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At a certain committee meeting only associate professors and

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At a certain committee meeting only associate professors and

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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

Source: GMAT Prep

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BTGmoderatorDC wrote:
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

Source: GMAT Prep
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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scott@targettestprep.com



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__________________ Pencil ________ Chart
Associate__________ 2 _____________ 1
Assistant __________ 1 _____________ 2

Now, check

2a + b = 10 ---------> (1)
and
a + 2b = 11 ---------> (2)

In (1), 2P will always result in an even number, hence C must be Odd.
In (2), 2C will always result in an even number, hence P must be Odd.

Plug in the values the correct result satisfying both the equations, a will be 3 and b will be 4

Hence Total number of people is 7, the correct answer will be __B__

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BTGmoderatorDC wrote:
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
Total number of items brought to the meeting = 21. (10 charts and 11 pencils)
Number of items brought by each person = 3. (Either 2 pencils and 1 chart or 1 pencil and 2 charts)
Thus:
Number of people = (total number of items)/(number of items per person) = 21/3 = 7.

The correct answer is B.

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BTGmoderatorDC wrote:
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
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 assistant professors present.

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

Answer: B

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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