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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  [#permalink]

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New post 23 Nov 2012, 19:57
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Question Stats:

79% (02:07) correct 21% (02:26) wrong based on 193 sessions

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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

The solution suggests a formula, but I believe there is an easier way of doing this using something like a chart? I did it once before but I can't remember how to do it, can anyone shine a light in here?
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Re: At a certain committee meeting only associate professors and  [#permalink]

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New post 23 Nov 2012, 20:25
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anon1 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?

6
7
8
9
10


The solution suggests a formula, but I believe there is an easier way of doing this using something like a chart? I did it once before but I can't remember how to do it, can anyone shine a light in here?


Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 10
Total charts are 11 so A + 2B = 11
Add both: 3A + 3B = 21 so A + B = 7

Total number of people = 7
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Re: At a certain committee meeting only associate professors and  [#permalink]

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New post 24 May 2014, 04:10
I tried to solve the equations without thinking for the obvious solution.
when the two equations will be simply added it will give the required answer :(
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Re: At a certain committee meeting only associate professors and  [#permalink]

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New post 30 Oct 2016, 02:43
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anon1 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
Attachment:
Capture.PNG
Capture.PNG [ 2.17 KiB | Viewed 3149 times ]

Now, Check -

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

In ( I ) , 2a will always result in an even number , hence b must be Odd
In ( II ) , 2b will always result in an even number , hence a 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 , correct answer will be (B)

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Re: At a certain committee meeting only associate professors and  [#permalink]

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New post 09 Mar 2018, 16:09
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Hi All,

This question actually has a fantastic shortcut built into it that allows you to avoid almost all the long-winded math:

Associates bring 2 pencils and 1 chart; a total of 3 items
Assistants bring 1 pencil and 2 charts; a total of 3 items

There are 10 pencils and 11 charts; a total of 21 items

Since each person (regardless of his/her title) brings 3 items and there are 21 items total….

21/3 = 7

There must be 7 people in the meeting.

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Re: At a certain committee meeting only associate professors and  [#permalink]

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New post 03 Oct 2018, 17:48
anon1 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


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 were 7 people in the meeting.

Answer: B
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Re: At a certain committee meeting only associate professors and  [#permalink]

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New post 21 Feb 2019, 07:50
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anon1 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 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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Re: At a certain committee meeting only associate professors and   [#permalink] 21 Feb 2019, 07:50
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