At a certain committee meeting only associate professors and assistant professors are present. Each associate professor

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At a certain committee meeting, only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 11 charts have been brought to the meeting, how many people are present?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: B

Source: GMAT Prep

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VJesus12 wrote:
Fri Jun 11, 2021 8:00 am
At a certain committee meeting, only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 11 charts have been brought to the meeting, how many people are present?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: B

Source: GMAT Prep
Here, we have the following equations
\begin{cases}
2a + b = 10 \\
a + 2b = 11
\end{cases}

Now, adding the above equations we get

\(3a+3b=21 \quad\Longrightarrow\quad a+b=7\)

Therefore, the total number of people is \(7.\)

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VJesus12 wrote:
Fri Jun 11, 2021 8:00 am
At a certain committee meeting, only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 11 charts have been brought to the meeting, how many people are present?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: B

Source: GMAT Prep
Notice that the question asks us to find that TOTAL number of people present.
In other words, it the question does NOT ask us to find the number of associate professors or the number of assistant professors present.

Since each person brings THREE items, and since a total of 21 items were brought (10 pencils and 11 charts), the number of people = 21/3 = 7

Answer: B

Cheers,
Brent
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