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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, 18:57
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Question Stats:

84% (01:25) correct 16% (01:46) wrong based on 220 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, 19:25
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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, 03:10
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, 01:43
1
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 2113 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, 15:09
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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, 16:48
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 &nbs [#permalink] 03 Oct 2018, 16:48
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