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# A market research firm surveyed 400 citizens of city A amd 600 citizen

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Manager
Joined: 13 Sep 2016
Posts: 118
GMAT 1: 800 Q51 V51
A market research firm surveyed 400 citizens of city A amd 600 citizen  [#permalink]

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16 Oct 2016, 02:45
00:00

Difficulty:

5% (low)

Question Stats:

97% (01:29) correct 3% (01:07) wrong based on 41 sessions

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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

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Joined: 02 Sep 2009
Posts: 56244
Re: A market research firm surveyed 400 citizens of city A amd 600 citizen  [#permalink]

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16 Oct 2016, 02:50
1
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

(0.63*400 + 0.48*600)/(400 + 600) = 0.54.

P.S. Since the overall average must be between the individual averages, then the only acceptable answers are C and D.
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Re: A market research firm surveyed 400 citizens of city A amd 600 citizen  [#permalink]

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16 Oct 2016, 03:28
1
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

Total Number of people is 1000 ( ie, 600 + 400 )

No of People in city A who likes the new beverage = 63% of 400 => 252
No of People in city B who likes the new beverage = 48% of 600 => 288

Total no of People in city A and city B who likes the new beverage = 540 ( ie, 252 + 288 )

So, %age of the total number of citizens surveyed enjoyed the new beverage = 540/1000*100 => 54%

Hence answer will be (C) 54%
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Joined: 16 Oct 2016
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A market research firm surveyed 400 citizens of city A amd 600 citizen  [#permalink]

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16 Oct 2016, 03:56
2
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

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.
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Re: A market research firm surveyed 400 citizens of city A amd 600 citizen  [#permalink]

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22 Dec 2017, 19:55
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Re: A market research firm surveyed 400 citizens of city A amd 600 citizen   [#permalink] 22 Dec 2017, 19:55
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