tue Jan 31, 2012 10:00 pm
Hey hii guys .If this is the right answer then how would there be 32 ppl (2*16= 2*x)be neither of the writers or editors? where the question says that there are 45 writers and more than 38 editors.??
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by gmatdriller » Tue Jan 31, 2012 11:18 pm
avigaggy wrote:Hey hii guys .If this is the right answer then how would there be 32 ppl (2*16= 2*x)be neither of the writers or editors? where the question says that there are 45 writers and more than 38 editors.??
in the case at hand:
Writers: 45-16=29
Editors(more than 38):16+23=39 (Yes!)
Neither: 2*16 = 32
Total = 29+39+32 = 100
The number of Editors has to be more than 38 while Total must be 100.

Does that answer your question?
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