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
Why OAB why not C
newspaper conference
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Total = writers + editors - both + neither.j_shreyans 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 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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Hi j_shreyans
Since you asked about answer C, I think that you may have misread the prompt. It states that "MORE than 38 are editors...." If EXACTLY 38 were editors, then the answer to the question would have been C.
Here's how you can use the Tic-Tac-Toe Board to answer this question:
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
Since you asked about answer C, I think that you may have misread the prompt. It states that "MORE than 38 are editors...." If EXACTLY 38 were editors, then the answer to the question would have been C.
Here's how you can use the Tic-Tac-Toe Board to answer this question:
Final Answer: B
GMAT assassins aren't born, they're made,
Rich