This is a MIXTURE problem.
The MIXTURE:
A total of 10 pencils and 11 charts are brought to the meeting.
Thus, of the 22 items brought to the meeting, the fraction that are pencils = 10/21.
ASSOCIATE professors in the mixture:
Each associate professor brings 2 pencils and 1 chart.
Thus, of every 3 items brought by the associate professors, the fraction that are pencils = 2/3 = 14/21.
ASSISTANT professors in the mixture:
Each assistant professor brings 1 pencil and 2 charts.
Thus, of every 3 items brought by the assistant professors, the fraction that are pencils = 1/3 = 7/21.
To determine the ratio of associate professors to assistant professors in the "mixture", use ALLIGATION.
Step 1: Plot the 3 fractions on a number line, with the fractions for the two types of professors (14/21 and 7/21) on the ends and the fraction for the whole group (10/21) in the middle.
associate 14/21---------------------10/21----------------------7/21 assistant
Step 2: Calculate the distances between the fractions.
associate 14/21---------
4/21--------10/21---------
3/21---------7/21 assistant
Step 3: Determine the ratio in the mixture.
The ratio of associate professors to assistant professors is the RECIPROCAL of the distances in red.
associate : assistant = 3/21 : 4/21 = 3:4.
Since the sum of the parts of the ratio = 3+4 = 7, the total number of professors must be a multiple of 7.
The correct answer is
B.
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