alanforde800Maximus wrote:

A market research firm surveyed 400 citizens of city A and 600 citizens of city B during a consumer preference study for a new beverage. If 63% of the citizens surveyed from city A and 48% of the citizens surveyed from city B indicated that they enjoyed the new beverage, what %age of the total number of citizens surveyed enjoyed the new beverage?

a) 45

b) 48

c) 54

d) 56

e) 63

Please assist with above problem.

Such type of weighted average questions can be more efficiently done through a mental map. Though at first it may seem cumbersome, but after a bit of practice, such question types can effectively be solved within 40-50 seconds, saving precious time for the more difficult questions. The GMAT will, more often than not, provide round numbers that can be solved through such mental maps.

First, I see that the weights can reduced to a 2:3 ratio. Second, I calculate the overall 'distance' between the two numbers (in this case percentages): 15. The weights represents the 'distance' that the weighted average will be from each of the two numbers. Therefore, the weighted average will travel 3/5 distance from the lower weighted number, and 2/5 distance from the higher weighted number (visualize: more the mass, more the resistance, less the travel) I.e. 9% downwards from 63% or 6% upwards from 48%. The weighted average converges on 54%. The answer is C.