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
At a certain committee meeting only associate professors and assistant professors are present. Each associate professor
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Here, we have the following equationsVJesus12 wrote: ↑Fri Jun 11, 2021 8:00 amAt 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
\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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Notice that the question asks us to find that TOTAL number of people present.VJesus12 wrote: ↑Fri Jun 11, 2021 8:00 amAt 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
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