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. \(10\)

OA B

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AAPL wrote:
Tue Oct 04, 2022 10:50 am
GMAT Prep

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. \(10\)

OA B
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
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AAPL wrote:
Tue Oct 04, 2022 10:50 am
GMAT Prep

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. \(10\)

OA B
Solution:

We can let the number of associate professors = a and the number of assistant professors = n, and create two equations:

Pencil equation:

2a + n = 10

Chart equation:

a + 2n = 11

Let’s add the two equations together:

3a + 3n = 21

a + n = 7

Thus, there are 7 people at the meeting.

Answer: B

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